subject stringclasses 1
value | question stringlengths 3 1.14k | options listlengths 5 5 | solution stringlengths 18 3.7k | answer stringclasses 5
values |
|---|---|---|---|---|
mathematics | A child must place 7 different toys in 4 different bins. If any of the toys can go in any of the bins, in how many ways can the child place the toys into the bins? | [
"6^6",
"6^4",
"4^7",
"4^4",
"6^4-4^6"
] | there are 4 different bins and each of the toy can go to any of these bins..
so answer 7∗7∗7∗7∗7∗7∗7=4^7
ANSWER:C
The answer is: C | C |
mathematics | 70% of the employees in a multinational corporation have VCD players, 83 percent have microwave ovens, 80 percent have ACs and 85 percent have washing machines. At least what percentage of employees has all four gadgets? | [
"(a) 15%",
"(b) 5%",
"(c) 10%",
"(d) 18%",
"(e) 25%"
] | so 30% employees don't have VCD devices.
17% employees don't have MO
20% employees don't have ACs
15% employees don't have WM
Summ of employees that don't have some device = 30%+17%+20%+15% = 82% < 100%
So definitely at least 18% employees have 4 devices.
ans: D
The answer is: D | D |
mathematics | An article is listed at Rs. 920. A customer pays Rs. 742.90 for it after getting two successive discounts. If the rate of first discount is 15%, the rate of 2nd discount is: | [
"3%",
"5%",
"8%",
"12%",
"None"
] | Solution: MP = 920.
After first discount Marked Price (MP) become,
= 920 - 15% of 920 = 782.
The Selling Price (SP) = 742.90.
Let second discount was x% on 782.
782 - x% of 782 = 742.90
782x/100 = 39.1
782x = 3910
x = 5%.
Second Discount = 5%.
Answer: Option B
The answer is: B | B |
mathematics | ASvennumber is defined as a five-digit number which goes according to the following rules: the leftmost digit is even, any digit to the right of an even digit must be an odd digit, and any digit to the right of an odd digit can only be one of the digits 1 or 9. How many different 5-digit numbers areSvennumbers? | [
"20",
"80",
"160",
"220",
"250"
] | ASvennumber is defined as a five-digit number which goes according to the following rules: the leftmost digit is even, any digit to the right of an even digit must be an odd digit, and any digit to the right of an odd digit can only be one of the digits 1 or 7. How many different 5-digit numbers areSvennumbers?
4/9*5/1... | E |
mathematics | Find the value of 72519 x 9999 = m? | [
"456578972",
"436567874",
"653658791",
"725117481",
"357889964"
] | 72519 x 9999 = 72519 x (10000 - 1)
= 72519 x 10000 - 72519 x 1
= 725190000 - 72519
= 725117481
D
The answer is: D | D |
mathematics | Two numbers are in ratio P:Q. when 1 is added to both the numerator and the denominator, the ratio gets changed to R/S. again, when 1 is added to both the numerator and denominator, it becomes 1/2. Find the sum of P and Q. | [
"3",
"4",
"5",
"6",
"7"
] | Solution: If we go through normal method, It will be quite cumbersome,so,
We will solve this question through options.
Taking option a: It has P+Q = 3. The possible value of P/Q is 1/2 or 2/1.
Using 1/2, we see that on adding 2 in both the numerator and denominator we get 3/4 (not required value.
Similarly we check for... | C |
mathematics | A chair is bought for Rs.500/- and sold at a loss of 10% find its selling price | [
"Rs.450/-",
"Rs.451/-",
"Rs.440/-",
"Rs.455/-",
"Rs.445/-"
] | Loss = 500*10/100 = 50
S.P = C.P - Loss
= 500- 50
=Rs.450/-
Answer : A
The answer is: A | A |
mathematics | A train passes a man standing on the platform. If the train is 240 meters long and its speed is 72 kmph, how much time it took in doing so? | [
"16 sec",
"14 sec",
"9 ½ sec",
"8 ½ sec",
"12 sec"
] | D = 240
S = 72 * 5/18 = 20 mps
T = 240/20 = 12 sec
Answer: E
The answer is: E | E |
mathematics | The average mark of the students of a class in a particular exam is 60. If 5 students whose average mark in that exam is 44 are excluded, the average mark of the remaining will be 80. Find the number of students who wrote the exam? | [
"12",
"10",
"7",
"9",
"8"
] | Let the number of students who wrote the exam be x.
