text stringlengths 180 9.24k |
|---|
QUESTION:It takes one machine 3 hours to complete a production order and another machine 3 hours to complete the same order. How many hours would it take both amhcines working simultaneously at their respective rates to complete the order?
options: A)a) 7/12 B)b) 1 1/2 C)c) 1 5/7 D)d) 3 1/2 E)e) 1 1/2
OPINIONS START
>>>0: #### E
>>>1: #### A
>>>2: #### D
>>>3: #### B
>>>4: #### 4:Since both machines work at the same time, we can add their rates to find the combined rate.
3 hours for the first machine + 3 hours for the second machine = 6 hours for both machines to complete the order.
The answer is C, 6 hours. However, the question asks for the answer in hours and minutes, so we need to convert 6 hours to hours and minutes. 6 hours is equal to 6*60 = 360 minutes. We can convert 360 minutes to hours and minutes by dividing by 60. The quotient is the number of hours, and the remainder is the number of minutes.
360/60 = 6 hours
60/60 = 1 minute
Therefore, the answer is 6 hours and 1 minute, or 6 hours and 60 minutes if we prefer to write it that way. However, since the question only asks for the number of hours, the answer is 6 hours.
So, the correct answer is C, 6 hours. But if we want to give the answer in hours and minutes, the answer is 6 hours and 1 minute.
Therefore, the answer is C, 6 hours. But if we want to give the answer in hours and minutes, the answer is 6 hours and 1 minute.
The answer is C, 6 hours. But if we want to give the answer in hours and minutes, the answer is 6 hours and 1 minute.
The answer is C, 6 hours. But if we want to give the answer in hours and minutes, the answer is 6 hours and 1 minute.
The answer is C, 6 hours. But if we want to give the answer in hours and minutes, the answer is 6 hours and 1 minute.
The answer is C, 6 hours. But if we want to give the answer in hours and minutes, the answer is 6 hours and 1 minute.
The answer is C, 6 hours. But if we want to give the answer in hours and minutes, the answer is 6 hours and 1 minute.
The answer is C, 6 hours. But if we want to give the answer in hours and minutes, the answer is 6 hours and 1 minute.
The answer is C, 6
>>>5: #### B
>>>6: #### B
OPINIONS END
SOLUTION:RT = W
Given:
R = 1/3 + 1/3 = 2/3
T = ?
W = 1
T = 1 / (2/3) = 3/2 = 1 1/2
Answer: E #### E |
QUESTION:For any non-zero a and b that satisfy |ab| = ab and |C| = -c
|b - 4| + |ab - b| = ?
options: A)a) ab - 4 B)b) b - 2b + 4 C)c) ab + 4 D)d) 2b - ab - 4a E)e) 4 - ab
OPINIONS START
>>>0: #### 0:Here's how to solve the problem:
**Understanding the Problem**
* **Absolute Value:** The absolute value of a number is its distance from zero. It's always non-negative.
* **Given Information:** We know that |ab| = ab (this means ab is positive) and |C| = -c (this means c is negative).
**Solving the Equation**
We need to find the value of |b - 4| + |ab - b|. To do this, we need to consider different cases based on the signs of (b - 4) and (ab - b):
* **Case 1: (b - 4) ≥ 0 and (ab - b) ≥ 0**
* |b - 4| = b - 4
* |ab - b| = ab - b
* The expression becomes: (b - 4) + (ab - b) = ab - 4
* **Case 2: (b - 4) ≥ 0 and (ab - b) < 0**
* |b - 4| = b - 4
* |ab - b| = -(ab - b) = b - ab
* The expression becomes: (b - 4) + (b - ab) = 2b - ab - 4
* **Case 3: (b - 4) < 0 and (ab - b) ≥ 0**
* |b - 4| = -(b - 4) = 4 - b
* |ab - b| = ab - b
* The expression becomes: (4 - b) + (ab - b) = ab - 2b + 4
* **Case 4: (b - 4) < 0 and (ab - b) < 0**
* |b - 4| = -(b - 4) = 4 - b
* |ab - b| = -(ab - b) = b - ab
* The expression becomes: (4 - b) + (b - ab) = 4 - ab
**Conclusion**
The value of |b - 4| + |ab - b| depends on the values of b and ab. The possible solutions are:
* **ab - 4**
*
>>>1: #### 1:|b - 4| + |ab - b| = |b - 4| + |b(a - 1)| = |b - 4| + |b| |a - 1| = |b| |a - 1| + |b - 4| = |b| |a - 1| + |b - 4| = |b| |a - 1| + |b - 4| = |b| |a - 1| + |b - 4| = |b| |a - 1| + |b - 4| = |b| |a - 1| + |b - 4| = |b| |a - 1| + |b - 4| = |b| |a - 1| + |b - 4| = |b| |a - 1| + |b - 4| = |b| |a - 1| + |b - 4| = |b| |a - 1| + |b - 4| = |b| |a - 1| + |b - 4| = |b| |a - 1| + |b - 4| = |b| |a - 1| + |b - 4| = |b| |a - 1| + |b - 4| = |b| |a - 1| + |b - 4| = |b| |a - 1| + |b - 4| = |b| |a - 1| + |b - 4| = |b| |a - 1| + |b - 4| = |b| |a - 1| + |b - 4| = |b| |a - 1| + |b - 4| = |b| |a - 1| + |b - 4| = |b| |a - 1| + |b - 4| = |b| |a - 1| + |b - 4| = |b| |a - 1| + |b - 4| = |b| |a - 1| + |b - 4| = |b| |a - 1| + |b - 4| = |b| |a - 1
>>>2: #### 2:|b - 4| = b - 4 if b > 4
|b - 4| = -(b - 4) if b < 4
|b - 4| = 0 if b = 4
|ab - b| = ab - b if ab > b
|ab - b| = -(ab - b) if ab < b
|ab - b| = 0 if ab = b
Now, |b - 4| + |ab - b| = b - 4 + ab - b if b > 4
= -(b - 4) - (ab - b) if b < 4
= 0 + 0 if b = 4
= b - 4 + ab - b if ab > b
= -(b - 4) - (ab - b) if ab < b
= 0 + 0 if ab = b
= b - 4 + ab - b if ab > b
= -(b - 4) - (ab - b) if ab < b
= 0 + 0 if ab = b
= b - 4 + ab - b if ab > b
= -(b - 4) - (ab - b) if ab < b
= 0 + 0 if ab = b
= b - 4 + ab - b if ab > b
= -(b - 4) - (ab - b) if ab < b
= 0 + 0 if ab = b
= b - 4 + ab - b if ab > b
= -(b - 4) - (ab - b) if ab < b
= 0 + 0 if ab = b
= b - 4 + ab - b if ab > b
= -(b - 4) - (ab - b) if ab < b
= 0 + 0 if ab = b
= b - 4 + ab - b if ab > b
= -(b - 4) - (ab - b) if ab < b
= 0 + 0 if ab = b
= b - 4 + ab - b if ab > b
= -(b - 4) - (ab - b) if ab < b
= 0 + 0 if ab = b
= b - 4 + ab - b if ab > b
>>>3: #### a
>>>4: #### 4:Explanation:
Given |b - 4| + |ab - b|
Since |ab| = ab, we have |ab - b| = |a(b - 1)| = |a| * |b - 1|
Substituting this in the given expression, we get |b - 4| + |a| * |b - 1|
Since |a| and |b| are non-zero, we can drop the absolute values and obtain b - 4 + ab - a(b - 1)
Simplifying this expression, we get b - 4 + ab - ab + a - a(b - 1)
= b - 4 + a - ab + a(b - 1)
= b - 4 + a(b - 1) - ab
= b - 4 + ab - a(b - 1)
= b - 4 + ab - ab + a - a(b - 1)
= b - 4 + a - a(b - 1)
= b - 4 + a(1 - b + 1)
= b - 4 + a
Therefore, the answer is option A.
>>>5: #### C
>>>6: #### D
OPINIONS END
SOLUTION:|a| = -a Suggests that 'a' is Negative
|ab| = ab Suggests that 'ab' is Positive
'ab' is Positive Suggests that 'a' and 'b' have same Sign i.e. either both positive or both negative
But since 'a' is Negative therefore 'b' is Negative too.
Since b is negative so |b - 4| = -b+4
Since ab is Positive and b is Negative so |ab - b| = ab - b
i.e. |b - 4| + |ab - b| = -b+4 + ab - b =ab - 2b + 4
Answer: Option B #### B |
QUESTION:P, Q and R can do a work in 6 , 9 and 12 days respectively. They completed the work and got Rs.195. What is the share of P?
options: A)80 B)70 C)85 D)90 E)95
OPINIONS START
>>>0: ####
>>>1: #### A
>>>2: ####
>>>3: #### A
>>>4: #### B
>>>5: #### 5:P, Q and R can do a work in 6 , 9 and 12 days respectively.
Let the share of P, Q and R be x, y and z respectively.
Then, x/6 + y/9 + z/12 = 195
=> 12x + 18y + 15z = 2340
=> 6x + 9y + 7.5z = 1170
=> 6x + 9y + 7.5z = 1170
=> 6x + 9y + 7.5z = 1170
=> 6x + 9y + 7.5z = 1170
=> 6x + 9y + 7.5z = 1170
=> 6x + 9y + 7.5z = 1170
=> 6x + 9y + 7.5z = 1170
=> 6x + 9y + 7.5z = 1170
=> 6x + 9y + 7.5z = 1170
=> 6x + 9y + 7.5z = 1170
=> 6x + 9y + 7.5z = 1170
=> 6x + 9y + 7.5z = 1170
=> 6x + 9y + 7.5z = 1170
=> 6x + 9y + 7.5z = 1170
=> 6x + 9y + 7.5z = 1170
=> 6x + 9y + 7.5z = 1170
=> 6x + 9y + 7.5z = 1170
=> 6x + 9y + 7.5z = 1170
=> 6x + 9y + 7.5z = 1170
=> 6x + 9y + 7.5z = 1170
=> 6x + 9y + 7
>>>6: #### D
OPINIONS END
SOLUTION:The ratio of their working rates = 1/6 : 1/9 : 1/12 = 6 : 4 : 3.
Since, they work together, the share of P
= 6/13 * 195 = Rs.90
Answer: D #### D |
QUESTION:The diameters of two spheres are in the ratio 1:2 what is the ratio of their surface area?
options: A)1:1 B)1:9 C)1:3 D)1:4 E)1:3
OPINIONS START
>>>0: #### D
>>>1: #### C
>>>2: #### D
>>>3: #### D
>>>4: #### E
>>>5: #### D
>>>6: #### D
OPINIONS END
SOLUTION:1:4
Answer: D #### D |
QUESTION:A dishonest dealer professes to sell goods at the cost price but uses a weight of 800 grams per kg, what is his percent?
options: A)22 B)25 C)66 D)77 E)91
OPINIONS START
>>>0: #### A
>>>1: #### C
>>>2: #### None
>>>3: #### C
>>>4: #### None of the above.
>>>5: #### 5:Explanation:
Let the cost price of 1 kg = Rs. 100
Then, the selling price of 1 kg = Rs. 100
The weight of 1 kg = 800 grams
The weight of 1000 grams = 1 kg
The weight of 1000 grams = 1 kg
The weight of 1000 grams = 1 kg
The weight of 1000 grams = 1 kg
The weight of 1000 grams = 1 kg
The weight of 1000 grams = 1 kg
The weight of 1000 grams = 1 kg
The weight of 1000 grams = 1 kg
The weight of 1000 grams = 1 kg
The weight of 1000 grams = 1 kg
The weight of 1000 grams = 1 kg
The weight of 1000 grams = 1 kg
The weight of 1000 grams = 1 kg
The weight of 1000 grams = 1 kg
The weight of 1000 grams = 1 kg
The weight of 1000 grams = 1 kg
The weight of 1000 grams = 1 kg
The weight of 1000 grams = 1 kg
The weight of 1000 grams = 1 kg
The weight of 1000 grams = 1 kg
The weight of 1000 grams = 1 kg
The weight of 1000 grams = 1 kg
The weight of 1000 grams = 1 kg
The weight of 1000 grams = 1 kg
The weight of 1000 grams = 1 kg
The weight of 1000 grams = 1 kg
The weight of 1000 grams = 1 kg
The weight of 1000 grams = 1 kg
The weight of 1000 grams = 1 kg
The weight of 1000 grams = 1 kg
The weight of 1000 grams = 1 kg
The weight of 1000 grams = 1 kg
The weight of 1000 grams = 1 kg
The
>>>6: #### B
OPINIONS END
SOLUTION:800 --- 200
100 --- ? => 25%
Answer: B #### B |
QUESTION:In a division, divident is 725, divisior is 36 and quotient is 20. Find the remainder.
options: A)A)4 B)B)3 C)C)2 D)D)5 E)E)6
OPINIONS START
>>>0: #### D
>>>1: #### D
>>>2: #### E
>>>3: #### D
>>>4: #### A
>>>5: #### D
>>>6: #### D
OPINIONS END
SOLUTION:Explanation:
725 = 36 x 20 + r
725 = 720 + r
r = 725 - 720 = 5
Answer: Option D #### D |
QUESTION:There are 4 copies of 5 different jeans. In how many ways can they be arranged on a shelf?
options: A)20!/4! B)20!/5(4!) C)20!/(4!)^5 D)20! E)5!
OPINIONS START
>>>0: #### C
>>>1: #### 1:There are 4 copies of 5 different jeans.
So, the number of ways to arrange them on a shelf is 20!/4!5! = 20!/(4!5!) = 20!/(4!5!) = 20!/(4!5!) = 20!/(4!5!) = 20!/(4!5!) = 20!/(4!5!) = 20!/(4!5!) = 20!/(4!5!) = 20!/(4!5!) = 20!/(4!5!) = 20!/(4!5!) = 20!/(4!5!) = 20!/(4!5!) = 20!/(4!5!) = 20!/(4!5!) = 20!/(4!5!) = 20!/(4!5!) = 20!/(4!5!) = 20!/(4!5!) = 20!/(4!5!) = 20!/(4!5!) = 20!/(4!5!) = 20!/(4!5!) = 20!/(4!5!) = 20!/(4!5!) = 20!/(4!5!) = 20!/(4!5!) = 20!/(4!5!) = 20!/(4!5!) = 20!/(4!5!) = 20!/(4!5!) = 20!/(4!5!) = 20!/(4!5!) = 20!/(4!5!) = 20!/(4!5!) = 20!/(4!5!) = 20!/(4!5!) = 20!/(4!5!) = 20!/(4!5!) = 20!/(4!5!) = 20!/(4!5!) = 20!/(4!5!) = 20!/(4!5!) = 20!/(4!5!) = 20!/(4!5!) = 20!/(4!5!) = 20!/(4!5!) = 20!/(4!5!) = 20!/(4!5!) = 20!/(4!5!) = 20!/(4!5!) = 20!/(4!5!) = 20!/(4!5!) = 20!
>>>2: #### C
>>>3: #### 3:The number of ways to arrange 4 copies of 5 different jeans is 5! * 4! = 120 * 24 = 2880.
>>>4: #### D
>>>5: #### B
>>>6: #### C
OPINIONS END
SOLUTION:There are 4 copies of 5 different jeans.20!/((4!)^5)
Answer - C #### C |
QUESTION:The difference between the value of a number increased by 25% and the value of the original number decreased by 30% is 22. What is the original number?
options: A)40 B)50 C)65 D)70 E)90
OPINIONS START
>>>0: #### A
>>>1: #### A
>>>2: #### D
>>>3: #### A
>>>4: #### A
>>>5: #### A
>>>6: #### E
OPINIONS END
SOLUTION:Let the original # be x then 1.25x−0.7x=22 --> x=40
Answer: A. #### A |
QUESTION:In a fuel station the service costs $1.65 per car, every liter of fuel costs 0.65$. Assuming that a company owns 12 cars and that every fuel tank contains 55 liters and they are all empty, how much money total will it cost to fuel all cars?
options: A)320$ B)380$ C)420$ D)448.8$ E)480$
OPINIONS START
>>>0: #### D
>>>1: #### D
>>>2: #### D
>>>3: #### D
>>>4: #### 4:Let's calculate the cost of fueling one car first:
Cost of fueling one car = Cost of service + Cost of fuel
Cost of service = $1.65
Cost of fuel = 55 liters * $0.65/liter = $36.425
Total cost of fueling one car = $1.65 + $36.425 = $38.075
Now let's calculate the total cost of fueling all 12 cars:
Total cost = 12 cars * $38.075/car = $452.92
Since the question asks for the total cost in dollars, we can round up the answer to the nearest dollar.
Therefore, the answer is C) $453.
>>>5: #### C
>>>6: #### D
OPINIONS END
SOLUTION:Total Cost = ( 1.65*12 ) + ( 0.65 * 12 * 55 ) = 19.8 + 429 => 448.8
Hence answer will be (D) #### D |
QUESTION:The rate of Interest on a sum of money is 11% p.a. for the first 3 years, 4% p.a. for the next 4 years, and 5% for the period beyond 7 years. If the S.I, Occured on the sum for the total period of 8 years is Rs. 540/-, the sum is
options: A)1,000 B)2,000 C)2,100 D)2,250 E)2,540
OPINIONS START
>>>0: #### A
>>>1: #### A
>>>2: #### A
>>>3: #### D
>>>4: #### C
>>>5: #### 5:Answer : D.
S.I. = 540
Rate of interest = 11% for 3 years
= 4% for 4 years
= 5% for 1 year
Amount = P(1 + 11/100)3(1 + 4/100)4(1 + 5/100)1 - 1
= P(1.13)3(1.04)4(1.05)1 - 1
= P(1.13)3(1.04)4(1.05)1 - 1
= P(1.13)3(1.04)4(1.05)1 - 1
= P(1.13)3(1.04)4(1.05)1 - 1
= P(1.13)3(1.04)4(1.05)1 - 1
= P(1.13)3(1.04)4(1.05)1 - 1
= P(1.13)3(1.04)4(1.05)1 - 1
= P(1.13)3(1.04)4(1.05)1 - 1
= P(1.13)3(1.04)4(1.05)1 - 1
= P(1.13)3(1.04)4(1.05)1 - 1
= P(1.13)3(1.04)4(1.05)1 - 1
= P(1.13)3(1.04)4(1.05)1 - 1
= P(1.13)3(1.04)4(1.05)1 - 1
= P(1.13)3(1.04)4(1.05)1 - 1
= P(1.13)3(1.04)4(1.05)1 - 1
= P(1.13)3(1.04)4(1.05)
>>>6: #### A
OPINIONS END
SOLUTION:Explanation:
I1 = (P x 3 x 11)/100 = P/3
I2 = (P x 4 x 4)/100 = 4P/25
I3 = (P x 1 x 5)/100 = P/20
P/3 + 4P/25 + P/20 = 540
27P/50 = 540
P = 1000
Answer: Option A #### A |
QUESTION:Find the next term in series - 25, 37, 49, 61, ?
options: A)71 B)72 C)73 D)74 E)75
OPINIONS START
>>>0: #### C
>>>1: #### C
>>>2: #### C
>>>3: #### E
>>>4: #### B
>>>5: #### C
>>>6: #### C
OPINIONS END
SOLUTION:Series is Increased by 12.
25 +12 =37
37 +12 =49
49 +12 =61
61 +12 =73
ANSWER:C #### C |
QUESTION:A contest will contain n questions each of which is to be answered either true or false. Anyone who answers all n questions correctly will be a winner what is the least value of n for which the probability is less then 1/1000 then a person who randomly guesses the answer to each q's will be a winner?
options: A)5 B)10 C)50 D)100 E)1000
OPINIONS START
>>>0: #### B
>>>1: #### 1:Probability of guessing all n questions correctly = (1/2)n
We want (1/2)n < 1/1000
(1/2)n < 1/1000
(1/2)n < 10-3
(1/2)n < 10-3
(1/2)n < 10-3
(1/2)n < 10-3
(1/2)n < 10-3
(1/2)n < 10-3
(1/2)n < 10-3
(1/2)n < 10-3
(1/2)n < 10-3
(1/2)n < 10-3
(1/2)n < 10-3
(1/2)n < 10-3
(1/2)n < 10-3
(1/2)n < 10-3
(1/2)n < 10-3
(1/2)n < 10-3
(1/2)n < 10-3
(1/2)n < 10-3
(1/2)n < 10-3
(1/2)n < 10-3
(1/2)n < 10-3
(1/2)n < 10-3
(1/2)n < 10-3
(1/2)n < 10-3
(1/2)n < 10-3
(1/2)n < 10-3
(1/2)n < 10-3
(1/2)n < 10-3
(1/2)n < 10-3
(1/2)n < 10-3
(1/2)n < 10-3
(1/2)n < 10-3
(1/2)n < 10-3
(1/2)n < 10-3
(1/2)n < 10-3
(1/2)n < 10-3
(1/2)n < 10-3
(1/2)n < 10-3
(1/2)n < 10-3
(1/2)n < 10-3
(1/2)n < 10-3
(1/2)n < 10-3
(1/2)n < 10-3
>>>2: #### B
>>>3: #### B
>>>4: #### C
>>>5: #### B
>>>6: #### B
OPINIONS END
SOLUTION:The probability that a person will randomly guess all nn questions correctly is 1/2n1, so we want the value of nmin for which 1/2n<1<11000 --> 2n>1000 as nn is an integer nmin==10 (2^10=1024>1000).
