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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
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
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
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
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
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
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!
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
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$
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
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
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
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
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
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
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
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
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
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
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
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%
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
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
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
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
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
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%
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
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%
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%
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
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
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
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
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
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
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
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
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
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
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
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
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$
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
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
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
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
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
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
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
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%
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
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
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
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
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
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
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.
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
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
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
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
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
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
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
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
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
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
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
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
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
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%
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
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
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
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
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
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
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
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
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
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
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
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 %
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
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
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
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
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
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
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
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
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
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
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
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%
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
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
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
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
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 |
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