Total marks of students = 60 x.
Total marks of (x - 5) students = 90(x - 5)
60x - (5 * 44) = 80(x - 5)
180 = 20x => x = 9
Answer: D
The answer is: D | D |
mathematics | A machine puts c caps on bottles in m minutes. How many W hours will it take to put caps on b bottles? | [
"60bm/c",
"W=bm/60c",
"bc/60m",
"60b/cm",
"b/60cm"
] | The machine puts c caps in m minutes or c caps in m/60 hours.
Rate = c/m/60 = 60c/m.
To put b caps the machine CCwill take:-
Time = Work/Rate
T = b/60c/m = bm/60c
Answer is B.
The answer is: B | B |
mathematics | A man can swim in still water at 6 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is? | [
"1.7",
"1.9",
"1.1",
"2",
"1.2"
] | M = 6
S = x
DS = 6 + x
US = 6 - x
6 + x = (6 - x)2
6 + x = 12 -2x
3x = 12-6=6
x = 2
Answer:D
The answer is: D | D |
mathematics | What is the remainder when 1044 * 1047 * 1050 * 1053 is divided by 33? | [
"3",
"27",
"30",
"21",
"18"
] | Explanatory Answer
Useful result pertaining to remainders
You can solve this problem if you know this rule about remainders.
Let a number x divide the product of A and B.
The remainder will be the product of the remainders when x divides A and when x divides B.
Using this rule,
The remainder when 33 divides 1044 is 21.... | C |
mathematics | Radha bought a watch for Rs. 144 and got a percentage of profit equal to the cost price of the watch. What is the cost price of the watch? | [
"Rs. 72",
"Rs. 78",
"Rs. 80",
"Rs. 90",
"Rs. 92"
] | SP=144
CP=x
profit %=x
C.P.= (100/(100+gain%))*S.P.
x=(100/100+x) *144
x^2+100x=14400
x^2+180x-80x-14400=0
(x+180) (x-80)=0
x=-180
x=80
ANSWER:D
The answer is: D | D |
mathematics | A certain series is defined by the following recursive rule: Sb=K(Sb-1) , where k is a constant. If the 1st term of this series is 64 and the 25th term is 192, what is the 9th term? | [
"ROOT 2",
"ROOT 3",
"64*ROOT 3",
"64*3^1/3",
"64*3^24"
] | Ans...D
No need for any GP formula here
The rule is that bth term is K times the (b-1)th term.
1st = 64
2nd = k.64
3rd = k^2.64
.
.
.
9th term = k^8 *64
.
.
.
so 25th = k^24*64
Using this solve for k and substitute k in the equation for the 9th term
The answer is: D | D |
mathematics | For any integer p, *p is equal to the product of all the integers between 1 and p, inclusive. How many prime numbers are there between *6 + 3 and *6 + 6, inclusive? | [
"One",
"None",
"Two",
"Three",
"Four"
] | Generally *p or p! will be divisible by ALL numbers from 1 to p. Therefore, *6 would be divisible by all numbers from 1 to 6.
=> *6+3 would give me a number which is a multiple of 3 and therefore divisible (since *6 is divisible by 3)
In fact adding anyprimenumber between 1 to 6 to *6 will definitely be divisible.
So t... | B |
mathematics | Sam has forgotten his friend’s seven-digit telephone number. He remembers the following: the first three digits are either 635 or 674, the number is odd, and the number nine appears once. If Sam were to use a trial and error process to reach his friend, what is the minimum number of trials he has to make before he can ... | [
"1000",
"2430",
"3402",
"3006",
"None of these"
] | Explanation :
Let's check the number of ways for the first telephone number.