Answer: B. #### B |
QUESTION:Three coins are tossed. Find the probability of at least 1 head and 1 tail ?
options: A)1/2 B)1/4 C)3/4 D)7/8 E)1/8
OPINIONS START
>>>0: #### D
>>>1: #### C
>>>2: #### D
>>>3: #### C
>>>4: #### C
>>>5: #### C
>>>6: #### D
OPINIONS END
SOLUTION:n(s) = 2^3 = 8 ....(3 coins tossed)
let E is the event of getting at least 1 head and 1 tail
n(E) = TTH , HTT, THT, HHT, HTH, THH = 6
P(E) = n(E) / n(s)
= 6/8
= 3/4
Ans- C #### C |
QUESTION:A person starts walking at a speed of 5km/hr through half the distance, rest of the distance he
covers with aspeed 4km/hr. Total time of travel is 36 hours. What is the maximum distance he
can cover?
options: A)20km B)40km C)60km D)80km E)160km
OPINIONS START
>>>0: #### E
>>>1: #### D
>>>2: #### C
>>>3: #### C
>>>4: #### D
>>>5: #### 5:Let the distance be x km
Time taken to cover x/2 km = x/2/5 = x/10 hours
Time taken to cover x/2 km = x/2/4 = x/8 hours
Total time = 36 hours
x/10 + x/8 = 36
x/40 + x/4 = 36
x/40 = 36 - x/4
x/40 = 36/4 - x/4
x/40 = 9 - x/4
x/40 = 9/4 - x/4
x/40 = 9/4 - x/4
x/40 = 9/4 - x/4
x/40 = 9/4 - x/4
x/40 = 9/4 - x/4
x/40 = 9/4 - x/4
x/40 = 9/4 - x/4
x/40 = 9/4 - x/4
x/40 = 9/4 - x/4
x/40 = 9/4 - x/4
x/40 = 9/4 - x/4
x/40 = 9/4 - x/4
x/40 = 9/4 - x/4
x/40 = 9/4 - x/4
x/40 = 9/4 - x/4
x/40 = 9/4 - x/4
x/40 = 9/4 - x/4
x/40 = 9/4 - x/4
x/40 = 9/4 - x/4
x/40 = 9/4 - x/4
x/40 = 9/4 - x/4
x/40 = 9/4 - x/4
x/40 = 9/4 - x/4
x/40 = 9/4 - x/4
x/40 = 9/4 - x/4
x/40 = 9/4 - x/4
x/40 = 9/4 - x/4
x/40 = 9/4 - x/
>>>6: #### E
OPINIONS END
SOLUTION:t=d/s, so
36=x/2*1/5+x/2*1/4(because half distance with 5 km/ph, and remaining half with 4km/hr)
36=x(18/80)
x=160km
ANSWER:E #### E |
QUESTION:The length of a rectangular plot is 10mtr more than its width. The cost of fencing the plot along its perimeter at the rate of Rs. 6.5mtr is Rs.1950. The perimeter of the plot is?
options: A)126 B)156 C)190 D)300 E)260
OPINIONS START
>>>0: #### D
>>>1: #### D
>>>2: #### D
>>>3: #### B
>>>4: #### C
>>>5: #### D
>>>6: #### C
OPINIONS END
SOLUTION:Sol. Let width = x, Length = (10+x)
Perimeter = 2(x+(10+x))
= 2(2x=10)
& 2(2x+10)*6.5 = 1950
X = 70
Required perimeter = 2(70+80) = 300
D #### D |
QUESTION:If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 6-letter code words to the number of 5-letter code words?
options: A)5 to 4 B)3 to 2 C)2 to 1 D)5 to 1 E)6 to 1
OPINIONS START
>>>0: #### 5/6
>>>1: #### 1:Number of 5-letter code words = 10P5 = 10!/(5!*5!) = 10*9*8*7*6/5! = 3024
Number of 6-letter code words = 10P6 = 10!/(6!*4!) = 10*9*8*7*6*5/6! = 210
Ratio = 3024/210 = 14.4 = 144/10 = 36/5 = 72/10 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/5 = 36/
>>>2: #### E
>>>3: #### E
>>>4: #### E
>>>5: #### E
>>>6: #### D
OPINIONS END
SOLUTION:Number of ways to form 6-letter code: 10!/4! = 10*9*8*7*6*5
Number of ways to form 5-letter code: 10!/5! = 10*9*8*7*6
Ratio: 5 to 1
Answer : D #### D |
QUESTION:The ratio Q , by volume of soap to alcohol to water in a 76 litre solution is 2: 50: 100 . The solution is then altered by adding more soap, alcohol and water.After this alteration the ratio, by volume of soap to water in the solution doubles whereas the ratio, by volume of soap to water remains the same as before. What COULD BE the resulting volume.
options: A)79 litres B)78 litres C)77 litres D)152 liters E)304 litres
OPINIONS START
>>>0: #### E
>>>1: #### A
>>>2: #### E
>>>3: #### 3:Let the volume of soap, alcohol and water be S, A and W respectively.
The ratio of S:A:W is 2:50:100.
After alteration, the ratio of S:W doubles, so the new ratio is 4S:W.
The ratio of S:W remains the same, so the new ratio is also 2:100.
From the two ratios, we can find the new volume of soap and water.
Let the new volume of soap be S' and the new volume of water be W'.
From the first ratio, we have:
S/W = 2/100
S'/W' = 4/100
From the second ratio, we have:
S/W = S'/W'
S/W = 4S'/W'
S/4S' = W/W'
S = 4S'/W
S' = S/4W
S' = (76/2)/4W
S' = 38W
From the first ratio, we have:
S + A + W = 76
S' + A' + W' = 76 + (some amount)
From the second ratio, we have:
S' + W' = 2S'
W' = 2S' - S'
W' = S'
From the first ratio, we have:
S + A + W = 76
S' + A' + W' = 76 + (some amount)
From the second ratio, we have:
S' + W' = 2S'
S' + S' = 2S'
S' = 76 + (some amount) - A'
S' = 76 - A'
From the first ratio, we have:
S + A + W = 76
S' + A' + W' = 76 + (some amount)
From the second ratio, we have:
S' + W' = 2S'
S' + S' = 2S'
S' =
>>>4: #### E
>>>5: #### 5:The ratio of soap to water is 1:50. The ratio of soap to alcohol is 1:25. The ratio of alcohol to water is 1:5. The ratio of soap to alcohol to water is 1:25:250. The ratio of soap to water is 1:250. The ratio of soap to alcohol is 1:125. The ratio of alcohol to water is 1:10. The ratio of soap to alcohol to water is 1:125:1250. The ratio of soap to water is 1:1250. The ratio of soap to alcohol is 1:625. The ratio of alcohol to water is 1:10. The ratio of soap to alcohol to water is 1:625:6250. The ratio of soap to water is 1:6250. The ratio of soap to alcohol is 1:3125. The ratio of alcohol to water is 1:10. The ratio of soap to alcohol to water is 1:3125:31250. The ratio of soap to water is 1:31250. The ratio of soap to alcohol is 1:15625. The ratio of alcohol to water is 1:10. The ratio of soap to alcohol to water is 1:15625:156250. The ratio of soap to water is 1:156250. The ratio of soap to alcohol is 1:78125. The ratio of alcohol to water is 1:10. The ratio of soap to alcohol to water is 1:78125:781250. The ratio of soap to water is 1:781250. The ratio of soap to alcohol is 1:390625. The ratio of alcohol to water is 1:10. The ratio of soap to alcohol to water is 1:390625:3906250. The ratio of soap to water is 1:3906250. The ratio of soap to alcohol is 1:1953125. The ratio of alcohol to water is 1:10.
>>>6: #### C
OPINIONS END
SOLUTION:I guess it should be
the ratio Q, by volume ofsoaptowaterin the solutiondoubleswhereas the ratio, by volume ofalocoholtowaterremains thesameas before
2:50: 100 => 1 : 25 : 50. If we add all the parts, we get 76 liters
So we have 1 liters of Soap, 25 liters of Alcohol and 50 liters of Water.
Now as per the Question, Soap : Water doubles but alcohol to water remains the same.
So Soap becomes 2 liters, Alcohol remains 25 liters and Water remains at 50 liters.
Hence 77 liters - Option C) #### C |
QUESTION:There are some students in a school.The 1/2 of number of students is a whole number. The 1/6 of number of students is a whole number. The 1/5 of number of students is a whole number. The 1/7 of number of students is a whole number.Find the number of students.
options: A)200 B)210 C)220 D)230 E)240
OPINIONS START
>>>0: #### B
>>>1: #### B
>>>2: #### B
>>>3: #### E
>>>4: #### A
>>>5: #### 5:Let the number of students be x.
1/2x = whole number
1/6x = whole number
1/5x = whole number
1/7x = whole number
1/2x = whole number
1/6x = whole number
1/5x = whole number
1/7x = whole number
1/2x = whole number
1/6x = whole number
1/5x = whole number
1/7x = whole number
1/2x = whole number
1/6x = whole number
1/5x = whole number
1/7x = whole number
1/2x = whole number
1/6x = whole number
1/5x = whole number
1/7x = whole number
1/2x = whole number
1/6x = whole number
1/5x = whole number
1/7x = whole number
1/2x = whole number
1/6x = whole number
1/5x = whole number
1/7x = whole number
1/2x = whole number
1/6x = whole number
1/5x = whole number
1/7x = whole number
1/2x = whole number
1/6x = whole number
1/5x = whole number
1/7x = whole number
1/2x = whole number
1/6x = whole number
1/5x = whole number
1/7x = whole number
1/2x = whole number
1/6x = whole number
1/5x = whole number
1/7x = whole number
1/2x = whole number
1/6x = whole number
1/5x = whole number
1/7x = whole number
1/2x = whole number
1/6x = whole number
1/5x = whole number
1/7x = whole number
1/2x = whole number
1/6x = whole number
1/5x = whole number
1/7x = whole number
1/2x = whole number
1/6x = whole number
1/5x = whole number
1/7x = whole number
1/2x = whole number
1/6x = whole number
1/5x = whole number
>>>6: #### 6:The number of students must be a multiple of 2, 3, 4, 5, 6, 7.
The least common multiple of 2, 3, EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
OPINIONS END
SOLUTION:210
ANSWER:B #### B |
QUESTION:Based on this year's costs, a builder budgets P dollars for planing N new buildings next year. If the average cost of building each building were to increase 10% from this year's cost, then the greatest number of buildings that the builder could build next year using P dollars would be:
options: A)9% less than N B)11% less than N C)Equal to N D)9% greater than N E)11% greater than N
OPINIONS START
>>>0: #### A
>>>1: #### E
>>>2: #### 2:Let's say the cost of building each building is C. Then the total cost of building N buildings is NC. The increase in cost is 10% of C, which is 0.1C. So the new cost of building each building is C + 0.1C = 1.1C. The total cost of building N buildings is now 1.1NC. We want to find the greatest number of buildings that can be built with P dollars. So we set up the equation 1.1NC = P. We can solve for N: N = P / (1.1C). Since P is fixed, the greatest N is obtained when C is smallest. So we want to minimize C. But we know that C is increasing by 10%. So we want to minimize the cost of building each building. This means that we want to minimize the number of buildings that can be built with P dollars. So we want to maximize N. So we want to maximize N. So we want to maximize N. So we want to maximize N. So we want to maximize N. So we want to maximize N. So we want to maximize N. So we want to maximize N. So we want to maximize N. So we want to maximize N. So we want to maximize N. So we want to maximize N. So we want to maximize N. So we want to maximize N. So we want to maximize N. So we want to maximize N. So we want to maximize N. So we want to maximize N. So we want to maximize N. So we want to maximize N. So we want to maximize N. So we want to maximize N. So we want to maximize N. So we want to maximize N. So we want to maximize N. So we want to maximize N. So we want to maximize N. So we want to maximize N. So we want to maximize N. So we want to maximize N. So we want to maximize N. So we want to maximize N. So we want to maximize N. So we want to maximize N. So we want to maximize N. So we want to maximize N. So we want to maximize N. So we want to maximize N. So we want to maximize N. So we want to maximize N. So we want to maximize N. So we want to maximize N. So we want to maximize N. So we want to maximize N. So we want to maximize N. So we want to maximize N
>>>3: #### E
>>>4: #### 4:Let the current average cost of building a building be C dollars.
Then, the number of buildings that can be built next year with P dollars is N = P/C.
If the average cost of building a building increases by 10%, then the new average cost of building a building is C + 10C = 11C.
The number of buildings that can be built next year with P dollars under the new conditions is N' = P/(11C).
Since we want to find the greatest number of buildings that can be built next year, we need to maximize N'.
To maximize N', we need to minimize C.
Therefore, the answer is:
C = P/N
C = P/(P/C) = C
This equation has only one solution, which is C = P.
Substituting C = P into the equation for N', we get:
N' = P/(11P) = 1/11
N' = N/11
N' = 0.0909N
Therefore, the greatest number of buildings that the builder could build next year using P dollars is 1/0.0909N = 11N/9 = 1.2222N = 1.2222 x N = 1.2222 x (P/C) = 1.2222 x P/P = 1.2222 x 1 = 1.2222N = 1.1111N = 1.1111 x N = 1.1111 x (P/C) = 1.1111 x P/(P/C) = 1.1111 x C = 1.1111 x (P/P) = 1.1111 x 1 = 1.1111N = 1.1111 x N = 1.1111 x (P/C) = 1.1111 x P/(P/C) = 1.1111 x C = 1.1111 x 1 = 1.1111N = 1.1111 x N = 1.1111 x
>>>5: #### 5:Explanation:
Let the average cost of building each building be C dollars.
Then, P = N * C
If the average cost of building each building were to increase 10% from this year's cost, then the average cost of building each building would be 1.1C dollars.
So, P = N * 1.1C
=> N = 9P/11C
=> N = 9P/11C
=> N = 9P/11C
=> N = 9P/11C
=> N = 9P/11C
=> N = 9P/11C
=> N = 9P/11C
=> N = 9P/11C
=> N = 9P/11C
=> N = 9P/11C
=> N = 9P/11C
=> N = 9P/11C
=> N = 9P/11C
=> N = 9P/11C
=> N = 9P/11C
=> N = 9P/11C
=> N = 9P/11C
=> N = 9P/11C
=> N = 9P/11C
=> N = 9P/11C
=> N = 9P/11C
=> N = 9P/11C
=> N = 9P/11C
=> N = 9P/11C
=> N = 9P/11C
=> N = 9P/11C
=> N = 9P/11C
=> N = 9P/11C
=> N = 9P/11C
=> N = 9P/11C
=> N = 9P/11C
=> N = 9P/11C
=> N = 9P/11C
=> N = 9P/11C
=> N = 9P/11C
=> N = 9P/11C
=> N = 9P/11C
=> N = 9P/11C
=> N = 9P/11C
=> N = 9P/11C
>>>6: #### A
OPINIONS END
SOLUTION:Correct answer is (A).
This year, the price of a building is price1=P/N.
If this price increases by 50% it becomes Price2=P/N*1.1
Then with P dollars, you can build P/Price2 buildings i.e. P/(P/N*1.1) i.e. N/1.1 i.e. 0.91*N
Which is 9% less than N. #### A |
QUESTION:The average weight of 16 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg. Find the average weights of all the boys in the class.
options: A)47.55 kg B)48 kg C)48.55 kg D)49.25 kg E)59.25 kg
OPINIONS START
>>>0: #### C
>>>1: #### C
>>>2: #### C
>>>3: #### C
>>>4: #### D
>>>5: #### C
>>>6: #### C
OPINIONS END
SOLUTION:16*50.25+8*45.15/24=48.55
ANSWER:C #### C |
QUESTION:Calculate the % profit or loss, if the cost price of 9 balls is equal to the selling price of 14 balls.
options: A)35.7% B)25.7% C)15.7% D)55.7% E)45.7%
OPINIONS START
>>>0: #### None of the above
>>>1: #### A
>>>2: #### A
>>>3: #### D
>>>4: #### 4:Let the cost price of one ball be x.
Then, the cost price of 9 balls = 9x
The selling price of 14 balls = 14x
Since 9x = 14x, we can find that x = 9/14 * 14 = 9
Therefore, the cost price of one ball is Rs.9.
The cost price of 9 balls = Rs.81
The selling price of 14 balls = Rs.144
The profit = Selling price - Cost price = Rs.63
Profit percentage = (Profit / Cost price) * 100%
Profit percentage = (63 / 81) * 100%
Profit percentage = 78.33%
However, since the question asks for a percentage, not a decimal, we round up to the nearest whole number.
Therefore, the answer is D) 79%.
>>>5: #### D
>>>6: #### E
OPINIONS END
SOLUTION:Let the cost price of 1 balls be Rs 1
Cost of 14 balls= Rs 14
Selling price of 14 balls = 9
Gain/loss = 14 - 9 = 5
%=5/14∗100= 35.7
Answer: A #### A |
QUESTION:In what time will Rs.4000 lent at 3% per annum on simple interest earn as much interest as Rs.5000 will earn in 5 years at 4% per annum on simple interest?
options: A)8 1/3 B)8 1/6 C)8 1/9 D)8 1/1 E)8 1/5
OPINIONS START
>>>0: #### A
>>>1: #### A
>>>2: #### A
>>>3: #### A
>>>4: #### None
>>>5: #### A
>>>6: #### A
OPINIONS END
SOLUTION:(4000*3*R)/100 = (5000*5*4)/100
R = 8 1/3
Answer: A #### A |
QUESTION:If w and y are positive integer and w/y is an even integer, which of the following can be an odd integer?
options: A)x B)xy C)x−y D)x+2y E)w/3
OPINIONS START
>>>0: #### 0:Here's how to solve this:
* **Understanding the
>>>1: #### A
>>>2: #### E
>>>3: #### A
>>>4: #### B
>>>5: #### C
>>>6: #### D
OPINIONS END
SOLUTION:C w-Y
Let says w =12 Y=3 iT BECOMES w-Y =9 This is odd True
w = 12 Y = 6 THEN w-Y = 2, Which is even hence this is False.
so both Yes and NO situations are exists for this Option. C can't be the correct answer same logic goes for E. I believe this question is incomplete b'coz of Irrelevant Options. #### E |
QUESTION:An office supply store stocks two sizes of notebooks, each in six colors: orange, blue, green, yellow, red, or pink. The store packs the notebooks in packages that contain either 4 notebooks of the same size and the same color or 4 notebooks of the same size and of 4 different colors. If the order in which the colors are packed is not considered, how many different packages of the types described above are possible?
options: A)20 B)24 C)32 D)36 E)42
OPINIONS START
>>>0: #### B
>>>1: #### B
>>>2: #### C
>>>3: #### B
>>>4: #### E
>>>5: #### E
>>>6: #### E
OPINIONS END
SOLUTION:First let's consider the small notebooks.
There are 6 ways to choose notebooks of the same color.
The number of ways to choose four notebooks with different colors is 6C4=15.
There are 21 different packages we can make with the small notebooks.
We can use the same process to find 21 different packages with large notebooks.
The total number of different packages is 42.
The answer is E. #### E |
QUESTION:62467 × 9998 = ?
options: A)624545037 B)627745452 C)624545077 D)624545066 E)625454211
OPINIONS START
>>>0: #### D
>>>1: #### C
>>>2: #### A
>>>3: #### A
>>>4: #### A
>>>5: #### D
>>>6: #### D
OPINIONS END
SOLUTION:D
624545066
62467 × 9998 = 62467 × (10000 - 2)
= 62467 × 10000 - 62467 × 2
= 624670000 - 124934
= 624545066 #### D |
QUESTION:A store’s selling price of $2500 for a certain printer would yield a profit of 40 percent of the store’s cost for the printer. What selling price would yield a profit of 50 percent of the printer’s cost?
options: A) $2400 B) $2464 C) $2650 D) $2478 E) $2800
OPINIONS START
>>>0: #### C
>>>1: #### C
>>>2: #### D
>>>3: #### E
>>>4: #### 4:Let the cost price of the printer be x.
Profit = 40% of x => 0.4x = 2500 => x = 6250
Profit = 50% of x => 0.5x = ?
>>>5: #### C
>>>6: #### D
OPINIONS END
SOLUTION:1.4x = 2500
x=2500/1.4
so, 1.5X = 2500*1.5/1.4= 2478
Answer:- D #### D |
QUESTION:The length, breadth and height of a room are in the ratio 12 : 4 : 4. If the breadth and height are halved while the length is doubled, then the total area of the four walls of the room will
options: A)(a) remain the same B)(b) decrease by 13.64% C)(c) decrease by 15% D)(d) decrease by 18.75% E)(e) decrease by 30%
OPINIONS START
>>>0: #### None of the above
>>>1: #### D
>>>2: #### E
>>>3: #### (a) remain the same
>>>4: #### C
>>>5: #### C
>>>6: #### B
OPINIONS END
SOLUTION:Length (L) = 12
Breadth (B) = 4
Height (H) = 4
Total Area of Walls = 2(BH + LH) = 2*(4*4 + 12*4) = 2*(16+48) = 128
Then, Finally
Length (L) = 2*12 = 24
Breadth (B) = 4/2 = 2
Height (H) = 4/2 = 2
Total Area of Walls = 2(BH + LH) = 2*(2*2 + 24*2) = 2*(4+48) = 104
% change in Area of four walls = (Final Area-Initial Area)*100 /Initial Area
i.e. % change in Area of four walls = (104-128)*100 /128=- 18.75% (Decrease)
Answer: Option D #### D |
QUESTION:The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 16000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is
options: A)20 B)21 C)22 D)35 E)NONE
OPINIONS START
>>>0: #### D
>>>1: #### A
>>>2: #### D
>>>3: #### D
>>>4: #### 4:Let the number of technicians be x and the number of other workers be y.
x + y = total number of workers
We have two equations:
1) x * 16000 + y * 6000 = total salary
2) x + y = total number of workers
From equation 1, we can find x = (total salary - y * 6000) / 16000
Substituting x in equation 2, we get y = total number of workers - x
Substituting x in terms of y from equation 1, we get x = (total salary - 6000y) / 16000
Substituting x in equation 2, we get y = total number of workers - (total salary - 6000y) / 16000
Multiplying both sides by 16000, we get 16000y + y(total salary - 6000y) = total number of workers * 16000
Simplifying, we get 16001y = total number of workers * 16000
Dividing both sides by 16000, we get y = (total number of workers - 1)
Substituting y = total number of workers - 1 in equation 1, we get x = (total salary - 6000(total number of workers - 1)) / 16000
Substituting x = (total salary - 6000y) / 16000 from equation 1 in the above equation, we get
(total salary - 6000(total number of workers - 1)) / 16000 = (total salary - 6000y) / 16000
Multiplying both sides by 16000, we get total salary - 6000y = total salary - 6000(total number of workers - 1)
Subtracting total salary from both sides, we get 6000y = 6000(total number of workers - 1)
Dividing both sides by 6000, we get
>>>5: #### C
>>>6: #### D
OPINIONS END
SOLUTION:Sol.
Let the total number of workers be x. Then,
8000x = (16000 × 7) + 6000 ( x – 7)
‹=› 2000x = 70000
‹=› x = 35.
Answer D #### D |
QUESTION:What percent is 2 gm of 1 kg?
options: A)0.5 % B)0.2% C)1.5% D)2% E)3%
OPINIONS START
>>>0: #### B
>>>1: #### B
>>>2: #### B
>>>3: #### B
>>>4: #### B
>>>5: #### B
>>>6: #### B
OPINIONS END
SOLUTION:1 kg = 1000 gm
2/1000 × 100 = 200/1000
=1/5 = 0.2 %
B) #### B |
QUESTION:A shopkeeper sold an article offering a discount of 5% and earned a profit of 19.7%. What would have been the percentage of profit earned if no discount was offered?
options: A)60% B)26% C)30% D)56% E)73%
OPINIONS START
>>>0: #### B
>>>1: #### C
>>>2: #### C
>>>3: #### E
>>>4: #### C
>>>5: #### 5:Let the cost price be Rs. 100
Selling price = Rs. 100 - 5% of 100 = Rs. 95
Profit = 19.7% of 100 = Rs. 19.7
Selling price = Rs. 100 + 19.7 = Rs. 119.7
Profit = 19.7% of 100 = Rs. 19.7
Selling price = Rs. 100 + 19.7 = Rs. 119.7
Profit = 19.7% of 100 = Rs. 19.7
Selling price = Rs. 100 + 19.7 = Rs. 119.7
Profit = 19.7% of 100 = Rs. 19.7
Selling price = Rs. 100 + 19.7 = Rs. 119.7
Profit = 19.7% of 100 = Rs. 19.7
Selling price = Rs. 100 + 19.7 = Rs. 119.7
Profit = 19.7% of 100 = Rs. 19.7
Selling price = Rs. 100 + 19.7 = Rs. 119.7
Profit = 19.7% of 100 = Rs. 19.7
Selling price = Rs. 100 + 19.7 = Rs. 119.7
Profit = 19.7% of 100 = Rs. 19.7
Selling price = Rs. 100 + 19.7 = Rs. 119.7
Profit = 19.7% of 100 = Rs. 19.7
Selling price = Rs. 100 + 19.7 = Rs. 119.7
Profit = 19.7% of 100 = Rs. 19.7
Selling price = Rs. 100 + 19.7 = Rs.
>>>6: #### C
OPINIONS END
SOLUTION:Let C.P. be Rs. 100.
Then, S.P. = Rs. 19.70
Let marked price be Rs. x. Then, 95/100 x = 119.70
x = 11970/95 = Rs. 126
Now, S.P. = Rs. 126, C.P. = Rs. 100
Profit % = 26%.
Answer: B #### B |
QUESTION:If December 3rd, 1999 is a Friday, what day is January 8th, 2000?
options: A)Wednesday B)Thursday C)Friday D)Saturday E)Sunday
OPINIONS START
>>>0: #### D
>>>1: #### 1:1999 is not a leap year.
So, 1999 has 365 days.
365 = 52 weeks + 1 day
So, 1999 is 1 day ahead of 1998.
1998 is a leap year.
So, 1998 has 366 days.
366 = 52 weeks + 14 days
So, 1998 is 14 days ahead of 1997.
1997 is 1 day behind 1996.
1996 is a leap year.
So, 1996 has 366 days.
366 = 52 weeks + 14 days
So, 1996 is 14 days ahead of 1995.
1995 is 1 day behind 1994.
1994 is a leap year.
So, 1994 has 366 days.
366 = 52 weeks + 14 days
So, 1994 is 14 days ahead of 1993.
1993 is 1 day behind 1992.
1992 is a leap year.
So, 1992 has 366 days.
366 = 52 weeks + 14 days
So, 1992 is 14 days ahead of 1991.
1991 is 1 day behind 1990.
1990 is a leap year.
So, 1990 has 366 days.
366 = 52 weeks + 14 days
So, 1990 is 14 days ahead of 1989.
1989 is 1 day behind 1988.
1988 is a leap year.
So, 1988 has 366 days.
366 = 52 weeks + 14 days
So, 1988 is 14 days ahead of 1987.
1987 is 1 day behind 1986.
1986 is a leap year.
So, 1986 has 366 days.
366 = 52 weeks + 14 days
So, 1986 is 14 days ahead of 1985.
1985 is 1 day behind 1984.
1984 is a leap year.
So, 1984 has 366 days.
366 = 52 weeks + 14 days
So, 1984 is 14 days ahead of 1983.
1983 is 1 day behind 1982.
1982 is a leap year.
So, 1982 has 366 days.
366 = 52 weeks + 14 days
So, 1982 is 14 days ahead of 1981.
1981
>>>2: #### C
>>>3: #### E
>>>4: #### 4:To find the day of the week for January 8th, 2000, we need to find the number of days that have passed since January 1st, 2000, which is a Thursday.
First, let's find the number of days in December from 1st to 3rd:
December 1st is on a Thursday (since it's a known fact that the first of the month is always on a Thursday in a given year).
December 2nd is on a Friday (by calculating the difference between December 1st and December 2nd).
December 3rd is on a Saturday (by calculating the difference between December 2nd and December 3rd).
So, December 3rd, 1999 is a Saturday.
Now, let's find the number of days between December 3rd, 1999, and January 8th, 2000:
- December 31st, 1999, is on a Friday (since it's always the last day of the month).
- January 1st, 2000, is on a Friday (since it's a known fact that the first of the month is always on the same weekday as New Year's Day).
- January 2nd, 2000, is on a Saturday.
- January 3rd, 2000, is on a Sunday.
- January 4th, 2000, is on a Monday.
- January 5th, 2000, is on a Tuesday.
- January 6th, 2000, is on a Wednesday.
- January 7th, 2000, is on a Thursday.
So, January 7th, 2000, is a Thursday.
To find the number of days between December 3rd, 1999, and January 8th, 2000, we can subtract the number of days in December 1999 (31 days) and the number of days from December 31st, 1999, to January 8th, 2000 (5 days).
Total number of days = 31 (
>>>5: #### D
>>>6: #### D
OPINIONS END
SOLUTION:There is difference of 36 days from Dec. 3rd 1999 to Jan. 8th 2000.
36/7 has a remainder of 1.
Jan. 8th is: Friday + 1 day = Saturday
The answer is D. #### D |
QUESTION:A woman is 18 years older than her son. In 4 years, her age will be twice the age of her son. The present age of her son is
options: A)12 B)14 C)16 D)18 E)20
OPINIONS START
>>>0: #### B
>>>1: #### B
>>>2: #### B
>>>3: #### B
>>>4: #### B
>>>5: #### C
>>>6: #### C
OPINIONS END
SOLUTION:Explanation:
Let the son's present age be x years. Then, woman's present age = (x + 18) years
=> (x + 18) + 4 = 2(x + 4)
=> x + 22 = 2x +8
So, x = 14 Answer: B #### B |
QUESTION:Two pens and three pencils cost Rs 86. four Pens and a pencil cost Rs. 112. find the cost of a pen and that of a pencil.
options: A)12 B)10 C)15 D)19 E)20
OPINIONS START
>>>0: #### A
>>>1: #### D
>>>2: #### A
>>>3: #### C
>>>4: #### A: Rs 12, C: Rs 10
>>>5: #### 5:Sol. Let the cost of a pen = x and that of a pencil = y.
Then, 2x + 3y = 86 ……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………
>>>6: #### A
OPINIONS END
SOLUTION:Let the cost of a pen ands a pencil be Rs. X and Rs. Y respectively.
Then, 2x + 3y = 86 ….(i) and 4x + y =112.
Solving (i) and (ii), we get: x = 25 and y = 12.
Cost of a pen =Rs. 25 and the cost of a pencil =Rs. 12.
Answer is A. #### A |
QUESTION:What is the remainder when 103 * 505 * 607 is divided by 9
options: A)6 B)18 C)2 D)4 E)7
OPINIONS START
>>>0: #### E
>>>1: #### 1:103 * 505 * 607 = 103 * 5 * 101 * 7 * 607
103 + 5 + 101 + 7 + 607 = 723
723/9 = 80 remainder 3
103 * 505 * 607 = 3 * 9 * 9 * 9 * 3
103 * 505 * 607 = 3^4 * 9^3
103 * 505 * 607 = 3^7 * 9^3
103 * 505 * 607 = 3^7 * (3^2)^3
103 * 505 * 607 = (3^7) * (3^6)
103 * 505 * 607 = 3^13
103 * 505 * 607 = 3^7 * 3^6
103 * 505 * 607 = 3^13
103 * 505 * 607 = 3^7 * 3^6
103 * 505 * 607 = 3^13
103 * 505 * 607 = 3^7 * 3^6
103 * 505 * 607 = 3^13
103 * 505 * 607 = 3^7 * 3^6
103 * 505 * 607 = 3^13
103 * 505 * 607 = 3^7 * 3^6
103 * 505 * 607 = 3^13
103 * 505 * 607 = 3^7 * 3^6
103 * 505 * 607 = 3^13
103 * 505 * 607 = 3^7 * 3^6
103 * 505 * 607 = 3^13
103 * 505 * 607 = 3^7 * 3^6
103 * 505 * 607 = 3^13
103 * 505 * 607 = 3^7 * 3^6
103 * 505 * 607 = 3^13
103 * 505 * 607 = 3^7 * 3^6
103 * 505 * 607 = 3^13
103 * 505 * 607 = 3^7 * 3^6
103 * 505 * 607 = 3^13
103 * 505 * 607 =
>>>2: #### C
>>>3: #### A
>>>4: #### B
>>>5: #### A
>>>6: #### C
OPINIONS END
SOLUTION:103/9==> Remainder=4
505/9==> Remainder=1
607/9==> Remainder=4
=4*4*1=16/9==> Remainder=7
Answer: E #### E |
QUESTION:In an election between 2 candidates, 50% of the voters cast their votes, out of which 10% of the votes were declared invalid. A candidate got 5000 votes which were 50% of the total valid votes. Find the total number of votes enrolled in that election?
options: A)16200 B)18000 C)17500 D)15823 E)15000
OPINIONS START
>>>0: #### A
>>>1: #### E
>>>2: #### A
>>>3: #### B
>>>4: #### A
>>>5: #### B
>>>6: #### E
OPINIONS END
SOLUTION:Let the total number of votes enrolled be x.
Then, number of votes cast = 50% of x.
Valid votes = 90% of (50% of x)
50% of (90% of (50% of x)) = 4050
(50/100)*(90/100)*(50/100)x = 4050
x = 18000
Answer is B #### B |
QUESTION:The average monthly salary of 8 workers and one supervisor in a factory was 430.@SSWhen@SSthe@SSsupervisor@CC@SSwhose@SSsalary@SSwas@SS430.@SSWhen@SSthe@SSsupervisor@CC@SSwhose@SSsalary@SSwas@SS430.Whenthesupervisor,whosesalarywas430. When the supervisor, whose salary was 870 per month, retired, a new person was appointed and then the average salary of 9 people was $$430 per month. The salary of the new supervisor is:
options: A)870 B)600 C)287 D)771 E)191
OPINIONS START
>>>0: #### A
>>>1: #### D
>>>2: #### A
>>>3: #### E
>>>4: #### D
>>>5: #### E
>>>6: #### E
OPINIONS END
SOLUTION:Explanation:
Total salary of 8 workers and supervisor together = 9 × 430 = 3870
Now total salary of 8 workers = 3870 − 870 = 3000
Total salary of 9 workers including the new supervisor = 9 × 430 = 3870
Salary of the new supervisor = 3870 − 3000 = 870
Answer: A #### A |
QUESTION:If 4a = 16b and 9b = 14c, Find a:b:c?
options: A)52:13:7 B)13:7:52 C)7:13:52 D)64:14:9 E)None of these
OPINIONS START
>>>0: #### E
>>>1: #### D
>>>2: #### A
>>>3: #### A
>>>4: #### A:7:13
>>>5: #### B
>>>6: #### 6:4a = 16b => a = 4b
9b = 14c => c = 9b/14
a:b:c = 4b:b:9b/14
= 4:1:9/14
= 56:14:9
= 4:1:9/4
= 4:1:9/4
= 4:1:9/4
= 4:1:9/4
= 4:1:9/4
= 4:1:9/4
= 4:1:9/4
= 4:1:9/4
= 4:1:9/4
= 4:1:9/4
= 4:1:9/4
= 4:1:9/4
= 4:1:9/4
= 4:1:9/4
= 4:1:9/4
= 4:1:9/4
= 4:1:9/4
= 4:1:9/4
= 4:1:9/4
= 4:1:9/4
= 4:1:9/4
= 4:1:9/4
= 4:1:9/4
= 4:1:9/4
= 4:1:9/4
= 4:1:9/4
= 4:1:9/4
= 4:1:9/4
= 4:1:9/4
= 4:1:9/4
= 4:1:9/4
= 4:1:9/4
= 4:1:9/4
= 4:1:9/4
= 4:1:9/4
= 4:1:9/4
= 4:1:9/4
= 4:1:9/4
= 4:1:9/4
= 4:1:9/4
= 4:1:9/4
= 4:1:9/4
= 4:1:9/4
= 4:1:9/4
=
OPINIONS END
SOLUTION:Explanation:
(4a = 16b ==> a/b = 16/4)
and (9b = 14c ==> b/c = 14/9)
==> a:b = 16:4 and b:c = 14:9
a:b:c = 64:14:9
Answer: Option D #### D |
QUESTION:How much is 80% of 40 is greater than 4/5 of 25?
options: A)15 B)57 C)16 D)12 E)73
OPINIONS START
>>>0: #### D
>>>1: #### D
>>>2: #### D
>>>3: #### D
>>>4: #### C
>>>5: #### C
>>>6: #### D
OPINIONS END
SOLUTION:(80/100) * 40 – (4/5) * 25
32 - 20 = 12
Answer: D #### D |
QUESTION:In the x-y plane, the area of the region bounded by the graph of |x+y| + |x-y| = 10 is
options: A)8 B)625 C)16 D)20 E)24
OPINIONS START
>>>0: ####
>>>1: #### 1:|x+y| + |x-y| = 10
x+y = 10, x-y = 10
x+y = 10, x-y = -10
x+y = -10, x-y = 10
x+y = -10, x-y = -10
Area = 2*(area of square with side 10)
Area = 2*100
Area = 200
Area = 200/2
Area = 100
Area = 100/2
Area = 50
Area = 50*2
Area = 100
Area = 100/2
Area = 50
Area = 50*2
Area = 100
Area = 100/2
Area = 50
Area = 50*2
Area = 100
Area = 100/2
Area = 50
Area = 50*2
Area = 100
Area = 100/2
Area = 50
Area = 50*2
Area = 100
Area = 100/2
Area = 50
Area = 50*2
Area = 100
Area = 100/2
Area = 50
Area = 50*2
Area = 100
Area = 100/2
Area = 50
Area = 50*2
Area = 100
Area = 100/2
Area = 50
Area = 50*2
Area = 100
Area = 100/2
Area = 50
Area = 50*2
Area = 100
Area = 100/2
Area = 50
Area = 50*2
Area = 100
Area = 100/2
Area = 50
Area = 50*2
Area = 100
Area = 100/2
Area = 50
Area = 50*2
Area = 100
Area = 100/2
Area = 50
Area = 50*2
Area = 100
Area = 100/2
Area = 50
Area = 50*2
Area = 100
Area = 100/2
Area = 50
Area = 50*2
Area = 100
Area = 100/2
Area = 50
Area = 50*2
Area = 100
Area = 100/2
>>>2: #### D
>>>3: #### C
>>>4: #### A
>>>5: #### B
>>>6: #### 6:Explanation:
The equation |x+y| + |x-y| = 10 represents a square in the x-y plane.
To see this, consider the four cases for the signs of x+y and x-sin:
1. x+y ≥ 0 and x-y ≥ 0: x+y + x-y = 2x = 10, so x = 5.
2. x+y ≥ 0 and x-y < 0: x+y - (x-y) = 2y = 10, so y = 5.
3. x+y < 0 and x-y ≥ 0: -(x+y) + (x-y) = -2y = 10, so y = -5.
4. x+y < 0 and x-y < 0: -(x+y) - (x-y) = -2x = 10, so x = -5.
These four cases give the vertices of the square: (5,5), (5,-5), (-5,-5), and (-5,5).
The side length of the square is the distance between any two adjacent vertices, which is 10.
The area of the square is the side length squared, which is 10^2 = 100.
However, the question asks for the area of the region bounded by the graph, which is half of the square.
So the answer is 100/2 = 50.
Answer: None of the options match the correct answer.
OPINIONS END
SOLUTION:I've never seen such kind of question in GMAT before.
OK there can be 4 cases:
|x+y| + |x-y| = 10
A. x+y+x-y = 10 --> x=5
B. x+y-x+y = 10 --> y=5
C. -x-y +x-y= 10 --> y=-5
D. -x-y-x+y=10 --> x=-5
The area bounded by 4 graphs x=5, x=-5, y=5, y=-5 will be square with the side of 4 so the area will be25*25=625
Answer: B #### B |
QUESTION:Six lights begin to flash together at 12:00 noon and flash respectively at intervals of 3, 4, 5, 6, 7, and 8 seconds. Not including the flash at 12:00 noon, how many more times will all six lights flash together before 1:00 pm (i.e. one hour later)?
options: A)4 B)6 C)8 D)10 E)12
OPINIONS START
>>>0: #### A
>>>1: #### A
>>>2: #### D
>>>3: #### E
>>>4: #### C
>>>5: #### 5:The six lights flash together at 12:00 noon, 12:00:03, 12:00:04, 12:00:05, 12:00:06, 12:00:07, 12:00:08, 12:00:09, 12:00:10, 12:00:11, 12:00:12, 12:00:13, 12:00:14, 12:00:15, 12:00:16, 12:00:17, 12:00:18, 12:00:19, 12:00:20, 12:00:21, 12:00:22, 12:00:23, 12:00:24, 12:00:25, 12:00:26, 12:00:27, 12:00:28, 12:00:29, 12:00:30, 12:00:31, 12:00:32, 12:00:33, 12:00:34, 12:00:35, 12:00:36, 12:00:37, 12:00:38, 12:00:39, 12:00:40, 12:00:41, 12:00:42, 12:00:43, 12:00:44, 12:00:45, 12:00:46, 12:00:47, 12:00:48, 12:00:49, 12:00:50, 12:00:51, 12:00:5
>>>6: #### None of the above
OPINIONS END
SOLUTION:The least common multiple is 2*2*2*3*5*7=840.
3600 seconds / 840 = 4 + remainder.
The answer is A. #### A |
QUESTION:Let n~ be defined for all positive integers n as the remainder when (n - 1)! is divided by n.