6 3 5 - - - -
a) 6 3 5 9 - - -
4 choices for last digit (1,3,5,7).
9 * 9 choices for 5th and 6th digits together.
So, 9 * 9 * 4 choices = 324 ways.
Similarly,
b.) 6 3 5 - 9 - - = 324 ways.
c.) 6 3 5 - - 9 - = 324 ways.
d.) 6 3 5 - - - 9 = 9 * ... | C |
mathematics | A painting at an art gallery is framed such that the area of the square frame is 1/3 the area of the painting itself. If the diagonal line connecting corners of the frame has a length of 12, what is the area of the painting inside the frame? | [
"10",
"20",
"30",
"40",
"54"
] | Suppose side of the painting(which is a square) is a and side of the outer square(painting+frame) is b
Area of painting = a^2 and we know that the area of the frame is (1/3) of that of the painting so
Area of frame = (1/3) * a^2
Area of Frame + Painting = a^2 + (1/3)*a^2 = (4/3)*a^2 which is equal to b^2
Line connectin... | E |
mathematics | If 4 (A's capital) = 6 (B's capital) = 8 (C's capital). Then the ratio of their capitals is? | [
"6:4:5",
"6:4:3",
"6:4:2",
"6:2:3",
"6:5:3"
] | 4A = 6B = 8 C
A:B:C = 1/4:1/6:1/8
= 6:4:3
Answer: B
The answer is: B | B |
mathematics | A alone can finish a work in 10 days which B alone can finish in 15 days. If they work together and finish it, then out of a total wages of Rs.3000, A will get: | [
"Rs.1200",
"Rs.1500",
"Rs. 1800",
"Rs.2000",
"None of these"
] | Explanation:
Ratio of working days of A : B = 10 : 15
Therefore, their wages ratio = reverse ratio = 15 : 10
Therefore, A will get 15 units of ratio
Total ratio = 25
1 unit of ratio =3000/25 = 120
So, A’s amount = 120 × 15 = Rs.1800.
Answer: Option C
The answer is: C | C |
mathematics | What is the remainder when 121212.......(300) digits is divided by 99. | [
"18",
"36",
"72",
"0",
"1"
] | 12/99=12
1212/99=24
121212/99=36
.
.
.
121212...(300)/99=(12*300)%99=36
if they say 300 digits then (12*150)%99=18
ANSWER:A
The answer is: A | A |
mathematics | The price of a TV was increased by 30 percent. The new price was then increased by 20 percent. A single increase of what percent is equivalent to these two successive increases? | [
"50%",
"60%",
"65%",
"56%",
"45%"
] | consider base price - $100
25% increase = 1.30*100 = $130
another 20% increase on new price = 1.2* 130 = $156
so final price of radio - $156
therefore a 56% increase
correct option - D
The answer is: D | D |
mathematics | The area of a rectangle plot is 460 square metres. If the length is 15% more than the breadth, what is the breadth of the plot? | [
"10m",
"20m",
"50m",
"40m",
"30m"
] | lb = 460 m power2...(Equation 1)
Let the breadth = b
Then length, l = b × (100+15)/100 = 115b/100 ...(Equation 2)
From Equation 1 and Equation 2,
115b/100 × b = 460
b2 = 46000/115 = 400
⇒ b = √400 = 20 m
Answer is B.