What is the value of 30~ ?
options: A)1 B)0 C)2 D)8 E)31
OPINIONS START
>>>0: #### B
>>>1: #### 1:30~ = (30 - 1)!/30
= 29!/30
= (29 * 28 * 27 * 26 * 25 * 24 * 23 * 22 * 21 * 20 * 19 * 18 * 17 * 16 * 15 * 14 * 13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1)/30
= (29 * 28 * 27 * 26 * 25 * 24 * 23 * 22 * 21 * 20 * 19 * 18 * 17 * 16 * 15 * 14 * 13 * 12 * 11 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1)/30
= (29 * 28 * 27 * 26 * 25 * 24 * 23 * 22 * 21 * 19 * 18 * 17 * 16 * 15 * 14 * 13 * 12 * 11 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1)/30
= (29 * 28 * 27 * 26 * 25 * 24 * 23 * 22 * 21 * 19 * 18 * 17 * 16 * 15 * 14 * 13 * 12 * 11 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1)/30
= (29 * 28 * 27 * 26 * 25 * 24 * 23 * 22 * 21 * 19 * 18 * 17 * 16 * 15 * 14 * 13 * 12 * 11 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1)/30
= (29 * 28 * 27 * 26 * 25 * 24 * 23 * 22 * 21 * 19 * 18 * 17 * 16 * 15 * 14 * 13 * 12 * 11 * 9 * 8 * 7 *
>>>2: #### E
>>>3: #### A
>>>4: #### B
>>>5: #### 5:30~ = 30 - 1 = 29
29! = 29 x 28 x 27 x 26 x 25 x 24 x 23 x 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
= 29 x 28 x 27 x 26 x 25 x 24 x 23 x 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2
= 29 x 28 x 27 x 26 x 25 x 24 x 23 x 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
= 29 x 28 x 27 x 26 x 25 x 24 x 23 x 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
= 29 x 28 x 27 x 26 x 25 x 24 x 23 x 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15 x 14
>>>6: #### B
OPINIONS END
SOLUTION:n~ = (n-1)!
so 30~ = (30-1)! = 29!
when 29!/30 we have 16*2 inside 29!
hence 30 gets cancelled and we get remainder as 0
B #### B |
QUESTION:The average amount with a group of seven numbers is Rs. 30. If the newly joined member has Rs. 60 with him, what was the average amount with the group before his joining the group?
options: A)s. 25.6 B)s. 25 C)s. 16.6 D)s. 26 E)s. 25.6
OPINIONS START
>>>0: #### A
>>>1: #### D
>>>2: #### 30
>>>3: #### D
>>>4: #### C
>>>5: #### E
>>>6: #### B
OPINIONS END
SOLUTION:Total members in the group = 7
Average amount = Rs. 30
Total amount with them = 7 * 30 = Rs. 210
One number has Rs. 60. So, the amount with remaining 6 people = 210 - 60 = Rs. 150
The average amount with them = 150/6 = Rs. 25
ANSWER:B #### B |
QUESTION:In a fuel station the service costs $1.05 per car, every liter of fuel costs 0.6$. Assuming that you fill up 3 mini-vans and 2 trucks, how much money will the fuel cost to all the cars owners total, if a mini- van's tank is 65 liters and a truck's tank is 120% bigger and they are all empty-?
options: A)122.6$ B)128.9$ C)243.7$ D)293.85$ E)312.12$
OPINIONS START
>>>0: ####
>>>1: #### D
>>>2: #### E
>>>3: #### C
>>>4: #### D
>>>5: #### B
>>>6: #### B
OPINIONS END
SOLUTION:Service cost of 3 van and 2 truck = 1.05*(3+2)=5.25
Fuel in 3 Van = 3*65=195 litre
Fuel in 2 Trucks =2 * 65(1+120/100)= 286
Total fuel(Van+Truck) = 481 Litre
Total Fuel cost = 481*0.6 =288.6
TOTAL COST =FUEL+SERVICE=288.6+5.25=293.85
ANSWER IS D #### D |
QUESTION:A rectangular courtyard 3.78 metres long and 2.25 metres wide is to be paved exactly with square title, all of the same size. What is the largest size of the tile which could be used for the purpose ?
options: A)11 cms B)21 cms C)42 cms D)None of these E)46 cms
OPINIONS START
>>>0: #### D
>>>1: #### 1:The area of the courtyard = 3.78 x 2.25 = 8.47 m^2
The area of the tile = a^2
The area of the courtyard = number of tiles x area of the tile
8.47 = number of tiles x a^2
number of tiles = 8.47/a^2
The number of tiles must be a whole number.
The largest possible value of a is 3.5 m
The largest possible value of a is 3.5 m
The largest possible value of a is 3.5 m
The largest possible value of a is 3.5 m
The largest possible value of a is 3.5 m
The largest possible value of a is 3.5 m
The largest possible value of a is 3.5 m
The largest possible value of a is 3.5 m
The largest possible value of a is 3.5 m
The largest possible value of a is 3.5 m
The largest possible value of a is 3.5 m
The largest possible value of a is 3.5 m
The largest possible value of a is 3.5 m
The largest possible value of a is 3.5 m
The largest possible value of a is 3.5 m
The largest possible value of a is 3.5 m
The largest possible value of a is 3.5 m
The largest possible value of a is 3.5 m
The largest possible value of a is 3.5 m
The largest possible value of a is 3.5 m
The largest possible value of a is 3.5 m
The largest possible value of a is 3.5 m
The largest possible value of a is 3.5 m
The largest possible value of a is 3.5 m
The largest possible value of a is 3.5 m
The largest possible value of a is 3.5 m
The largest possible value of a is 3.5 m
The largest possible value of a is 3.5 m
The largest possible value of a is 3.5 m
The largest possible value of a is 3.5 m
The largest possible value of a is 3.5 m
The largest possible value of a is 3.5 m
The largest possible value of a is 3.5 m
>>>2: #### None of these
>>>3: #### B
>>>4: #### A
>>>5: #### A
>>>6: #### D
OPINIONS END
SOLUTION:Solution
Largest size of the tile = H.C.F. of 378 cm an= 21 cm = 525 cm. Answer B #### B |
QUESTION:A motorcyclist made 3 roundtrips to the park until he ran out of gas back at home. Te park is 1500 meters away from his home. His speedometer was broke and he wanted to calculate his speed. It took him two and half hours to complete the journey. How fast was the motorcyclist traveling?
options: A)25 B)60 C)36 D)45 E)32
OPINIONS START
>>>0: #### 1.8 km/h
>>>1: #### A
>>>2: #### E
>>>3: #### C
>>>4: #### C
>>>5: #### D
>>>6: #### C
OPINIONS END
SOLUTION:The distance from the park to the motorcyclist home was 15000 meters.
He made the trip 3 times in total with each trip being 30000 meters.
multiply 3 by 30000 to get 90000 meters or 90km in total.
D= ST
90000/2.5 = T which comes to 36000 meters or 36 km per hour
Correct answer = 36 #### C |
QUESTION:A and B together can do a piece of work in 8 days. If A alone can do the same work in 12 days, then B alone can do the same work in?
options: A)22 days B)77 days C)24 days D)17 days E)18 days
OPINIONS START
>>>0: #### C
>>>1: #### C
>>>2: #### C
>>>3: #### B
>>>4: #### E
>>>5: #### C
>>>6: #### C
OPINIONS END
SOLUTION:B = 1/8 – 1/2 = 1/24 => 24 days
Answer: C #### C |
QUESTION:If x and y are integers, what is the least positive number of 24x+9y?
options: A)1 B)3 C)4 D)6 E)9
OPINIONS START
>>>0: #### B
>>>1: #### 1:24x+9y = 3(8x+3y) = 3(3(8x/3)+3y/3) = 3(3(8x/3)+y) = 3(3(8x/3)+y) = 3(3(8x/3)+y) = 3(3(8x/3)+y) = 3(3(8x/3)+y) = 3(3(8x/3)+y) = 3(3(8x/3)+y) = 3(3(8x/3)+y) = 3(3(8x/3)+y) = 3(3(8x/3)+y) = 3(3(8x/3)+y) = 3(3(8x/3)+y) = 3(3(8x/3)+y) = 3(3(8x/3)+y) = 3(3(8x/3)+y) = 3(3(8x/3)+y) = 3(3(8x/3)+y) = 3(3(8x/3)+y) = 3(3(8x/3)+y) = 3(3(8x/3)+y) = 3(3(8x/3)+y) = 3(3(8x/3)+y) = 3(3(8x/3)+y) = 3(3(8x/3)+y) = 3(3(8x/3)+y) = 3(3(8x/3)+y) = 3(3(8x/3)+y) = 3(3(8x/3)+y) = 3(3(8x/3)+y) = 3(3(8x/3)+y) = 3(3(8x/3)+y) = 3(3(8x/3)+y) = 3(3(8x/3)+y) = 3(3(8x/3)+y) = 3(3(8x/3)+y) = 3(3(8x/3)+y) = 3(3(8x/3)+y
>>>2: #### B
>>>3: #### D
>>>4: #### C
>>>5: #### 5:Explanation :
24x+9y=3(8x+3y)
=3(4x+3y+4x)
=3(4x+3y+4x+3y+4x+3y+4x+3y)
=3(4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x+3y+4x
>>>6: #### E
OPINIONS END
SOLUTION:24x+9y = 3(8x+3y) which will be a minimum positive number when 8x+3y = 1.
8(-1) + 3(3) = 1
Then 3(8x+3y) can have a minimum positive value of 3.
The answer is B. #### B |
QUESTION:In a Quiz the points in each round for the first,second and third were 1000,50,20 . No other points were given. Sam participated in several rounds in the competition and the product of his score was 50000. In How many rounds did he participate?
options: A)Cannot be determined B)43 C)3 D)6 E)10
OPINIONS START
>>>0: #### A
>>>1: #### 1:Let the number of rounds in which Sam participated be x.
Then, 1000x × 50x × 20x = 50000
1000 × 50 × 20 × x3 = 50000
1000000 × x3 = 50000
x3 = 50000/1000000
x3 = 1/20
x = 1/2
x = 0.5
x = 1/2
x = 0.5
x = 1/2
x = 0.5
x = 1/2
x = 0.5
x = 1/2
x = 0.5
x = 1/2
x = 0.5
x = 1/2
x = 0.5
x = 1/2
x = 0.5
x = 1/2
x = 0.5
x = 1/2
x = 0.5
x = 1/2
x = 0.5
x = 1/2
x = 0.5
x = 1/2
x = 0.5
x = 1/2
x = 0.5
x = 1/2
x = 0.5
x = 1/2
x = 0.5
x = 1/2
x = 0.5
x = 1/2
x = 0.5
x = 1/2
x = 0.5
x = 1/2
x = 0.5
x = 1/2
x = 0.5
x = 1/2
x = 0.5
x = 1/2
x = 0.5
x = 1/2
x = 0.5
x = 1/2
x = 0.5
x = 1/2
x = 0.5
x = 1/2
x = 0.5
x = 1/2
x = 0.5
x = 1/2
x = 0.5
x = 1/2
x = 0.5
x = 1/2
x = 0.5
x
>>>2: #### A
>>>3: #### E
>>>4: #### D
>>>5: #### E
>>>6: #### C
OPINIONS END
SOLUTION:Correct answer is A because we are given that there won't be any points awarded for rounds other than 1st three position.
Thus, it may happen that he played 100 rounds out of only 7 rounds were there in which he was awarded some points. #### A |
QUESTION:?% of 360 = 126
options: A)277 B)35 C)64 D)72 E)None of these
OPINIONS START
>>>0: #### B
>>>1: #### C
>>>2: #### 35
>>>3: #### 3:126 = 360 * 126/360
126/360 = 1/3
126 = 360 * 1/3
126 = 120 + 6
6 = 360 * 1/3 - 120
6 = 120 * 1/3
6 = 40
360 = 6 * 360/40
360 = 6 * 9
360 = 36 * 10
360 = 360 * 1
360 = 360
360/360 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
1 = 1
>>>4: #### E
>>>5: #### B
>>>6: #### B
OPINIONS END
SOLUTION:?% of 360 = 126
or, ? = 126×100/360=35
Answer B #### B |
QUESTION:In one hour, a boat goes 14 km/hr along the stream and 8 km/hr against the stream. The speed of the boat in still water (in km/hr) is:
options: A)12 km/hr B)11 km/hr C)10 km/hr D)8 km/hr E)15 km/hr
OPINIONS START
>>>0: #### B
>>>1: #### A
>>>2: #### A
>>>3: #### B
>>>4: #### C
>>>5: #### A
>>>6: #### B
OPINIONS END
SOLUTION:EXPLANATION
Let speed of the boat in still water = a and speed of the stream = b
Then
a + b = 14
a - b = 8
Adding these two equations, we get 2a = 22
=> a = 11
ie, speed of boat in still water = 11 km/hr
ANSWER IS B #### B |
QUESTION:An article is bought for Rs.750 and sold for Rs.700, find the loss percent?
options: A)6 2/5% B)6 2/9% C)6 5/3% D)6 3/3% E)6 2/3%
OPINIONS START
>>>0: #### A
>>>1: #### E
>>>2: #### E
>>>3: #### A
>>>4: #### E (6.67%)
>>>5: #### E
>>>6: #### E
OPINIONS END
SOLUTION:750 ---- 50
50 ---- ? => 6 2/3%
Answer: E #### E |
QUESTION:Two numbers are in the ratio of 5:7. If 25 be subtracted from each, they are in the ratio of 35:59. Find the numbers?
options: A)60,87 B)60,81 C)60,88 D)60,84 E)60,89
OPINIONS START
>>>0: #### D
>>>1: #### D
>>>2: #### A
>>>3: #### A
>>>4: #### None of the above.
>>>5: #### 5:Let the numbers be 5x and 7x
5x-25 = 35y
7x-25 = 59y
5x-25 = 35y
7x-25 = 59y
5x-35y = 25
7x-59y = 25
5x-35y = 25
7x-59y = 25
5x-7x = 25+59y
2x = 25+59y
x = 12.5+29.5y
x = 12.5+29.5y
x = 12.5+29.5y
x = 12.5+29.5y
x = 12.5+29.5y
x = 12.5+29.5y
x = 12.5+29.5y
x = 12.5+29.5y
x = 12.5+29.5y
x = 12.5+29.5y
x = 12.5+29.5y
x = 12.5+29.5y
x = 12.5+29.5y
x = 12.5+29.5y
x = 12.5+29.5y
x = 12.5+29.5y
x = 12.5+29.5y
x = 12.5+29.5y
x = 12.5+29.5y
x = 12.5+29.5y
x = 12.5+29.5y
x = 12.5+29.5y
x = 12.5+29.5y
x = 12.5+29.5y
x = 12.5+29.5y
x = 12.5+29.5y
x = 12.5+29.5y
x = 12.5+2
>>>6: #### D
OPINIONS END
SOLUTION:(5x-25):(7x-25) = 35:59
x = 12 => 60,84
Answer:D #### D |
QUESTION:What is the next number in the given series
4,18,100,294,....?
options: A)1210 B)1220 C)1230 D)1240 E)1250
OPINIONS START
>>>0: #### 3880
>>>1: ####
>>>2: #### D
>>>3: #### E
>>>4: #### 4:The next number in the series is 1272.
The pattern is that each number is obtained by multiplying the previous number by 2 and then adding 2.
So, 4 * 2 + 2 = 18,
18 * 2 + 2 = 38 (which is not given),
38 * 2 + 2 = 82,
82 * 2 + 2 = 168,
168 * 2 + 2 = 338,
338 * 2 + 2 = 686,
686 * 2 + 2 = 1378,
1378 * 2 + 2 = 2762,
2762 * 2 + 2 = 5530,
5530 * 2 + 2 = 11062,
11062 * 2 + 2 = 22130,
22130 * 2 + 2 = 44262,
44262 * 2 + 2 = 88530,
88530 * 2 + 2 = 177114,
177114 * 2 + 2 = 354232,
354232 * 2 + 2 = 708468,
708468 * 2 + 2 = 1416960,
1416960 * 2 + 2 = 2833932,
2833932 * 2 + 2 = 5668008,
5668008 * 2 + 2 = 11336032,
11336032 * 2 + 2 = 22672112,
22672112 * 2 + 2 = 45344308,
45344308 * 2 + 2 = 90688712,
90688
>>>5: #### A
>>>6: #### 6:The pattern is +14, +82, +194, +306
So next number = 294+306 = 598+14 = 612
None of the above options match the answer.
OPINIONS END
SOLUTION:The given series is difference of cubes and squares of consecutive prime numbers.
2*2*2-2*2=4,
3*3*3-3*3=18,
5*5*5-5*5=100,
7*7*7-7*7=294,
11*11*11-11*11=1210
ANSWER:A #### A |
QUESTION:A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train.
options: A)150 meter B)250 meter C)200 meter D)480 meter E)153 meter
OPINIONS START
>>>0: #### A**
>>>1: #### A
>>>2: #### A
>>>3: #### C
>>>4: #### A
>>>5: #### 5:Let the length of the train be x meters. Then, the length of the train = x meters. The distance covered by the train in 9 seconds = 60 km/hr * 9/3600 km/hr = 150/36 meters. The distance covered by the train in 9 seconds = x + 150/36 meters. The distance covered by the train in 9 seconds = x + 150/36 meters. The distance covered by the train in 9 seconds = x + 150/36 meters. The distance covered by the train in 9 seconds = x + 150/36 meters. The distance covered by the train in 9 seconds = x + 150/36 meters. The distance covered by the train in 9 seconds = x + 150/36 meters. The distance covered by the train in 9 seconds = x + 150/36 meters. The distance covered by the train in 9 seconds = x + 150/36 meters. The distance covered by the train in 9 seconds = x + 150/36 meters. The distance covered by the train in 9 seconds = x + 150/36 meters. The distance covered by the train in 9 seconds = x + 150/36 meters. The distance covered by the train in 9 seconds = x + 150/36 meters. The distance covered by the train in 9 seconds = x + 150/36 meters. The distance covered by the train in 9 seconds = x + 150/36 meters. The distance covered by the train in 9 seconds = x + 150/36 meters. The distance covered by the train in 9 seconds = x + 150/36 meters. The distance covered by the train in 9 seconds = x + 150/36 meters. The distance covered by the train in 9 seconds = x + 150/36 meters. The distance covered by the train in 9 seconds = x + 150/36 meters. The distance covered by the train in 9 seconds = x + 150/36 meters. The distance covered by the train in 9 seconds = x +
>>>6: #### A
OPINIONS END
SOLUTION:Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 9 = 150 meter
Answer:A #### A |
QUESTION:Two trains are running in opposite directions in the same speed. The length of each train is 120 meter. If they cross each other in 12 seconds, the speed of each train (in km/hr) is
options: A)42 B)36 C)28 D)20 E)24
OPINIONS START
>>>0: #### B
>>>1: #### B
>>>2: #### E
>>>3: #### E
>>>4: #### A
>>>5: #### B
>>>6: #### 6:Relative speed = Total distance/time
= (120+120)/12 = 200/12 = 50/3 m/s
= (50/3)*(18/5) = 60 km/hr
Speed of each train = 60/2 = 30 km/hr
Answer: None of the above
OPINIONS END
SOLUTION:Explanation:
Distance covered = 120+120 = 240 m
Time = 12 s
Let the speed of each train = v. Then relative speed = v+v = 2v
2v = distance/time = 240/12 = 20 m/s
Speed of each train = v = 20/2 = 10 m/s
= 10×36/10 km/hr = 36 km/hr
Answer: Option B #### B |
QUESTION:Eighteen years ago, a father was three times as old as his son. Now the father is only twice as old his son. Then the sum of the present ages of the son and the father is?
options: A)109 B)106 C)104 D)108 E)101
OPINIONS START
>>>0: #### D
>>>1: #### D
>>>2: #### D
>>>3: #### C
>>>4: #### D (108)
>>>5: #### E
>>>6: #### D
OPINIONS END
SOLUTION:Let the present ages of the father and son be 2x and x years respectively.
Then, (2x - 18) = 3(x - 18) => x = 36
Required sum = (2x + x) = 108 years.Answer: D #### D |
QUESTION:A flagpole 18 meters high casts a shadow of length 45 meters. If a building under similar conditions casts a shadow of length 50 meters, what is the height of the building (in meters)?
options: A)16 B)20 C)24 D)28 E)32
OPINIONS START
>>>0: #### B
>>>1: #### B
>>>2: #### C
>>>3: #### C
>>>4: #### C
>>>5: #### B
>>>6: #### B
OPINIONS END
SOLUTION:The height:length ratio will be equal in both cases.
18 / 45 = x / 50
x = 20
The answer is B. #### B |
QUESTION:If n is the product of three consecutive integers, and n is divisible by 6, which of the following is not necessarily a divisor of n ?
options: A)242 B)4 C)6.8 D)5 E)0.
OPINIONS START
>>>0: #### A
>>>1: #### C
>>>2: #### E
>>>3: #### 3:Let the three consecutive integers be x, x+1, x+2.
n = x*(x+1)*(x+2)
n is divisible by 6, so x, x+1, x+2 are all divisible by 2 or 3.
Since x+2 is the largest of the three, it is divisible by 2, so x+2 = 2k, where k is an integer.
x = 2k - 2 and x+1 = 2k - 1
Since x+1 is also divisible by 2, k must be even.
So x = 2(2n - 2) - 2 = 4n - 6 and x+1 = 4n - 5
n = (4n - 6)(4n - 5)(2n)
n is divisible by 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 72, 80, 90, 120, 160, 180, 240, 300, 360, 480, 720, 960, 1200, 1440, 1680, 1920, 2400, 2880, 3600, 4320, 4800, 5760, 7200, 8640, 10080, 12960, 14400, 17280, 20736, 24880, 29856, 34560, 38880, 43744, 48672, 53920, 59520, 65616, 71728, 77840, 83960, 89088, 94224
>>>4: #### A
>>>5: #### A
>>>6: #### D
OPINIONS END
SOLUTION:IF ONE NO. IS 6 THEN OTHER CONSEQUTIVE NO. ARE 4*5*6 =120 , 5*6*7=210 , 6*7*8 =336
NO NUMBER WILL NO BE DIVISOR OF N
E #### E |
QUESTION:The factorial expression 10!/2! is not divisible by which of the following integers?
options: A)3 B)5 C)6 D)7 E)None of these
OPINIONS START
>>>0: #### D
>>>1: #### E
>>>2: #### E
>>>3: #### # E
>>>4: #### E
>>>5: #### 5:10!/2!=10*9*8*7*6*5*4*3*2/2!=10*9*8*7*6*5*4*3*2*2*1/2!=10*9*8*7*6*5*4*3*2*1=10*9*8*7*6*5*4*3=10*9*8*7*6*5*4*3*2*1=10*9*8*7*6*5*4*3*2*1=10*9*8*7*6*5*4*3*2*1=10*9*8*7*6*5*4*3*2*1=10*9*8*7*6*5*4*3*2*1=10*9*8*7*6*5*4*3*2*1=10*9*8*7*6*5*4*3*2*1=10*9*8*7*6*5*4*3*2*1=10*9*8*7*6*5*4*3*2*1=10*9*8*7*6*5*4*3*2*1=10*9*8*7*6*5*4*3*2*1=10*9*8*7*6*5*4*3*2*1=10*9*8*7*6*5*4*3*2*1=10*9*8*7*6*5*4*3*2*1=10*9*8*7*6*5*4*3*2*1=10*9*8*7*6*5*4*3*2*1=10*9*8*7*6*5*4*3*2*1=10*9*8*7*6*5*4*3*2*1=10*9*8*7*6*5*4*3*2*1=10*9*8*7*6*5*4*3*2*1=1
>>>6: #### E
OPINIONS END
SOLUTION:10!/2! => 10 x 9 x 8 x7 x 6 x 5 x 4x3
(A) 3 Can divide 12 or 9
(B) 5 Can divide 10
(C) 6 Can divide 12
(D) 7 can divide 7,21,28
Hence answer will be (E) #### E |
QUESTION:A crate of mangoes contains one bruised mango for every thirty mango in the crate. If three out of every four bruised mango are considerably unsaleable and there are 12 unsaleable mangoes in the crate then how many mango are there in the crate?
options: A)480 B)580 C)680 D)280 E)380
OPINIONS START
>>>0: #### A 480
>>>1: #### 1:Let the total number of mangoes in the crate be x.
Then the number of unsaleable mangoes = 12
The number of unsaleable mangoes = 1/30 * x
12 = 1/30 * x
x = 360
The number of unsaleable mangoes = 1/30 * x = 12
The number of unsaleable mangoes = 3/4 * 12 = 9
The number of unsaleable mangoes = 1/30 * x = 12
x = 360
The number of unsaleable mangoes = 1/30 * x = 12
The number of unsaleable mangoes = 3/4 * 12 = 9
The number of unsaleable mangoes = 1/30 * x = 12
The number of unsaleable mangoes = 3/4 * 12 = 9
The number of unsaleable mangoes = 1/30 * x = 12
The number of unsaleable mangoes = 3/4 * 12 = 9
The number of unsaleable mangoes = 1/30 * x = 12
The number of unsaleable mangoes = 3/4 * 12 = 9
The number of unsaleable mangoes = 1/30 * x = 12
The number of unsaleable mangoes = 3/4 * 12 = 9
The number of unsaleable mangoes = 1/30 * x = 12
The number of unsaleable mangoes = 3/4 * 12 = 9
The number of unsaleable mangoes = 1/30 * x = 12
The number of unsaleable mangoes = 3/4 * 12 = 9
The number of unsaleable mangoes = 1/30 * x = 12
The number of unsaleable mangoes = 3/4 * 12 = 9
The number of unsaleable mangoes = 1/30 * x = 12
The number of unsaleable mangoes = 3/4 * 12 = 9
The number of unsaleable mangoes = 1/30 * x = 12
The number of unsaleable mangoes = 3/4 * 12 = 9
The number of
>>>2: #### A
>>>3: #### C
>>>4: #### A
>>>5: #### A
>>>6: #### A
OPINIONS END
SOLUTION:Let the total no of mangoes in the crate be x
Then the no of bruised mango = 1/30 x
Let the no of unsalable mangoes =3/4 (1/30 x)
1/40 x =12
x=480
Answer is A. #### A |
QUESTION:Abel can complete a work in 10 days, Ben in 12 days and Carla in 15 days. All of them began the work together, but Abel had to leave after 2 days and Ben 5 days before the completion of the work. How long did the work last?
options: A)6 B)7 C)8 D)8 1/9 E)10
OPINIONS START
>>>0: #### D
>>>1: #### C
>>>2: #### E
>>>3: #### C
>>>4: #### D
>>>5: #### D
>>>6: #### E
OPINIONS END
SOLUTION:Abel in the 2 days that he worked completed 1/5 of the job = 4/5 remains
Then if Ben had to leave 5 days before the completion, this means that Carla had to work alone for these 5 days in which she completed 1/3 of the job.
Now together, Ben and Carla completed the job in (1/12 + 1/15)(t) = 7/15
3/20 (t) = 7/15 ---> t = 3 1/9
Therefore, these 3 1/9 days worked plus the 5 days that Carla had to work by herself add to 8 1/9 days
Answer: D #### D |
QUESTION:If the number 653ab is divisible by 90, then (a + b) = ?
options: A)2 B)3 C)4 D)6 E)8
OPINIONS START
>>>0: #### C
>>>1: #### D
>>>2: #### C
>>>3: #### 3:Let's break down the problem:
1. The number 653ab is divisible by 90, which means that the sum of its digits (a + b) must be a multiple of 9.
2. The number 6 + 5 + 3 = 14, which is not a multiple of 9.
3. However, if we add a zero to the number, it becomes 6530ab, and the sum of its digits is 6 + 5 + 3 + 0 = 14, which is not a multiple of 9.
4. But if we add another zero to the number, it becomes 65300ab, and the sum of its digits is 6 + 5 + 3 + 0 + 0 = 14, which is not a multiple of 9.
5. However, if we add another zero to the number, it becomes 653000ab, and the sum of its digits is 6 + 5 + 3 + 0 + 0 + 0 = 14, which is not a multiple of 9.
6. But if we add another zero to the number, it becomes 6530000ab, and the sum of its digits is 6 + 5 + 3 + 0 + 0 + 0 + 0 = 14, which is not a multiple of 9.
7. However, if we add another zero to the number, it becomes 65300000ab, and the sum of its digits is 6 + 5 + 3 + 0 + 0 + 0 + 0 + 0 = 14, which is not a multiple of 9.
8. But if we add another zero to the number, it becomes 653000000ab, and the sum of its digits is 6 + 5 + 3 + 0 + 0 + 0 + 0 + 0 + 0 = 14, which is not a multiple of 9.
9. However, if we add another zero to the number, it becomes 6530000000ab, and the sum of its digits is 6 + 5 +
>>>4: #### 4:If 653ab is divisible by 90, then 653a is divisible by 90 and b is also divisible by 90.
Since 90 is a multiple of 3, 653 is an odd number and a is an even number.
Let a = 2x, b = 2y
653 * 2x * 2y = 90n
Simplifying the above equation, we get
653 * x * y = 90n/2
Since 653 is an odd number, x and y must be integers.
Now, we need to find the value of x and y.
We know that a = 2x, so x = a/2
Similarly, b = 2y, so y = b/2
Substituting the values of x and y in the equation 653 * x * y = 90n/2, we get
653 * (a/2) * (b/2) = 90n/2
Multiplying both sides by 2, we get
1306a * b = 180n
Since a and b are both even, we can write a = 2m and b = 2n
Substituting these values in the above equation, we get
1306 * 4mn = 180n
Simplifying the above equation, we get
1306mn = 9n
Since n cannot be zero, we have
mn = 9/1306
Since m and n are both integers, 9/1306 is not an integer.
Therefore, the given equation has no solution.
Hence, the answer is 'No solution' or 'None of the above'.
>>>5: #### 5:Explanation :
653ab = 90x
653ab = 90x
653ab = 90x
653ab = 90x
653ab = 90x
653ab = 90x
653ab = 90x
653ab = 90x
653ab = 90x
653ab = 90x
653ab = 90x
653ab = 90x
653ab = 90x
653ab = 90x
653ab = 90x
653ab = 90x
653ab = 90x
653ab = 90x
653ab = 90x
653ab = 90x
653ab = 90x
653ab = 90x
653ab = 90x
653ab = 90x
653ab = 90x
653ab = 90x
653ab = 90x
653ab = 90x
653ab = 90x
653ab = 90x
653ab = 90x
653ab = 90x
653ab = 90x
653ab = 90x
653ab = 90x
653ab = 90x
653ab = 90x
653ab = 90x
653ab = 90x
653ab = 90x
653ab = 90x
653ab = 90x
653ab = 90x
653ab = 90x
653ab = 90x
653ab = 90x
653ab = 90x
653ab = 90x
653ab = 90x
653ab = 90x
653ab = 90x
>>>6: #### C
OPINIONS END
SOLUTION:90 = 10 x 9
Clearly, 653ab is divisible by 10, so b = 0
Now, 653a0 is divisible by 9.
So, (6 + 5 + 3 + a + 0) = (14 + a) is divisible by 9. So, a = 4.
Hence, (a + b) = (4 + 0) = 4.
ANSWER:C #### C |
QUESTION:A car covers a distance of 624 km in 3 hours. Find its speed?
options: A)104 kmph B)194 kmph C)208 kmph D)174 kmph E)101 kmph
OPINIONS START
>>>0: #### C
>>>1: #### C
>>>2: #### C
>>>3: #### C
>>>4: #### C
>>>5: #### C
>>>6: #### C
OPINIONS END
SOLUTION:624/3
=208 kmph
Answer:C #### C |
QUESTION:If p/q =4/5, then the value of 1/7 + {(2q - p) / (2q + p)} is ?
options: A)4 / 7 B)34 C)1 D)2 E)3
OPINIONS START
>>>0: #### A
>>>1: #### A
>>>2: #### B
>>>3: #### D
>>>4: #### 4:Explanation:
Given p/q = 4/5
=> p = 4q
Substituting the value of p in the given expression, we get
1/7 + {(2q - 4q) / (2q + 4q)}
=> 1/7 + {(-2q) / (2q + 4q)}
=> 1/7 + {(-2) / (2 + 4/q)}
=> 1/7 + {-2 / (2 + (5/q))}
=> 1/7 + {-2 / (7/5)}
=> 1/7 + {-2 * (5/7)}
=> 1/7 + {-10/7}
=> -1/7
Since the answer is negative, it is not possible to represent it as a fraction in the given options.
Hence, the answer is not provided in the given options.
Therefore, the answer is NOT ONE OF THE GIVEN OPTIONS.
>>>5: #### 5:Solution
1/7 + {(2q - p) / (2q + p)} = 1/7 + {(2q - 4/5) / (2q + 4/5)} = 1/7 + {(10q - 8) / (10q + 8)} = 1/7 + {(10q - 8) / (10q + 8)} × 5/5 = 1/7 + {(10q - 8) / (10q + 8)} × 5/5 = 1/7 + {(10q - 8) / (10q + 8)} × 5/5 = 1/7 + {(10q - 8) / (10q + 8)} × 5/5 = 1/7 + {(10q - 8) / (10q + 8)} × 5/5 = 1/7 + {(10q - 8) / (10q + 8)} × 5/5 = 1/7 + {(10q - 8) / (10q + 8)} × 5/5 = 1/7 + {(10q - 8) / (10q + 8)} × 5/5 = 1/7 + {(10q - 8) / (10q + 8)} × 5/5 = 1/7 + {(10q - 8) / (10q + 8)} × 5/5 = 1/7 + {(10q - 8) / (10q + 8)} × 5/5 = 1/7 + {(10q - 8) / (10q + 8)} × 5/5 = 1/7 + {(10q - 8) / (10q + 8)} × 5/5 = 1/7 + {(10q - 8) / (10q + 8)} × 5/5 = 1/7 + {(10q - 8) / (10q + 8)} × 5/5 = 1/7 + {(10q - 8) / (10q + 8)} ×
>>>6: #### A
OPINIONS END
SOLUTION:Answer
Given Exp. = 4 / 7 + {(2q - p) / (2q + p)}
Dividing numerator as well as denominator by q,
Exp = 1/7 + {2-p/q) / (2 + p/q)}
= 1/7 + {(2 - 4/5) / (2 + 4/5)}
= 1/7 + 6/14
= 1/7 + 3/7
=4/7
Correct Option: A #### A |
QUESTION:The length of a room is 5.5 m and width is 3.75 m. Find the cost of paving the floor by slabs at the rate of Rs. 1200 per sq. metre.
options: A)Rs. 15000 B)Rs. 15550 C)Rs. 24750 D)Rs. 16500 E)None of these
OPINIONS START
>>>0: #### C
>>>1: #### C
>>>2: #### C
>>>3: #### C
>>>4: #### C
>>>5: #### C
>>>6: #### C
OPINIONS END
SOLUTION:Solution
Area of the floor = (5.5 × 3.75) m2 = 20.625 m2
∴ Cost of paving = Rs. (1200 × 20.625) = 24750. Answer C #### C |
QUESTION:City A to city B, Andrew drove for 1hr at 46 mph and for 3 hours at 60 mph. What was the average speed for the whole trip?
options: A)56.5 B)57.5 C)61 D)61.5 E)62.5
OPINIONS START
>>>0: #### A
>>>1: #### A
>>>2: #### A
>>>3: #### A
>>>4: #### A
>>>5: #### B
>>>6: #### A
OPINIONS END
SOLUTION:The total distance is 1×46+3×60=226
And the total time is 4 hours. Hence,
Average Speed=(Total Distance/Total Time)
=226/4=56.5
A #### A |
QUESTION:4,25,49,121,169,289,
options: A)361 B)169 C)189 D)209 E)219
OPINIONS START
>>>0: #### A
>>>1: #### 1:4,25,49,121,169,289
are squares of 2,5,7,11,13,17
Now 17^2 = 289
289+1 = 290
290 is not a perfect square
289+2 = 291
291 is not a perfect square
289+3 = 292
292 is not a perfect square
289+4 = 293
293 is not a perfect square
289+5 = 294
294 is not a perfect square
289+6 = 295
295 is not a perfect square
289+7 = 296
296 is not a perfect square
289+8 = 297
297 is not a perfect square
289+9 = 298
298 is not a perfect square
289+10 = 299
299 is not a perfect square
289+11 = 300
300 is not a perfect square
289+12 = 301
301 is not a perfect square
289+13 = 302
302 is not a perfect square
289+14 = 303
303 is not a perfect square
289+15 = 304
304 is not a perfect square
289+16 = 305
305 is not a perfect square
289+17 = 306
306 is not a perfect square
289+18 = 307
307 is not a perfect square
289+19 = 308
308 is not a perfect square
289+20 = 309
309 is not a perfect square
289+21 = 310
310 is not a perfect square
289+22 = 311
311 is not a perfect square
289+23 = 312
312 is not a perfect square
289+24 = 313
313 is not a perfect square
289+25 = 314
314 is not a perfect square
289+26 = 315
315 is not a perfect square
289+27 = 316
316 is not a perfect square
289+28 = 317
317 is not a perfect square
289+29 = 318
318 is not a perfect square
289+30 = 319
319 is not a perfect square
289+31 = 320
320 is not a perfect square
289+32 = 321
321 is not a perfect square
289+33 = 322
322 is not a perfect square
289+34 = 323
323 is not a perfect
>>>2: #### A
>>>3: #### E
>>>4: #### 4:The given sequence is the squares of consecutive natural numbers starting from 2.
=> 4, 25, 49, 121, 169, 289, ...
=> 2^2, 3^2, 4^2, 5^2, 6^2, 7^2, ...
=> The next number in the sequence is 8^2 = 64.
=> However, the options do not include 64.
=> None of the options is the correct answer.
Answer: None of the above.
>>>5: #### 5:Explanation:
4,25,49,121,169,289,
169,289,361,481,649,841
169,289,361,481,649,841
169,289,361,481,649,841
169,289,361,481,649,841
169,289,361,481,649,841
169,289,361,481,649,841
169,289,361,481,649,841
169,289,361,481,649,841
169,289,361,481,649,841
169,289,361,481,649,841
169,289,361,481,649,841
169,289,361,481,649,841
169,289,361,481,649,841
169,289,361,481,649,841
169,289,361,481,649,841
169,289,361,481,649,841
169,289,361,481,649,841
169,289,361,481,649,841
169,289,361,481,649,841
169,289,361,481,649,841
169,289,3
>>>6: #### A
OPINIONS END
SOLUTION:19^2= 361 because follow sequence of square of the prime numbers
ANSWER:A #### A |
QUESTION:An empty fuel tank to a car was filled with A type of petrol. When the tank was half empty, it was filled with B type of petrol. Again when the tank was half empty, it was filled with A type of petrol. When the tank was half empty again,it was filled with B type of petrol. At this time, what was the percentage of A type of petrol in the tank?
options: A)50% B)40% C)33.5% D)37.5% E)None of these
OPINIONS START
>>>0: #### A
>>>1: #### E
>>>2: #### D
>>>3: #### A
>>>4: #### A
>>>5: #### A
>>>6: #### E
OPINIONS END
SOLUTION:Now, amount of petrol A = A⁄4 + A⁄8 = 3A⁄8
∴ required% = 3A⁄ (8 × A) × 100 = 37.50%
Answer D #### D |
QUESTION:How much water should be added to 13 liters of a 20%-solution of alcohol to reduce the concentration of alcohol in the solution by 75% ?
options: A)25 liters B)27 liters C)30 liters D)32 liters E)35 liters
OPINIONS START
>>>0: #### 39
>>>1: #### 1:Let the amount of water to be added be x liters
So, the amount of alcohol in the solution = 13 * 20/100 = 2.6 liters
So, the amount of alcohol in the new solution = 2.6/4 = 0.65 liters
So, the amount of water in the new solution = 13 + x - 2.6 = 10.4 + x
So, the concentration of alcohol in the new solution = 0.65/ (10.4 + x) * 100
0.65/ (10.4 + x) * 100 = 25/100
0.65/ (10.4 + x) = 1/4
0.65 = (10.4 + x)/4
0.65 * 4 = 10.4 + x
2.6 = 10.4 + x
x = 7.8
So, the amount of water to be added = 7.8 liters
So, the amount of water to be added = 7.8 + 5.6 = 13.4 liters
So, the amount of water to be added = 13.4 + 13.4 = 26.8 liters
So, the amount of water to be added = 26.8 + 0.2 = 27 liters
So, the amount of water to be added = 27 + 0.2 = 27.2 liters
So, the amount of water to be added = 27.2 + 0.2 = 27.4 liters
So, the amount of water to be added = 27.4 + 0.2 = 27.6 liters
So, the amount of water to be added = 27.6 + 0.2 = 27.8 liters
So, the amount of water to be added = 27.8 + 0.2 = 28 liters
So, the amount of water to be added = 28 + 0.2 = 28.2 liters
So, the amount of water to be added = 28.2 + 0.2 = 28.4 liters
So, the amount of water to be added = 28.4 + 0.2 = 28.6 liters
So, the amount of water to be added = 28.6 + 0.2 =
>>>2: #### B
>>>3: #### A
>>>4: #### 4:Let the amount of water be x.
We have,
13 + x = (13/0.8) => x = 13*(1/0.8 - 1) = 13*(5/4 - 1) = 13*(1.25-1) = 13*0.25 = 3.25*13 = 32.65 liters
But the options are not matching with the answer.
So, the question seems to be incorrect.
>>>5: #### 5:Let x liters of water be added to 13 liters of 20% solution of alcohol. Then, the concentration of alcohol in the solution after adding x liters of water = 20% of 13 liters = 2.6 liters.
The concentration of alcohol in the solution after adding x liters of water = 25% of 13 liters = 3.25 liters.
Thus, 2.6 liters of alcohol is reduced to 0.6 liters of alcohol.
Hence, 2 liters of alcohol is reduced to 0.25 liters of alcohol.
Thus, 1 liter of alcohol is reduced to 0.125 liters of alcohol.
Hence, 1 liter of alcohol is reduced to 0.125 liters of alcohol.
Thus, 1 liter of alcohol is reduced to 0.125 liters of alcohol.
Thus, 1 liter of alcohol is reduced to 0.125 liters of alcohol.
Thus, 1 liter of alcohol is reduced to 0.125 liters of alcohol.
Thus, 1 liter of alcohol is reduced to 0.125 liters of alcohol.
Thus, 1 liter of alcohol is reduced to 0.125 liters of alcohol.
Thus, 1 liter of alcohol is reduced to 0.125 liters of alcohol.
Thus, 1 liter of alcohol is reduced to 0.125 liters of alcohol.
Thus, 1 liter of alcohol is reduced to 0.125 liters of alcohol.
Thus, 1 liter of alcohol is reduced to 0.125 liters of alcohol.
Thus, 1 liter of alcohol is reduced to 0.125 liters of alcohol.
Thus, 1 liter of alcohol is reduced to 0.125 liters of alcohol.
Thus, 1 liter of alcohol is reduced to 0.125 liters of alcohol.
Thus, 1 liter of alcohol is reduced to 0.125 liters of alcohol.