The answer is: B | B |
mathematics | According to the directions on a packet of smoothie mix, 1 3-ounce packet of smoothie mix is to be combined with 10 ounces of water to make a smoothie. How many 3-ounce packets of smoothie mix are required to prepare 150 12-ounce smoothies? | [
"120",
"150",
"180",
"240",
"600"
] | This question wasn't particularly grueling, but I think it's the first where I had the opportunity to solve it via theory andinspectionthat many on this board suggest as strategy on the GMAT. It actually came to me by accident. Basically, if we thought that the 3 packets of powder were included in the 12 ounces of wate... | B |
mathematics | A list of numbers has six positive integers. Three of those integers are known: 4, 5 and 24 and three of those are unknown: x, y and z. The three unknowns are known to be distinct. It is also known that the mean of the list is 10 and the median lies between 7 and 8 (exclusive). Which of the following CANNOT be the valu... | [
"13",
"12",
"11",
"10",
"5"
] | Mean = 10
Therefore sum of the 6 digits = 6*10 = 60 -------- (1)
The 3 digits are 4,5 & 24 -------------- (2)
Now, 7 < median < 8
-> 7 < (sum of 2 digits)/2 < 8
-> 14 < (sum of 2 digits) < 16
Therefore the sum of 2 digits = 15.
The 2 digits whose sum is 15 & whose median is b/w 7 & 8 can be :
1. 7, 8,
2. 6, 9,
3. 5, 10... | C |
mathematics | Margaret is 9 years more than twice the age of his son. The age of son is 12. Find the age of mother and find the difference between their ages | [
"21yrs",
"20yrs",
"30yrs",
"40yrs",
"50yrs"
] | Let, age of son x=12
Margaret is 9 years more than twice the age of his son, y = 9+2(x)
=9+2(12)
=9+24
=33yrs
Difference = 33 - 12
=21yrs
ANSWER:A
The answer is: A | A |
mathematics | Which of the following is(are) true for a@b=b@a?
I. a@b=ab+ba
II. a@b=(a+b+1)(a-b)
III. a@b=(a/b)+(b/a) | [
"only Ⅰ",
"only Ⅱ",
"only Ⅲ",
"only ⅠⅢ",
"only ⅡⅢ"
] | -> If I. a@b=ab+ba, a@b=ab+ba=ba+ab=b@a (O).
If II. a@b=(a+b+1)(a-b), a@b=(a+b)(a-b)≠(b+a)/(b-a)=b@a (X).
If III.a@b=(a/b)+(b/a), a@b=(a/b)+(b/a)=(b/a)+(a/b)=b@a (O).
Thus, ⅠⅢ are the answers. Therefore, D is the answer.
The answer is: D | D |
mathematics | 2^8×39+31=? | [
"34545",
"65657",
"65567",
"45677",
"56782"
] | 256*39+31
65567
C
The answer is: C | C |
mathematics | A trained covered x km at 40 kmph and another 2x km at 20 kmph. Find the average speed of the train in covering the entire 2x km. | [
"16kmph",
"20kmph",
"25kmph",
"30kmph",
"35kmph"
] | Total time taken = x/40 + 2x/20 hours
= 5x/40 = x/8 hours
Average speed = 2x/(x/8)
= 16 kmph
Answer:A
The answer is: A | A |
mathematics | If x^3 + y^3 = 200, then the greatest possible value of x is between | [
"2 and 3",
"3 and 4",
"4 and 5",
"5 and 6",
"7 and 8"
] | for the greatest possible value of x^3, we must minimize the value of y^3 i.e. lets say y^3 = 0
then we need to find a number x such that x^3 < 200. 5^3 = 125 and 6^3 = 216 so we can say that the maximum possible value of x can be a little more than 5 hence answer = between 5 and 6
hence D
The answer is: D | D |
mathematics | A certain car traveled twice as many miles from Town A to Town B as it did from Town B to Town C. From Town A to Town B, the car averaged 8 miles per gallon, and from Town B to Town C, the car averaged 18 miles per gallon. What is the average miles per gallon that the car achieved on its trip from Town A through Town B... | [
"13",
"15.5",
"14",
"14.5",
"15"
] | Ans is B
Given d_ab = 2*d_bc
let d_ab = d and d_bc = x so d=2x
for average miles per gallon = (d+x)/((d/8)+(x/18)) = 15.5 (formula avg speed = total distance/ total time)
The answer is: B | B |
mathematics | How many different ways can you select a pilot and a co pilot if you have 80 people to choose from? | [
"199",
"200",
"398",
"4950",
"6320"
] | You are not just choosing two from 80. Each of the two people chosen fills a particular slot. The first filling the pilot slot and the second filling the copilot slot is different from the first filling the copilot slot and the second filling the pilot slot.