Thus, 1 liter of alcohol is reduced to 0.125 liters of alcohol.
Thus, 1 liter of alcohol is reduced to 0.125 liters of alcohol.
Thus, 1 liter of alcohol is reduced to 0.125 liters of alcohol
>>>6: #### None
OPINIONS END
SOLUTION:Let x ltr water to be added
2ltr alcohol to be represented as (20(1-3/4(new soln.=13+x)))
2=5%*(13+x)-------->x=27
Ans B #### B |
QUESTION:If 3log(4*5^2) = x, find x
options: A)5 B)6 C)7 D)8 E)9
OPINIONS START
>>>0: #### B
>>>1: #### B
>>>2: #### B
>>>3: #### B
>>>4: #### 4:We have 3log(4*5^2) = x
= 3[log(4) + log(5^2)]
= 3[log(4) + 2log(5)]
= 3[1 + 2log(5)]
= 3[1 + 2*log(5)]
= 3[1 + 2*log(5)]
= 3[1 + 2*log(5)]
= 3[1 + 2*log(5)]
= 3[1 + 2*log(5)]
= 3[1 + 2*log(5)]
= 3[1 + 2*log(5)]
= 3[1 + 2*log(5)]
= 3[1 + 2*log(5)]
= 3[1 + 2*log(5)]
= 3[1 + 2*log(5)]
= 3[1 + 2*log(5)]
= 3[1 + 2*log(5)]
= 3[1 + 2*log(5)]
= 3[1 + 2*log(5)]
= 3[1 + 2*log(5)]
= 3[1 + 2*log(5)]
= 3[1 + 2*log(5)]
= 3[1 + 2*log(5)]
= 3[1 + 2*log(5)]
= 3[1 + 2*log(5)]
= 3[1 + 2*log(5)]
= 3[1 + 2*log(5)]
= 3[1 + 2*log(5)]
= 3[1 + 2*log(5)]
= 3[1 + 2*log(5)]
= 3[1 + 2*log(5)]
= 3[1 + 2*log(5)]
= 3[1 + 2*log(5)]
= 3[1 + 2*log(5)]
= 3[1 + 2*log(5)]
= 3[1 + 2*log(5)]
= 3[
>>>5: #### 6
>>>6: #### B
##.
OPINIONS END
SOLUTION:3(log2^2*5^2)=x
3log(5*2)^2=x
3*2log(5*2)=x
6log10=x
log10 base 10=1
so
6*1=x
x=6
ANSWER:B #### B |
QUESTION:Applying VBODMAS rule
options: A)31/120 B)31/129 C)31/1276 D)31/122 E)31/111
OPINIONS START
>>>0: #### A
>>>1: #### D
>>>2: #### A
>>>3: #### A
>>>4: #### C
>>>5: #### 5:31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 = 31/120 =
>>>6: #### 6:120/120 - 120/120 + 120/120 - 120/120 + 120/120 = 1
120/120 - 120/120 + 120/120 - 120/120 + 120/120 = 1
120/120 - 120/120 + 120/120 - 120/120 + 120/120 = 1
120/120 - 120/120 + 120/120 - 120/120 + 120/120 = 1
120/120 - 120/120 + 120/120 - 120/120 + 120/120 = 1
120/120 - 120/120 + 120/120 - 120/120 + 120/120 = 1
120/120 - 120/120 + 120/120 - 120/120 + 120/120 = 1
120/120 - 120/120 + 120/120 - 120/120 + 120/120 = 1
120/120 - 120/120 + 120/120 - 120/120 + 120/120 = 1
120/120 - 120/120 + 120/120 - 120/120 + 120/120 = 1
120/120 - 120/120 + 120/120 - 120/120 + 120/1
OPINIONS END
SOLUTION:Answer:A #### A |
QUESTION:In a certain parking lot, 4% of the cars are towed for parking illegally. However 80% of the cars which are parked illegally are not towed. What percentage of cars in the parking lot are parked illegally?
options: A)20% B)25% C)30% D)35% E)40%
OPINIONS START
>>>0: #### A
>>>1: #### E
>>>2: #### A
>>>3: #### A
>>>4: #### A
>>>5: #### 5:4% of cars are towed. 80% of cars which are parked illegally are not towed. So 20% of cars which are parked illegally are towed. So 20% of cars which are parked illegally are towed. So 80% of cars which are parked illegally are not towed. So 20% of cars which are parked illegally are towed. So 80% of cars which are parked illegally are not towed. So 20% of cars which are parked illegally are towed. So 80% of cars which are parked illegally are not towed. So 20% of cars which are parked illegally are towed. So 80% of cars which are parked illegally are not towed. So 20% of cars which are parked illegally are towed. So 80% of cars which are parked illegally are not towed. So 20% of cars which are parked illegally are towed. So 80% of cars which are parked illegally are not towed. So 20% of cars which are parked illegally are towed. So 80% of cars which are parked illegally are not towed. So 20% of cars which are parked illegally are towed. So 80% of cars which are parked illegally are not towed. So 20% of cars which are parked illegally are towed. So 80% of cars which are parked illegally are not towed. So 20% of cars which are parked illegally are towed. So 80% of cars which are parked illegally are not towed. So 20% of cars which are parked illegally are towed. So 80% of cars which are parked illegally are not towed. So 20% of cars which are parked illegally are towed. So 80% of cars which are parked illegally are not towed. So 20% of cars which are parked illegally are towed. So 80% of cars which are parked illegally are not towed. So 20% of cars which are parked illegally are towed. So 80% of cars which are parked illegally are not towed. So 20% of cars which are parked illegally are towed. So 80% of cars which are parked illegally are not towed. So 20% of cars which
>>>6: #### A
OPINIONS END
SOLUTION:Let x be the number of cars and let y be the number of cars parked illegally.
4%*x = 20%*y
y/x = 1/5 = 20%
The answer is A. #### A |
QUESTION:Farm Tax is levied on the 45% of the cultivated Land. The tax department collected total $ 3840 through the farm Tax from the village of Mr. willam. Mr. willam paid only $ 480 as farm tax. The percentage of total land of Mr. willam over the total taxable land of the village is :
options: A)15% B)25% C)15.125% D)27.78% E)none
OPINIONS START
>>>0: #### E
>>>1: #### D
>>>2: #### D
>>>3: #### C
>>>4: #### A
>>>5: #### C
>>>6: #### E
OPINIONS END
SOLUTION:Only trick n this question is to ignore 45% information as farm tax is levied uniformly in the village and that includes Mr William's land.
What percentage of tax Mr William paid ? This will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village. That leads to (480/3840)x100 =12.5%in percentage terms.
But the question asks ratio between his total land to total cultivated land. Hence the answer is 12.5%x (100/45) = 27.78% and the answer is not there in the options.
The correct answer is (D). #### D |
QUESTION:Amol was asked to calculate Arithmetic mean of 10 positive integers, each of which had 2 digits. By mistake, he interchanged the 2 digits, say a and b,in one of these 10 integers. As a result, his answer for the Arithmetic mean was 1.8 more than what it should have been. Then b - a equals
options: A)1 B)2 C)3 D)4 E)None of these
OPINIONS START
>>>0: #### A
>>>1: #### 1:Let the 10 numbers be a11, a12, a13, a14, a15, a16, a17, a18, a19, a10
Amol's mean = (a11 + a12 + a13 + a14 + a15 + a16 + a17 + a18 + a19 + a10)/10
= (10a1 + 10a2 + a3 + a4 + a5 + a6 + a7 + a8 + a9 + a10)/10
= (10a1 + 10a2 + 10a3 + 10a4 + 10a5 + 10a6 + 10a7 + 10a8 + 10a9 + 10a10)/10 + 1.8
= (10a1 + 10a2 + 10a3 + 10a4 + 10a5 + 10a6 + 10a7 + 10a8 + 10a9 + 10a10)/10 + 18/10
= (10a1 + 10a2 + 10a3 + 10a4 + 10a5 + 10a6 + 10a7 + 10a8 + 10a9 + 10a10)/10 + 9(2)/10
= (10a1 + 10a2 + 10a3 + 10a4 + 10a5 + 10a6 + 10a7 + 10a8 + 10a9 + 10a10)/10 + 9(a1 + a2 + a3 + a4 + a5 + a6 + a7 + a8 + a9 + a10)/10
= (10a1 + 10a2 + 10a3 + 10a4 + 10a5 + 10a6 + 10a7 + 10a8 + 10a9 + 10a10 + 9a1 + 9a2 + 9a3 + 9a4 + 9a5 + 9a6 + 9a7 + 9a8 + 9a9 + 9a10)/10
= (19a1 + 19a2 + 19a3 + 19a4 + 19a5 + 19a6 + 19a7
>>>2: #### D
>>>3: #### E
>>>4: #### E
>>>5: #### A
>>>6: #### B
OPINIONS END
SOLUTION:Explanation :
Arithmetic mean is more by 1.8 means sum is more by 18.
So, ba – ab = 18.
b > a because sum has gone up, e.g. 31 – 13 = 18.
Hence, b – a = 2.
Answer : B #### B |
QUESTION:Suresh started a business with Rs.20,000. Kiran joined him after 4 months with Rs.30,000. After 2 months, Suresh withdrew Rs.5,000 of his capital and 2 more months later, Kiran brought in Rs.20,000 more. What should be the ratio in which they should share their profits at the end of the year?
options: A)32:21 B)22:21 C)21:32 D)31:21 E)32:28
OPINIONS START
>>>0: #### 3:8
>>>1: #### A
>>>2: #### D
>>>3: #### A
>>>4: #### E
>>>5: #### 5:Explanation: Suresh's capital = Rs.20,000
Kiran's capital = Rs.30,000
Suresh's capital after 4 months = Rs.20,000
Kiran's capital after 4 months = Rs.30,000
Suresh's capital after 6 months = Rs.15,000
Kiran's capital after 6 months = Rs.30,000
Suresh's capital after 8 months = Rs.15,000
Kiran's capital after 8 months = Rs.50,000
Suresh's capital after 10 months = Rs.15,000
Kiran's capital after 10 months = Rs.50,000
Suresh's capital after 12 months = Rs.15,000
Kiran's capital after 12 months = Rs.50,000
Suresh's capital after 12 months = Rs.15,000
Kiran's capital after 12 months = Rs.50,000
Suresh's capital after 12 months = Rs.15,000
Kiran's capital after 12 months = Rs.50,000
Suresh's capital after 12 months = Rs.15,000
Kiran's capital after 12 months = Rs.50,000
Suresh's capital after 12 months = Rs.15,000
Kiran's capital after 12 months = Rs.50,000
Suresh's capital after 12 months = Rs.15,000
Kiran's capital after 12 months = Rs.50,000
Suresh's capital after 12 months = Rs.15,000
Kiran's capital after 12 months = Rs.50,000
Suresh's capital after 12 months = Rs.15,000
Kiran's capital after 12 months = Rs.50,000
Suresh's capital after 12 months = Rs.15,00
>>>6: #### C
OPINIONS END
SOLUTION:Here capital is not the same.
Suresh invest 20000 for initial 6 months and 15000 for the next 6 months.
Hence his term of ratio
=( 20000*6 + 15000*6)
Kiran invest Rs.30000 for 4 months and Rs.50000 for next 4 months.
Hence his term of ration
= (30000*4 : 50000*4)
Suresh : Kiran = ( 20000*6 + 15000*6) : (30000*4 : 50000*4)
= (20*6 + 15*6) : (30*4 + 50*4)
= (20*3 + 15*3) : (30*2 : 50*2)
= 105:160
= 21:32
Answer is C #### C |
QUESTION:The 8 spokes of a custom circular bicycle wheel radiate from the central axle of the wheel and are arranged such that the sectors formed by adjacent spokes all have different central angles, which constitute an arithmetic series of numbers (that is, the difference between any angle and the next largest angle is constant). If the largest sector has a central angle of 87°, what fraction of the wheel’s area is represented by the smallest sector?
options: A)1/120 B)1/100 C)1/80 D)1/60 E)1/40
OPINIONS START
>>>0: #### 0:Here's how to solve the problem:
**1. Understand the Arithmetic Series:**
* The central angles of the sectors form an arithmetic series.
* This means the difference between each consecutive angle is constant.
**2. Find the Common Difference:**
* Let the common difference be 'd'.
* The smallest sector has a central angle of 87° - 7d.
**3. Total Central Angles:**
* The sum of all central angles in a circle is 360°.
* Therefore, 87° + 87° - 7d + 87° - 7d + ... (8 terms) = 360°
**4. Simplify and Solve for 'd':**
* 696° - 56d = 360°
* -56d = -336°
* d = 6°
**5. Calculate the Smallest Sector's Angle:**
* Smallest sector angle = 87° - 7d = 87° - 7(6°) = 87° - 42° = 45°
**6. Calculate the Fractions of the Wheel's Area:**
* The area of a sector is proportional to its central angle.
* Fraction of area represented by the smallest sector = (45°/360°) = 1/8
**Answer: None of the provided options are correct. The fraction of the wheel's area represented by the smallest sector is 1/8.**
>>>1: #### A
>>>2: #### 2:Let the central angle of the smallest sector be x.
The central angle of the next sector is x + d, where d is the constant difference.
The central angle of the next sector is x + 2d, and so on.
The central angle of the largest sector is x + 7d.
We know that x + 7d = 87°.
x = 87° - 7d.
The area of the smallest sector is (x/360) * πr^2, where r is the radius of the wheel.
The area of the largest sector is (87°/360) * πr^2.
The area of the smallest sector is (x/360) * πr^2 = [(87° - 7d)/360] * πr^2.
The area of the smallest sector is (1/360) * πr^2 * (87° - 7d).
The area of the smallest sector is (1/360) * πr^2 * (87° - 7d) = (1/120) * πr^2.
The area of the smallest sector is (1/120) * πr^2.
The area of the smallest sector is (1/120) * πr^2.
The area of the smallest sector is (1/120) * πr^2.
The area of the smallest sector is (1/120) * πr^2.
The area of the smallest sector is (1/120) * πr^2.
The area of the smallest sector is (1/120) * πr^2.
The area of the smallest sector is (1/120) * πr^2.
The area of the smallest sector is (1/120) * πr^2.
The area of the smallest sector is (1/120) * πr^2.
The area of the smallest sector is (1/120) * πr^2.
The area of the smallest sector is (1/120) * πr^2.
The area of the smallest sector is (1/120) * πr^2.
The area of the smallest sector is (1/120) * πr^2.
The area of the smallest sector is (1/120) * πr^2.
The area of the smallest sector is (1/120) * πr^2.
The area of the smallest sector is (1/120) *
>>>3: #### 3:Let the common difference between the central angles of the sectors be x.
Since the largest sector has a central angle of 87°, the smallest sector will have a central angle of 87° - 8(x).
The area of a sector of a circle is given by the formula:
Area = (1/2) * r^2 * central angle
where r is the radius of the circle.
Since all the sectors have the same radius, the ratio of the areas of the sectors is equal to the ratio of their central angles.
So, the area of the smallest sector is:
Area of smallest sector = (1/2) * r^2 * (87° - 8x) / 360°
The area of the entire wheel is:
Area of entire wheel = (1/2) * r^2 * 360°
So, the fraction of the wheel’s area represented by the smallest sector is:
Fraction = (Area of smallest sector) / (Area of entire wheel)
= [(1/2) * r^2 * (87° - 8x)] / [(1/2) * r^2 * 360°]
= (87 - 8x) / 360
Since the central angles of the sectors form an arithmetic series, we can write:
87° - 8x = 8(a + (n-1)d)
where a is the first term, d is the common difference, and n is the number of terms.
Since the largest sector has a central angle of 87°, we have:
87° = 8a
So, a = 87° / 8 = 10.875°
Since the smallest sector is the 8th sector, we have:
87° - 8x = 8(10.875 + (8-1)d)
Solving this equation for x, we get:
x = 1.25°
So, the area of the smallest sector is:
Area of smallest sector = (1/2) * r^2 * (87° - 8x) / 3
>>>4: #### 4:Let the common difference between the central angles of adjacent sectors be x.
Since the largest sector has a central angle of 87°, the smallest sector will have a central angle of 87° - n*x, where n is the number of sectors between the largest sector and the smallest sector.
The total angle covered by the wheel is 360°.
Therefore, 360° = 87° + (n-1)*x + x + central angle of smallest sector
Solving for the central angle of the smallest sector, we get:
central angle of smallest sector = 360° - 87° - n*x
Let's find the value of n for which the central angle of the smallest sector is minimum.
Since the central angles of adjacent sectors form an arithmetic series, the central angle of the second smallest sector is 87° + x.
The central angle of the third smallest sector is 87° + 2x, and so on.
The central angle of the (n-1)th smallest sector is 87° + (n-1)x.
Since the central angles of all sectors are different, the central angle of the smallest sector is less than the central angle of the second smallest sector, which is less than the central angle of the third smallest sector, and so on.
Therefore, the central angle of the smallest sector is less than the central angle of the second smallest sector, which is less than the central angle of the third smallest sector, and so on.
Thus, the central angle of the smallest sector is the smallest number in the arithmetic series of central angles.
To find the minimum value of the central angle of the smallest sector, we need to find the smallest value of n for which the central angle of the smallest sector is less than 87°.
Since the central angle of the smallest sector is given by:
central angle of smallest sector = 360° - 87° - n*x
We want this angle to be less than 87°.
Therefore, we have:
360° - 87° - n*x < 87°
Simplifying, we get:
n*x < 273°
Since x is the difference between the central angles of adjacent sectors, x must be a positive number
>>>5: #### C
>>>6: #### None of the above
OPINIONS END
SOLUTION:The largest angle is 87.
Let d be the difference between any two angles in the progression.
The sum of all the angles will be:
87 + (87-d) + (87-2d) + ... + (87-7d) = 696 - 28d
The sum of all the central angles in a circle = 360
696 - 28d = 360
d = 336/28 = 12
The smallest sector is (87-7d) = 87-7*12 = 3
3/360 = 1/120
The answer is A. #### A |
QUESTION:The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 5 minutes, then the area of the park (in sq. m) is:
options: A)153601 B)153600 C)153602 D)60000 E)153604
OPINIONS START
>>>0: #### D
>>>1: #### A
>>>2: #### D
>>>3: #### A
>>>4: #### C
>>>5: #### D
>>>6: #### D
OPINIONS END
SOLUTION:Perimeter = Distance covered in 5 min. =(12000/60) x 5m = 1000 m.
Let length = 3x metres and breadth = 2x metres.
Then, 2(3x + 2x) = 1000 or x = 100.
Length = 300 m and Breadth = 200 m.
Area = (300 x 200) m2 = 60000 m2.
Answer: D #### D |
QUESTION:The average of 35 students in a class is 17 years. The average age of 25 students is 15. What is the average age of remaining 10 students?
options: A)26 years B)27 years C)28 years D)29 years E)30 years
OPINIONS START
>>>0: #### 22
>>>1: ####
>>>2: ####
>>>3: #### A
>>>4: #### C
>>>5: #### A
>>>6: #### C
OPINIONS END
SOLUTION:Sum of the ages of 14 students
= (17 * 35) - (15 * 21) = 595 - 315 = 280
Required average = (280/10) = 28 years.
Answer:C #### C |
QUESTION:If a and b are positive integers such that a/b = 3.98, which of the following must be a divisor of a?
options: A)67 B)197 C)91 D)199 E)42
OPINIONS START
>>>0: #### 0:Here's how to solve this problem:
* **Understanding the
>>>1: #### D
>>>2: #### 2:We can write a/b = 3.98 as a/b = 398/100
Now, a/b = 398/100 = 3.98
Now, 398 = 3 × 132 + 2
So, a = 3 × 132 + 2 = 398
Now, 398 = 2 × 199 + 0
So, a = 2 × 199 = 398
Now, 398 = 1 × 398 + 0
So, a = 1 × 398 = 398
Now, 398 = 67 × 6 + 2
So, a = 67 × 6 + 2 = 398
Now, 398 = 197 × 2 + 0
So, a = 197 × 2 = 398
Now, 398 = 91 × 4 + 2
So, a = 91 × 4 + 2 = 398
Now, 398 = 42 × 9 + 8
So, a = 42 × 9 + 8 = 398
Now, 398 = 199 × 2 + 0
So, a = 199 × 2 = 398
Now, 398 = 67 × 6 + 2
So, a = 67 × 6 + 2 = 398
Now, 398 = 197 × 2 + 0
So, a = 197 × 2 = 398
Now, 398 = 91 × 4 + 2
So, a = 91 × 4 + 2 = 398
Now, 398 = 42 × 9 + 8
So, a = 42 × 9 + 8 = 398
Now, 398 = 199 × 2 + 0
So, a = 199 × 2 = 398
Now, 398 = 67 × 6 + 2
So, a = 67 × 6 + 2 = 398
Now, 398 = 197 × 2 + 0
So, a = 197 × 2 = 398
Now, 398 = 91 × 4 + 2
So, a = 91 × 4 + 2 = 398
Now, 398 = 42 × 9 + 8
So, a =
>>>3: #### A
>>>4: #### None of these
>>>5: #### 5:3.98 = 3 + 0.98
0.98 = 0.98 × 100 = 98/100
a/b = 3 + 98/100
a/b = 300 + 98/100
a/b = 398/100
a/b = 398/100 × 100/100 = 398/100 × 1/100 = 398/100 × 100/100 = 398/100 × 100/100 = 398/100 × 100/100 = 398/100 × 100/100 = 398/100 × 100/100 = 398/100 × 100/100 = 398/100 × 100/100 = 398/100 × 100/100 = 398/100 × 100/100 = 398/100 × 100/100 = 398/100 × 100/100 = 398/100 × 100/100 = 398/100 × 100/100 = 398/100 × 100/100 = 398/100 × 100/100 = 398/100 × 100/100 = 398/100 × 100/100 = 398/100 × 100/100 = 398/100 × 100/100 = 398/100 × 100/100 = 398/100 × 100/100 = 398/100 × 100/10
>>>6: #### D
OPINIONS END
SOLUTION:1) A and B are positive INTEGERS
2) A/B = 3.98
A = 398
B = 100
398/100 = 3.98
These values are NOT the smallest possible values though (since they're both even, we can divide both by 2)...
A = 199
B = 50
199/50 = 2.86
There is no other way to reduce this fraction, so A must be a multiple of 199 and B must be an equivalent multiple of 50. At this point though, the value of B is irrelevant to the question. We're asked for what MUST divide into A....
Since A is a multiple of 199, we have to 'factor-down' 199. This gives us only (199), excluding 1 itself. So this number MUST be a factor of A. You'll find the match in the answer choices.
Answer: D #### D |
QUESTION:A distributor sells a product through an online store, which take a commission of 20% of the price set by the distributor. The distributor obtains the product from a producer at the price of $18 per item. What is the price that the buyer observers online if the distributor wants to maintain a 20% profit on the cost of the item?
options: A)$25 B)$26 C)$27 D)$28 E)$29
OPINIONS START
>>>0: #### A
>>>1: #### C
>>>2: #### B
>>>3: #### E
>>>4: #### B
>>>5: #### 5:Let the price of the product be x.
The distributor's profit = 20% of x = 0.2x
The price of the product = 18 + 0.2x
The price of the product = 18 + 0.2x
The price of the product = 18 + 0.2x
The price of the product = 18 + 0.2x
The price of the product = 18 + 0.2x
The price of the product = 18 + 0.2x
The price of the product = 18 + 0.2x
The price of the product = 18 + 0.2x
The price of the product = 18 + 0.2x
The price of the product = 18 + 0.2x
The price of the product = 18 + 0.2x
The price of the product = 18 + 0.2x
The price of the product = 18 + 0.2x
The price of the product = 18 + 0.2x
The price of the product = 18 + 0.2x
The price of the product = 18 + 0.2x
The price of the product = 18 + 0.2x
The price of the product = 18 + 0.2x
The price of the product = 18 + 0.2x
The price of the product = 18 + 0.2x
The price of the product = 18 + 0.2x
The price of the product = 18 + 0.2x
The price of the product = 18 + 0.2x
The price of the product = 18 + 0.2x
The price of the product = 18 + 0.2x
The price of the product = 18 + 0.2x
The price of the product = 18 + 0.2x
The price of the product = 18 + 0.2x
The price of the product = 18 + 0.2x
The price of the product = 18 + 0.2x
The price of the product
>>>6: #### C
OPINIONS END
SOLUTION:Let x be the price that buyers see online.
The distributor wants to receive 1.2(original price) which should be 80% of x.
1.2(18) = 0.8x
x = 1.2(18) / 0.8 = 1.5(18) = $27
The answer is C. #### C |
QUESTION:A can do a particular work in 6 days . B can do the same work in 8 days. A and B signed to do it for Rs. 3200. They completed the work in 3 days with the help of C. How much is to be paid to C?
options: A)Rs. 380 B)Rs. 600 C)Rs. 420 D)Rs. 400 E)Rs. 480
OPINIONS START
>>>0: ####
>>>1: #### D
>>>2: #### D
>>>3: #### D
>>>4: #### C
>>>5: #### 5:Explanation:
A can do the work in 6 days = 1/6
B can do the work in 8 days = 1/8
A and B together can do the work in 6 x 8 = 48 days = 1/48
A and B together can do the work in 3 days = 1/16
A and B together can do the work in 1 day = 16/48
A and B together can do the work in 1 day = 1/3
A and B together can do the work in 1 day = 1/3
C can do the work in 3 days = 1/3
C can do the work in 1 day = 3/3 = 1
C can do the work in 1 day = 1
C can do the work in 1 day = 1
C can do the work in 1 day = 1
C can do the work in 1 day = 1
C can do the work in 1 day = 1
C can do the work in 1 day = 1
C can do the work in 1 day = 1
C can do the work in 1 day = 1
C can do the work in 1 day = 1
C can do the work in 1 day = 1
C can do the work in 1 day = 1
C can do the work in 1 day = 1
C can do the work in 1 day = 1
C can do the work in 1 day = 1
C can do the work in 1 day = 1
C can do the work in 1 day = 1
C can do the work in 1 day = 1
C can do the work in 1 day = 1
C can do the work in 1 day = 1
C can do the work in 1 day = 1
C can do the work in 1 day = 1
C can do the work in 1 day = 1
C can do the work in 1 day = 1
C can do the work in 1 day = 1
C can do the work in 1 day = 1
C can do the work in 1 day = 1
C can do the work in
>>>6: #### D
OPINIONS END
SOLUTION:Explanation :
Amount of work A can do in 1 day = 1/6
Amount of work B can do in 1 day = 1/8
Amount of work A + B can do in 1 day = 1/6 + 1/8 = 7/24
Amount of work A + B + C can do = 1/3
Amount of work C can do in 1 day = 1/3 - 7/24 = 1/24
work A can do in 1 day: work B can do in 1 day: work C can do in 1 day
= 1/6 : 1/8 : 1/24 = 4 : 3 : 1
Amount to be paid to C = 3200 × (1/8) = 400
Answer : Option D #### D |
QUESTION:John and Jacob set out together on bicycle traveling at 12 and 9 miles per hour, respectively. After 40 minutes, John stops to fix a flat tire. If it takes John one hour to fix the flat tire and Jacob continues to ride during this time, how many hours will it take John to catch up to Jacob assuming he resumes his ride at 12 miles per hour? (consider John's deceleration/acceleration before/after the flat to be negligible)
options: A)3 B)2 1/3 C)3 1/2 D)4 E)4 1/2
OPINIONS START
>>>0: #### A
>>>1: #### 1:Jacob travels 9 miles in 40 minutes. So he travels 9*40/60 = 6 miles in 40 minutes. So Jacob is 6 miles ahead of John. Jacob travels 9 miles in 1 hour. So Jacob will be 9 miles ahead of John in 1 hour. So Jacob will be 15 miles ahead of John. Jacob travels 9 miles in 1 hour. So Jacob will be 9 miles ahead of John in 1 hour. So Jacob will be 9 miles ahead of John in 1 hour. So Jacob will be 9 miles ahead of John in 1 hour. So Jacob will be 9 miles ahead of John in 1 hour. So Jacob will be 9 miles ahead of John in 1 hour. So Jacob will be 9 miles ahead of John in 1 hour. So Jacob will be 9 miles ahead of John in 1 hour. So Jacob will be 9 miles ahead of John in 1 hour. So Jacob will be 9 miles ahead of John in 1 hour. So Jacob will be 9 miles ahead of John in 1 hour. So Jacob will be 9 miles ahead of John in 1 hour. So Jacob will be 9 miles ahead of John in 1 hour. So Jacob will be 9 miles ahead of John in 1 hour. So Jacob will be 9 miles ahead of John in 1 hour. So Jacob will be 9 miles ahead of John in 1 hour. So Jacob will be 9 miles ahead of John in 1 hour. So Jacob will be 9 miles ahead of John in 1 hour. So Jacob will be 9 miles ahead of John in 1 hour. So Jacob will be 9 miles ahead of John in 1 hour. So Jacob will be 9 miles ahead of John in 1 hour. So Jacob will be 9 miles ahead of John in 1 hour. So Jacob will be 9 miles ahead of John in 1 hour. So Jacob will be 9 miles ahead of John in 1 hour. So Jacob will be 9 miles ahead of John in 1 hour. So Jacob will be 9 miles ahead of John in 1 hour. So Jacob will be 9 miles ahead of John in 1 hour. So Jacob will be 9 miles ahead of John in 1 hour. So Jacob will be 9 miles ahead of John in 1 hour. So Jacob will be 9 miles ahead
>>>2: #### B
>>>3: #### C
>>>4: #### C
>>>5: #### 5:Explanation:
Let John and Jacob cover x miles in 40 minutes.
Then, John covers 12x/60 miles in 40 minutes.
Jacob covers 9x/60 miles in 40 minutes.
So, John covers 12x/60 miles in 1 hour.
Jacob covers 9x/60 miles in 1 hour.
So, John covers 12x/60 miles in 1 hour.
Jacob covers 9x/60 miles in 1 hour.
So, John covers 12x/60 miles in 1 hour.
Jacob covers 9x/60 miles in 1 hour.
So, John covers 12x/60 miles in 1 hour.
Jacob covers 9x/60 miles in 1 hour.
So, John covers 12x/60 miles in 1 hour.
Jacob covers 9x/60 miles in 1 hour.
So, John covers 12x/60 miles in 1 hour.
Jacob covers 9x/60 miles in 1 hour.
So, John covers 12x/60 miles in 1 hour.
Jacob covers 9x/60 miles in 1 hour.
So, John covers 12x/60 miles in 1 hour.
Jacob covers 9x/60 miles in 1 hour.
So, John covers 12x/60 miles in 1 hour.
Jacob covers 9x/60 miles in 1 hour.
So, John covers 12x/60 miles in 1 hour.
Jacob covers 9x/60 miles in 1 hour.
So, John covers 12x/60 miles in 1 hour.
Jacob covers 9x/60 miles in 1 hour.
So, John covers 12x/60 miles in 1 hour.
Jacob covers 9x/60 miles in 1 hour.
So, John covers 12x/60 miles in 1 hour.
Jacob covers 9x/60 miles in 1 hour.
So, John covers 12x/60 miles in 1 hour.
Jacob covers 9x/60 miles in 1 hour.
So, John covers 12x/60 miles in 1 hour.
Jacob covers 9x/60 miles in 1
>>>6: #### B
###Instaphoresis:A man has a beehive that produces honey. He sells the honey in jars. Each jar contains 250 grams of honey. The man sells the jars for $10 each. He has a total of 1000 jars of honey. How much money will the man make if he sells all the jars of honey?
options: A) $10,000 B) $15,000 C) $20,000 D) $25,000 E) $30,000 ###
OPINIONS END
SOLUTION:John's speed - 12 miles/hr
Jacob's speed - 9 miles/hr
After 40min (i.e 2/3hr), distance covered by John = 12x2/3 = 8 miles.
Jacob continues to ride for a total of 1hour and 40min (until John's bike is repaired). Distance covered in 1 hour 40min (i.e 5/3hr) = 9x5/3 = 15 miles.
Now, when John starts riding back, the distance between them is 7 miles. Jacob and John are moving in the same direction.For John to catch Jacob, the effective relative speed will be 12-9 = 3 miles/hr.
Thus, to cover 7 miles at 3 miles/hr, John will take 7/3 = 2 1/3 hours
Answer B #### B |
QUESTION:A young girl counted in the following way on the fingers of her left hand. She started collang the thumb 1, the index finger 2, the middle finger 3, the ring finger 4, the little finger 5, then reversed direction calling the ring finger 6, the the middle finger 7, the index finger 8, the thumb 9 then back to the index finger for 10, the middel finger for 11, and so on. She counted up to 1996. She ended on her
options: A)a) thumb B)b) the index finger C)c) the middle finger D)d) the ring finger E)e) the little finger
OPINIONS START
>>>0: #### D
>>>1: #### 1:1996 = 2 x 999 = 2 x (999 = 999 + 999)
= 2 x (999 = 999 + 999)
= 2 x (999 = 999 + 999)
= 2 x (999 = 999 + 999)
= 2 x (999 = 999 + 999)
= 2 x (999 = 999 + 999)
= 2 x (999 = 999 + 999)
= 2 x (999 = 999 + 999)
= 2 x (999 = 999 + 999)
= 2 x (999 = 999 + 999)
= 2 x (999 = 999 + 999)
= 2 x (999 = 999 + 999)
= 2 x (999 = 999 + 999)
= 2 x (999 = 999 + 999)
= 2 x (999 = 999 + 999)
= 2 x (999 = 999 + 999)
= 2 x (999 = 999 + 999)
= 2 x (999 = 999 + 999)
= 2 x (999 = 999 + 999)
= 2 x (999 = 999 + 999)
= 2 x (999 = 999 + 999)
= 2 x (999 = 999 + 999)
= 2 x (999 = 999 + 999)
= 2 x (999 = 999 + 999)
= 2 x (999 = 999 + 999)
= 2 x (999 = 999 + 999)
= 2 x (999 = 999 + 999)
= 2 x (999 = 999 + 999)
= 2 x (999 = 999 + 999)
= 2 x (999 = 999 + 999)
= 2 x (999 = 999 + 999)
= 2 x (999 = 999 + 999)
= 2 x (999 = 999 + 999)
= 2 x (999 = 999 + 999)
= 2 x (999 = 999 + 999)
= 2 x (999 = 999 + 999)
= 2 x (999 = 999 + 999)
= 2 x (999 = 999 + 999)
= 2 x (999 = 999
>>>2: #### A
>>>3: #### A
>>>4: #### C
>>>5: #### E
>>>6: #### B
OPINIONS END
SOLUTION:Notice the pattern. The thumb lansd up at numbers 1,9,17,25,33,... so every 8th number
By this patter the thumb is also at number 1993 (multiple of 8 + 1)
Hence 1996 has to be the ring finger
Answer is (D) #### D |
QUESTION:A shopkeeper buys mangoes at the rate of 6 a rupee and sells them at 4 a rupee. Find his net profit or loss percent?
options: A)33 1/8 % B)33 7/3 % C)50 % D)33 5/8 % E)34 1/3 %
OPINIONS START
>>>0: #### C
>>>1: #### D
>>>2: #### E
>>>3: #### E
>>>4: #### E
>>>5: #### 5:Solution
Let the number of mangoes bought be x.
Then, the cost price = 6x
Let the number of mangoes sold be y.
Then, the selling price = 4y
Profit = 4y - 6x
Profit % = (4y - 6x)/6x × 100
= 2y - 3x/6x × 100
= 2y/6x × 100 - 3x/6x × 100
= 2y/6x × 100 - 3x/6x × 100
= 2y/6x × 100 - 3x/6x × 100
= 2y/6x × 100 - 3x/6x × 100
= 2y/6x × 100 - 3x/6x × 100
= 2y/6x × 100 - 3x/6x × 100
= 2y/6x × 100 - 3x/6x × 100
= 2y/6x × 100 - 3x/6x × 100
= 2y/6x × 100 - 3x/6x × 100
= 2y/6x × 100 - 3x/6x × 100
= 2y/6x × 100 - 3x/6x × 100
= 2y/6x × 100 - 3x/6x × 100
= 2y/6x × 100 - 3x/6x × 100
= 2y/6x × 100 - 3x/6x × 100
= 2y/6x × 100 - 3x/6x × 100
= 2y/6x × 100 - 3x/6x × 100
= 2y/6x × 100 - 3x/6x × 1
>>>6: #### C
OPINIONS END
SOLUTION:The total number of mangoes bought by the shopkeeper be 24.
If he buys 6 a rupee, his CP = 4
He selling at 4 a rupee, his SP = 6
Profit = SP - CP = 6 - 4 = 2
Profit Percent = 2/4 * 100 = 50 %
Answer: C #### C |
QUESTION:12 welders work at a constant rate they complete an order in 3 days. If after the first day, 9 welders start to work on the other project, how many more days the remaining welders will need to complete the rest of the order?
options: A)5 B)2 C)8 D)4 E)6
OPINIONS START
>>>0: #### C
>>>1: #### 1:12 welders complete the order in 3 days
12 welders complete 1/3 of the order in 1 day
9 welders complete 1/3 of the order in 3 days
9 welders complete 1/3 of the order in 1 day
3 welders complete 1/3 of the order in 1 day
3 welders complete the order in 3 days
3 welders complete 2/3 of the order in 2 days
3 welders complete 1/3 of the order in 1 day
3 welders complete the order in 3 days
3 welders complete 2/3 of the order in 2 days
3 welders complete 1/3 of the order in 1 day
3 welders complete the order in 3 days
3 welders complete 2/3 of the order in 2 days
3 welders complete 1/3 of the order in 1 day
3 welders complete the order in 3 days
3 welders complete 2/3 of the order in 2 days
3 welders complete 1/3 of the order in 1 day
3 welders complete the order in 3 days
3 welders complete 2/3 of the order in 2 days
3 welders complete 1/3 of the order in 1 day
3 welders complete the order in 3 days
3 welders complete 2/3 of the order in 2 days
3 welders complete 1/3 of the order in 1 day
3 welders complete the order in 3 days
3 welders complete 2/3 of the order in 2 days
3 welders complete 1/3 of the order in 1 day
3 welders complete the order in 3 days
3 welders complete 2/3 of the order in 2 days
3 welders complete 1/3 of the order in 1 day
3 welders complete the order in 3 days
3 welders complete 2/3 of the order in 2 days
3 welders complete 1/3 of the order in 1 day
3 welders complete the order in 3 days
3 welders complete 2/3 of the order in 2 days
3 welders complete 1/3 of the order in 1 day
3 welders complete the order
>>>2: #### D
>>>3: #### B
>>>4: #### C
>>>5: #### 5:Let the number of welders be x. Then, 12x welders complete the order in 3 days. So, 1x welders complete the order in 3/12 days. So, 1x welders complete the order in 1 day. So, 9x welders complete the order in 1 day. So, 3x welders complete the order in 1 day. So, 3x welders complete the order in 3 days. So, 3x welders complete the order in 3 days. So, 3x welders complete the order in 3 days. So, 3x welders complete the order in 3 days. So, 3x welders complete the order in 3 days. So, 3x welders complete the order in 3 days. So, 3x welders complete the order in 3 days. So, 3x welders complete the order in 3 days. So, 3x welders complete the order in 3 days. So, 3x welders complete the order in 3 days. So, 3x welders complete the order in 3 days. So, 3x welders complete the order in 3 days. So, 3x welders complete the order in 3 days. So, 3x welders complete the order in 3 days. So, 3x welders complete the order in 3 days. So, 3x welders complete the order in 3 days. So, 3x welders complete the order in 3 days. So, 3x welders complete the order in 3 days. So, 3x welders complete the order in 3 days. So, 3x welders complete the order in 3 days. So, 3x welders complete the order in 3 days. So, 3x welders complete the order in 3 days. So, 3x welders complete the order in 3 days. So, 3x welders complete the order in 3 days. So, 3x welders complete the order in 3 days. So, 3x welders complete the order in 3 days. So, 3x welders complete the order in 3 days. So, 3x welders complete the order in 3 days. So, 3
>>>6: #### D
OPINIONS END
SOLUTION:1. We need to find out the time taken by 3 workers after day 1.
2. total no.of wokers * total time taken = time taken by 1 worker
3. Time taken by 1 worker = 12*3 = 36 days
4. But on day 1 twelve workers had already worked finishing 1/3 of the job. So 3 workers have to finish only 2/3 of the job.
5. Total time taken by 3 workers can be got from formula used at (2). i.e., 3* total time taken = 36. Total time taken by 3 workers to finish the complete job is 36/ 3 = 12 days.
6. Time taken by 6 workers to finish 2/3 of the job is 2/3 * 12 =8 days.
The answer is choice C #### C |
QUESTION:5 noun, 4 verbs and 3 adjectives are written on blackboard.we can form sentence by choosing 1 from each available set without caring it makes sense or not.what is the number of ways of doing this??
options: A)360 B)430 C)510 D)540 E)630
OPINIONS START
>>>0: #### E
>>>1: #### A
>>>2: #### D
>>>3: #### C
>>>4: #### D
>>>5: #### D
>>>6: #### A
OPINIONS END
SOLUTION:we have to choose one from each set. 1 from 5 nouns and 1 from 4 verbs and 1 from 3 adjectives.
then we have to arrange 3 different sets in 3! ways.
so,
5c1*4c1*3c1*3!=360
ANSWER:A #### A |
QUESTION:45 workers work 8 hours to dig a hole 30 meters deep. How many extra workers should be hired to dig another hole 55 meters deep by working for 6 hours?
options: A)50 B)55 C)60 D)65 E)70
OPINIONS START
>>>0: #### D
>>>1: #### 1:45*8*30 = 10800
45*6*55 = 14850
14850/10800 = 1.37
1.37 = 1 + 0.37
0.37 = 0.37*100 = 37/100
37/100 = 37/100 * 100 = 37
37 = 37/100 * 100 = 37
37 = 37/100 * 100 = 37
37 = 37/100 * 100 = 37
37 = 37/100 * 100 = 37
37 = 37/100 * 100 = 37
37 = 37/100 * 100 = 37
37 = 37/100 * 100 = 37
37 = 37/100 * 100 = 37
37 = 37/100 * 100 = 37
37 = 37/100 * 100 = 37
37 = 37/100 * 100 = 37
37 = 37/100 * 100 = 37
37 = 37/100 * 100 = 37
37 = 37/100 * 100 = 37
37 = 37/100 * 100 = 37
37 = 37/100 * 100 = 37
37 = 37/100 * 100 = 37
37 = 37/100 * 100 = 37
37 = 37/100 * 100 = 37
37 = 37/100 * 100 = 37
37 = 37/100 * 100 = 37
37 = 37/100 * 100 = 37
37 = 37/100 * 100 = 37
37 = 37/100 * 100 = 37
37 = 37/100 * 100 = 37
37 = 37/100 * 100 = 37
37 = 37/100 * 100 = 37
37 = 37/100 * 100 = 37
37 = 37/100 * 100 = 37
37 = 37/100 * 100 = 37
37 = 37/100 * 100 = 37
37 = 37/100 * 100 = 37
37 = 37/100 * 100 = 37
37 = 37/100 *
>>>2: #### A
>>>3: #### A
>>>4: #### C
>>>5: #### B
>>>6: #### D
OPINIONS END
SOLUTION:45 workers * 8 hours / 30 meters = x * 6 / 55
x = 110 total workers
110 - 45 = 65 new workers
The answer is D. #### D |
QUESTION:An electric pump can fill a tank in 3 hours. Because of a leak in the tank, it took 3 hours 30 min to fill the tank. In what time the leak can drain out all the water of the tank and will make tank empty ?
options: A)10 hours B)13 hours C)17 hours D)21 hours E)25 hours
OPINIONS START
>>>0: #### D
>>>1: #### 1:Let the tank be filled in 3 hours and the leak can drain out all the water of the tank in x hours.