So the answer is in a sense (80C2) x 2 = 6320=E
The answer is... | E |
mathematics | Each child has 12 crayons and 24 apples. If there are 18 children, how many crayons are there in total? | [
"220",
"65",
"216",
"219",
"230"
] | 12*18=216.Answer is C.
The answer is: C | C |
mathematics | A sells to B goods at five-thirds the rate of profit at which B has decided to sell it to C. C, on other hand sells it to D at one-third the rate of profit at which B sold it to C. If D gives Rs. 2145 to C at 10%, how much did A buy it for ? | [
"1000",
"1100",
"1200",
"1300",
"1400"
] | let profit rate of b = x
acc to question profit rate of a becomes 5/3 x
and that of c= 1/3 x which is given as 10%
1/3 x= 10
therefore x=30
now b=30% , a=50%
now we will find out c's price-
11/10 * price = 2145
price = 1950
in similar way we will find out b's price as we know that profit is 30%
therefore 130/100 * pric... | A |
mathematics | Alex deposited x dollars into a new account that earned 8 percent annual interest, compounded annually. One year later Alex deposited an additional x dollars into the account. If there were no other transactions and if the account contained w dollars at the end of two years, which of the following expresses x in terms ... | [
"w/(1+1.08)",
"w/(1.08+1.16)",
"w/(1.16+1.24)",
"w/(1.08+1.08^2)",
"w/(1.08^2+1.08^2)"
] | Account at the end of the first year would be 1.08x dollars. At this time x dollars was deposited, hence the account at the beginning of the second year would be (1.08x+x) dollars. Account at the end of the second year would be (1.08x+x)*1.08=w --> x(1.08^2+1.08)=w --> x=w/(1.08+1.08^2).
Answer: D.
The answer is: D | D |
mathematics | In an election a candidate who gets 60% of the votes is elected by a majority of 1040 votes. What is the total number of votes polled? | [
"A)4500",
"B)5200",
"C)6900",
"D)7520",
"E)6000"
] | Let the total number of votes polled be x
Then, votes polled by other candidate = (100-60)% of x = 40% of x
60% of x - 40% of x = 1040
20x/100 = 1040
x = 1040*100/20 = 5200
Answer is B
The answer is: B | B |
mathematics | A boat can travel with a speed of 42 km/hr in still water. If the speed of the stream is 10 km/hr, find the time taken by the boat to go 94 km downstream | [
"1 hour 40 min",
"2 hour 40 min",
"1 hour 20 min",
"1 hour 30 min",
"1 hour 50 min"
] | Speed of the boat in still water = 42 km/hr
speed of the stream = 10 km/hr
Speed downstream = (42+10) = 52 km/hr
Distance travelled downstream = 94 km
Time taken =distance/speed
=94/52
= 1.81 hours
= 1 hour 50 min.
ANSWER:E
The answer is: E | E |
mathematics | 3 + 3 + 3 + 2 × 3^2 + 2 × 3^3 + 2 × 3^4 + 2 × 3^5 + 2 × 3^6 + 2 × 3^7 = | [
"3^7",
"3^8",
"3^14",
"3^28",
"3^30"
] | We have the sum of 9 terms. Now, if all terms were equal to the largest term 2*3^7 we would have: sum=9*(2*3^7)=2*3^9=~3^10, so the actual sum is less than 3^10 and more than 3^7 (option A) as the last term is already more than that. So the answer is clearly B.
Answer: B.