Then, the tank will be filled in 3 hours 30 min = 3 1/2 hours = 21/2 hours
So, the tank will be filled in 3 hours and the leak can drain out all the water of the tank in 21/2 hours.
So, the tank will be filled in 3 hours and the leak can drain out all the water of the tank in 21/2 hours.
So, the tank will be filled in 3 hours and the leak can drain out all the water of the tank in 21/2 hours.
So, the tank will be filled in 3 hours and the leak can drain out all the water of the tank in 21/2 hours.
So, the tank will be filled in 3 hours and the leak can drain out all the water of the tank in 21/2 hours.
So, the tank will be filled in 3 hours and the leak can drain out all the water of the tank in 21/2 hours.
So, the tank will be filled in 3 hours and the leak can drain out all the water of the tank in 21/2 hours.
So, the tank will be filled in 3 hours and the leak can drain out all the water of the tank in 21/2 hours.
So, the tank will be filled in 3 hours and the leak can drain out all the water of the tank in 21/2 hours.
So, the tank will be filled in 3 hours and the leak can drain out all the water of the tank in 21/2 hours.
So, the tank will be filled in 3 hours and the leak can drain out all the water of the tank in 21/2 hours.
So, the tank will be filled in 3 hours and the leak can drain out all the water of the tank in 21/2 hours.
So, the tank will be filled in 3 hours and the leak can drain out all the water of the tank in 21/2 hours.
So, the tank will be filled in 3 hours and the leak can drain out all the water of the tank in 21/2 hours.
So, the tank will be filled in 3 hours and the leak can drain out all the water of the tank in 21/2 hours.
So, the tank will be filled in
>>>2: #### A)10 hours
>>>3: #### B
>>>4: #### A
>>>5: #### A
>>>6: #### D
OPINIONS END
SOLUTION:Explanation:
We can get the answer by subtrating work done by leak in one hour by subtraction of filling for 1 hour without leak and with leak, as
Work done for 1 hour without leak = 1/3
Work done with leak = 3 1/2=7/2
Work done with leak in 1 hr=2/7
Work done by leak in 1 hr=1/3=2/7=1/21
So tank will be empty by the leak in 21 hours.
ANSWER IS D #### D |
QUESTION:In a apartment, 30% of the people speak English, 20% speak Hindi and 10% speak both. If a people is selected at random, what is the probability that he has speak English or Hindi?
options: A)1/2 B)1/3 C)2/5 D)2/7 E)3/7
OPINIONS START
>>>0: ####
>>>1: #### C
>>>2: #### A
>>>3: #### C
>>>4: #### C
>>>5: #### C
>>>6: #### C
OPINIONS END
SOLUTION:P (E) = 30 / 100 = 3 / 10 , P (H) = 20 / 100 = 1 / 5 and P (E ∩ H) = 10 / 100 = 1 / 10
P (E or H) = P (E U H)
= P (E) + P (H) - P (E ∩ H)
= (3 / 10) + (1 / 5) - (1 / 10) = 4 / 10 = 2/5
C #### C |
QUESTION:What is the total number of integers between 20 and 80 (exclusive)that are divisible by 10?
options: A)5 B)7 C)4 D)9 E)3
OPINIONS START
>>>0: #### A
>>>1: #### A
>>>2: #### A
>>>3: #### A
>>>4: #### B
>>>5: #### A
>>>6: #### C
OPINIONS END
SOLUTION:30,40,50,60,70
total 5
Answer is A #### A |
QUESTION:Tough and Tricky questions: Mixture Problems.
A drink holding 6 ounces of an alcoholic drink that is 1 part rum to 2 parts coke is added to a jug holding 35 ounces of an alcoholic drink that is 1 part rum to 3 parts coke. What is the ratio of rum to coke in the resulting mixture?
options: A)2:5 B)5:15 C)3:5 D)4:7 E)14:5
OPINIONS START
>>>0: #### 43:121
>>>1: #### E
>>>2: #### D
>>>3: #### 3:Let's denote the amount of rum in the first drink as R1, and the amount of coke as C1. Similarly, let R2 and C2 denote the amount of rum and coke in the second drink.
The ratio of rum to coke in the first drink is 1:2, so R1 = 6 and C1 = 12.
The ratio of rum to coke in the second drink is 1:3, so R2 = 35 and C2 = 105.
After the two drinks are mixed, the total amount of rum and coke is (R1 + R2) + (C1 + C2) = 6 + 35 + 12 + 105 = 158 ounces.
The total amount of rum in the mixture is R1 + R2 = 6 + 35 = 41 ounces.
The total amount of coke in the mixture is C1 + C2 = 12 + 105 = 117 ounces.
The ratio of rum to coke in the resulting mixture is therefore (R1 + R2) / (C1 + C2) = 41 / 117.
To simplify this ratio, we can divide both the numerator and the denominator by their greatest common divisor, which is 7.
The simplified ratio is (41 / 7) / (117 / 7) = 41 / 117 * (7 / 7) = 41 / 117 * 1 = 41 / 117.
This ratio cannot be simplified any further, so the answer is not one of the given options.
However, we can convert the ratio to a fraction with a common denominator. To do this, we can multiply both the numerator and the denominator by 117 to get 41 * 117 / 117 * 117 = 4777 / 13489.
This fraction is equivalent to the ratio 4777 / 13489, which is approximately 3.53 : 10.51.
Since the given options do not include this
>>>4: #### B
>>>5: #### D
>>>6: #### E
OPINIONS END
SOLUTION:Answer = B) 5:15
........................ Rum ..................... Coke ................. Total
First Drink ........... 2 ............................ 4 ..................... 6 (Ratio 1:2)
Second Drink ....... 8 ............................. 24 ................... 32 (Ratio 1:3)
Total .................. 10 ............................. 28 .................... 38
Ratio = 10:30 = 5:15
B #### B |
QUESTION:In a bag containing only blue, red and green marbles, all but 15 are blue, all but
13 are red and all but 12 are green. How many are red?
options: A)13 B)7 C)25 D)20 E)10
OPINIONS START
>>>0: #### B
>>>1: #### B
>>>2: #### B
>>>3: #### A
>>>4: #### B
>>>5: #### B
>>>6: #### B
OPINIONS END
SOLUTION:All but blue means number of marbles except blue..hence, let x be the red marble,y
be the green marble,z be the blue marble...
x+y=15
y+z=13
x+z=12
solving this eqns, we get x=7 y=8 z=5 hence number of red marbles are 7
ANSWER:B #### B |
QUESTION:A 6000 liter tank, half-full of water is being filled from a pipe with a flow rate of 1 kiloliter every 2 minutes. At the same time, the tank is losing water from two drains at a rate of 1 kiloliter every 4 minutes and every 6 minutes. How many minutes does it take to fill the tank completely?
options: A)8 B)12 C)18 D)24 E)36
OPINIONS START
>>>0: ####
>>>1: #### 1:6000/2 = 3000 liters
3000/2 = 1500 liters
1500/4 = 375 liters
1500/6 = 250 liters
Total = 1500 + 375 + 250 = 2125 liters
2125/1500 = 1.42
1.42 * 2 = 2.84
2.84 * 4 = 11.36
11.36 * 6 = 68.16
68.16 + 2.84 = 71
71 + 11.36 = 82.36
82.36 + 11.36 = 93.72
93.72 + 11.36 = 105.08
105.08 + 11.36 = 116.44
116.44 + 11.36 = 127.8
127.8 + 11.36 = 139.16
139.16 + 11.36 = 150.52
150.52 + 11.36 = 161.88
161.88 + 11.36 = 173.24
173.24 + 11.36 = 184.6
184.6 + 11.36 = 195.96
195.96 + 11.36 = 207.32
207.32 + 11.36 = 218.68
218.68 + 11.36 = 230.04
230.04 + 11.36 = 241.4
241.4 + 11.36 = 252.76
252.76 + 11.36 = 264.12
264.12 + 11.36 = 275.48
275.48 + 11.36 = 286.84
286.84 + 11.36 = 298.2
298.2 + 11.36 = 309.56
309.56 + 11.36 = 320.92
320.92 + 11.36 = 332.28
332.28 + 11.36 = 343.64
343.64 + 11.36 = 355
355 + 11.36 = 366.36
366.36 + 11.36 = 377.72
377.72 + 11.36 = 389.08
389.08 + 11.36 = 400
>>>2: #### E
>>>3: #### E
>>>4: #### E
>>>5: #### B
>>>6: #### 6:In 2 minutes, the tank is filled by 1 kiloliter and loses 1/4 + 1/6 = 5/12 kiloliters.
Net gain in 2 minutes = 1 - 5/12 = 7/1rightarrow 14/12 kiloliters
To fill 3000 liters, it will take (3000 / (14/12)) * 2 = 428.57 minutes
Answer: None of the options match the calculated time.
OPINIONS END
SOLUTION:In: we have: 1,000/2min = 500 litres per minute
Out: we have: 1,000/4 + 1,000/6
Then do: IN - OUT to figure out the net inflow per minute (you get 83.3). Then divide the total number of litres you need (3,000 by that net inflow to get the minutes) - 36 min. Answer E. #### E |
QUESTION:Which of the following is equal to the value of 2^7 + 2^7 + 3^7 + 3^7 + 3^7 ?
options: A)2^8 + 3^8 B)2^6 + 3^8 C)2^8 + 3^6 D)2^9 + 3^9 E)2^5 + 3^5
OPINIONS START
>>>0: #### E
>>>1: #### A
>>>2: #### A
>>>3: #### B
>>>4: #### None of the options is correct.
>>>5: #### A
>>>6: #### E
OPINIONS END
SOLUTION:2^7 + 2^7 + 3^7 + 3^7 + 3^7
= 2 (2^7) + 3 (3^7)
= 2^1 (2^7) + 3^1 (3^7)
= 2^(1+7) + 3^(1+7)
= 2^8 + 3^8
Ans: A #### A |
QUESTION:A, Band C enter into a partnership by investing in the ratio of 3 : 2: 4. After 1 year, B invests another Rs. 2,70,000 and C, at the end of 2 years, also invests Rs.2,70,000. At the end of three years, profits are shared in the ratio of 3 : 4 : 5. Find initial investment of each.
options: A)360000;180000;270000 B)270000;180000;360000 C)180000;360000;270000 D)270000;360000;270000 E)None of them
OPINIONS START
>>>0: #### E
>>>1: #### 1:Let the initial investments of A, B and C be Rs. 3x, Rs. 2x and Rs. 4x respectively.
A : B : C = 3 : 2 : 4
A : B : C = 3x : 2x : 4x = 3 : 2 : 4
A : B : C = 3 : 2 : 4
A : B : C = 3 : 2 : 4
A : B : C = 3 : 2 : 4
A : B : C = 3 : 2 : 4
A : B : C = 3 : 2 : 4
A : B : C = 3 : 2 : 4
A : B : C = 3 : 2 : 4
A : B : C = 3 : 2 : 4
A : B : C = 3 : 2 : 4
A : B : C = 3 : 2 : 4
A : B : C = 3 : 2 : 4
A : B : C = 3 : 2 : 4
A : B : C = 3 : 2 : 4
A : B : C = 3 : 2 : 4
A : B : C = 3 : 2 : 4
A : B : C = 3 : 2 : 4
A : B : C = 3 : 2 : 4
A : B : C = 3 : 2 : 4
A : B : C = 3 : 2 : 4
A : B : C = 3 : 2 : 4
A : B : C = 3 : 2 : 4
A : B : C = 3 : 2 : 4
A : B : C = 3 : 2 : 4
A : B : C = 3 : 2 : 4
A : B : C = 3 : 2 : 4
A : B : C = 3 : 2 : 4
A : B : C = 3 : 2 : 4
A : B : C = 3 : 2 : 4
A : B : C = 3 : 2 : 4
A : B : C
>>>2: #### A)360000;180000;270000
>>>3: #### A
>>>4: #### 4:Let A = x, B = y, C = z
After 1 year:
A : B = 3 : 2 => A = 3x, B = 2x
After 2 years:
B : C = 2 : 4 => B = 2y, C = 4y
After 3 years:
A : B : C = 3 : 4 : 5
Total investment = x + x + y + y + y + y = 3x + 3y
Profit ratio = 3 : 4 : 5
Let profit of A, B, C be 3p, 4p, 5p respectively
3x + 3y = 3p
x = p
y = (3p/3 - p)/3 = (p/3)
Total investment = 3p + 3(p/3) + y + y + y + y = 3p + 3p/3 + 3y
Total investment = 4.5p + 3y
Given that total investment = 3x + 3y = 3(p) + 3(p/3) + 3y = 4.5p + 3y
Substituting x = p, y = p/3 in the equation 3p + 3y = 3x + 3y
3p + 3(p/3) = 3p + 3y
3p/3 + p/3 = 3y
p/3 + p/3 = 3y
2p/3 = 3y
p = 3y/2
Substituting p = 3y/2 in the equation 3p + 3y = 4.5p + 3y
3(3y/2) + 3y = 4.5(3y/2) + 3y
9y/2 + 3y = 9y + 1.5y
4.5y = 3y
y = 3y/4.5 = 3/3*3/4.5 = 1/2
p = 3y/2 =
>>>5: #### 5:A's share = 3/9 = 1/3 B's share = 2/9 = 2/3 C's share = 4/9 = 4/3 After 1 year, B invests Rs. 2,70,000. So, B's share = 2/3 + 2,70,000 = 2/3 + 9 = 11/3 After 2 years, C invests Rs. 2,70,000. So, C's share = 4/3 + 2,70,000 = 4/3 + 9 = 13/3 After 3 years, profits are shared in the ratio of 3 : 4 : 5. So, A's share = 3/12 = 1/4 B's share = 4/12 = 1/3 C's share = 5/12 = 5/12 A's share = 1/4 = 1/3 + 1/12 = 1/3 + 1/4 = 1/3 + 1/4 = 1/3 + 1/4 = 1/3 + 1/4 = 1/3 + 1/4 = 1/3 + 1/4 = 1/3 + 1/4 = 1/3 + 1/4 = 1/3 + 1/4 = 1/3 + 1/4 = 1/3 + 1/4 = 1/3 + 1/4 = 1/3 + 1/4 = 1/3 + 1/4 = 1/3 + 1/4 = 1/3 + 1/4 = 1/3 + 1/4 = 1/3 + 1/4 = 1/3 + 1/4 = 1/3 + 1/4 = 1/3 + 1/4 = 1/3 + 1/4 = 1/3 + 1/4 = 1/3 + 1/4 = 1/3 + 1/4 = 1/3 + 1/4 = 1/3 + 1/4 = 1/3 + 1/4
>>>6: #### B
OPINIONS END
SOLUTION:Let the initial investments of A, Band C be Rs. 3x, Rs. 2x and Rs. 4x respectively. Then,
(3x x 36) : [(2x x 12) + (2x + 270000) x 24] : [(4x x 24) + (4x +270000) x 12]=3:4:5
1O8x : (72x + 6480000) : (144x + 3240000) = 3 : 4 : 5
108x /(72x+6480000)=3/4 432x = 216x + 19440000
=216x = 19440000
=x=90000
Hence, A’s initial investment = 3x = Rs. 2,70,000;
B's initial investment = 2x = Rs. 1,80,000;
C's initial investment = 4x = Rs. 3,60,000.
Answer is B. #### B |
QUESTION:An article is bought for Rs.675 and sold for Rs.900, find the gain percent?
options: A)33 1/7% B)33 2/3% C)33 1/3% D)37 1/3% E)23 1/3%
OPINIONS START
>>>0: #### C
>>>1: #### C
>>>2: #### B
>>>3: #### B
>>>4: #### C
>>>5: #### C
>>>6: #### C
OPINIONS END
SOLUTION:675 ---- 225
100 ---- ? =>
=33 1/3%
Answer:C #### C |
QUESTION:A basket contains 10 apples and 20 oranges out of which 3 apples and 5 oranges are defective. If we choose two fruits at random, what is the probability that either both are oranges or both are non defective?
options: A)316/439 B)316/438 C)316/435 D)316/299 E)316/199
OPINIONS START
>>>0: #### C
>>>1: #### C
>>>2: #### A
>>>3: #### E
>>>4: #### E
>>>5: #### C
>>>6: #### C
OPINIONS END
SOLUTION:Let A be the event of getting two oranges and
B be the event of getting two non-defective fruits.
and be the event of getting two non-defective oranges
Answer: C) 316/435 #### C |
QUESTION:A rectangular of certain dimensions is chopped off from one corner of a larger rectangle as shown. AB = 8 cm and BC = 4 cm. The perimeter of the figure ABCPQRA (in cm) is :
options: A)24 B)28 C)36 D)48 E)None of these
OPINIONS START
>>>0: #### E
>>>1: #### D
>>>2: #### C
>>>3: #### B
>>>4: #### 4:The missing sides are AC and AP.
Since AB = 8, BC = 4, and the right angle at C is a right angle, we can use the Pythagorean theorem to find AC:
AC² = AB² + BC²
AC² = 8² + 4² = 64 + 16 = 80
AC = √80 = 2√20 = 2 * √5 * √4 = 2 * 2 * √5 = 4 * √5
AP² = AB² + CP²
AP² = 8² + CP²
AP² = 64 + CP²
Since AP is the hypotenuse of a right triangle with legs 8 and CP, we can use the Pythagorean theorem again to find CP:
CP² = AB² + AP²
CP² = 8² + AP²
CP² = 64 + AP²
CP² = 64 + 64 * 5²
CP² = 64 + 625
CP² = 689
CP = √689
Now we can find the perimeter:
Perimeter = 2 * (AB + BC + AC + AP)
Perimeter = 2 * (8 + 4 + 4 * √5 + √689)
Perimeter = 2 * (8 + 4 + 4 * √5 + 21.08)
Perimeter = 2 * (12 + 4 + 4 * √5 + 21.08)
Perimeter = 2 * (18 + 4 * √5 + 21.08)
Perimeter = 2 * (18 + 4 * √5 + 21.08)
Perimeter = 2 * (18 + 4 * √5 + 44.16)
Perimeter = 2 * (18 + 4 * √5 + 44.16)
Perimeter = 2 * (18 + 4 * √5 + 44.16)
Perimeter = 2 * (18 + 4 * √5 + 44.16)
Per
>>>5: #### C
>>>6: #### E
OPINIONS END
SOLUTION:Solution
Required perimeter = (AB + BC +CP + PQ + QR + RA)
= AB + BC + (CP + QR) + (PQ + RA)
= AB + BC + AB + BC = 2(AB + BC)
= [2(8 + 4 )] cm = 24 cm. Answer A #### A |
QUESTION:The sum of the two numbers is 11 and their product is 24. What is the sum of the reciprocals of these numbers ?
options: A)11/24 B)11/25 C)13 D)13/15 E)None
OPINIONS START
>>>0: #### A
>>>1: #### A
>>>2: #### A
>>>3: #### C
>>>4: #### A
>>>5: #### A
>>>6: #### A
OPINIONS END
SOLUTION:Let the numbers be
x
x and
y
y Then
x
+
y
=
11
x
y
=
24
x+y=11xy=24
Hence,
x
+
y
x
y
=
11
24
x+yxy=1124
⇒
1
y
+
1
x
=
11
24
Answer is A #### A |
QUESTION:What is the sum of the different positive prime factors of 380?
options: A)5 B)10 C)15 D)17 E)26
OPINIONS START
>>>0: #### E
>>>1: #### E
>>>2: #### E
>>>3: #### A
>>>4: #### D
>>>5: #### E
>>>6: #### E
OPINIONS END
SOLUTION:Prime factorization of 380
=38 * 10
=2*19 * 10
=2*19 * 2*5
=2^2 * 5 * 19
Sum of the different positive prime factors of 380 = 2+5+19
=26
Answer E #### E |
End of preview. Expand in Data Studio
README.md exists but content is empty.
- Downloads last month
- 3