The answer is: B | B |
mathematics | A milk man sells the milk at the cost price but he mixes the water in it and thus he gains 9.09%. The quantity of water in the mixture of 1 liter is | [
"83.33 ml",
"83.03 ml",
"93.33 ml",
"63.03 ml",
"82.33 ml"
] | Explanation:
Profit (%) = 9.09 % = \inline \frac{1}{11}
Since the ratio of water and milk is 1 : 11,
Therefore the ratio of water is to mixture = 1:12
Thus the quantity of water in mixture of 1 liter = \inline 1000\times \frac{1}{12} = 83.33 ml]
Answer: A) 83.33 ml
The answer is: A | A |
mathematics | A triangle has a perimeter 15. The two shorter sides have integer lengths equal to x and x + 1. Which of the following could be the length of the other side? | [
"7",
"6",
"8",
"9",
"10"
] | The SHORTER sides have integral lengths equal to x and x + 1
Let the longest side be 'a'
So, a + x + (x +1) = 15
a + 2x = 14.......eqn (1)
We know that the sum of the lengths of the shorter sides has to be more than the length of the longer one. i.e 2x+1> a
a =6
B
The answer is: B | B |
mathematics | Huey's Hip Pizza sells two sizes of square pizzas: a small pizza that measures 8 inches on a side and costs $10, and a large pizza that measures 12 inches on a side and costs $20. If two friends go to Huey's with $30 apiece, how many more square inches of pizza can they buy if they pool their money than if they each pu... | [
"5 square inches",
"10 square inches",
"16 square inches",
"25 square inches",
"350 square inches"
] | In the first case each can buy one pizza of $10 and one pizza of $20.
In square inches that would be (8*8=64) for the small pizza and (12*12=144) for the large pizza. In total sq inches that would be (64+144)*2= 416 sq inches.
In the second case if they pool their money together they can buy 3 large pizzas. In terms of... | C |
mathematics | A man brought some eggs of which 10% are rotten. He gives 80% of the remainder to his neighbour. Now he left out with 36 eggs. Hw many eggs he brought | [
"100",
"200",
"72",
"40",
"36"
] | Let he bought 100 eggs.
Eggs after removing rotten one = 90.
Eggs given to neighbour = 80% of 90 = 72 eggs.
Now he left with eggs = 90 - 72 = 18 eggs.
Now,
Comparing,
18 = 36
1 = 36/18
ANSWER : OPTION B
100 = 200.
So, he bought 200 eggs.
The answer is: B | B |
mathematics | If an object travels at two feet per second, how many feet does it travel in one hour? | [
"3488",
"3778",
"7200",
"1800",
"2881"
] | Explanation:
If an object travels at 2 feet per second it covers 2x60 feet in one minute, and 2x60x60 feet in one hour.
Answer = 7200
Answer: C) 7200
The answer is: C | C |
mathematics | A train 225 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is: | [
"86",
"50",
"12",
"13",
"67"
] | Speed of the train relative to man = (225/10) m/sec = (45/2) m/sec. [(45/2) * (18/5)] km/hr = 81 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 81 ==> x = 86 km/hr.
Answer: Option A
The answer is: A | A |
mathematics | If x > 3000, then the value of (x)/(2x-42) is closest to? | [
"1/6",
"1/3",
"10/21",
"1/2",
"3/2"
] | assume x = 3002
(x)/(2x-42) = 3002 / (3002*2-42)
=3002 / 5962
= = 1/2
Ans - D
The answer is: D | D |
mathematics | Last year John earned m dollars at company X and was promised an n-percent raise for this year. If John is paid the promised amount and a $10,000 bonus at the end of this year, by what percent has his total salary(including his bonus) increased this year over last in terms of n and m? | [
"(mn + 10000)/m %",
"(n + 10000)/m %",
"(mn + 100,000)/100m %",
"(mn + 1,000,000)/100m %",
"(mn + 1,000,000)/m %"
] | Old Salary = m dollars
New salary = M (1 + n/100) + 10,000
Net increase = m*n/100 + 10,000
Percentage change = (mn/100 + 10,000)*100/m
= (mn + 1,000,000)/m%
Answer: E.
The answer is: E | E |
mathematics | Two pipes A and B can fill a cistern in 12 and 24 minutes respectively, and a third pipe C can empty it in 36 minutes. How long will it take to fill the cistern if all the three are opened at the same time? | [
"10 2/7 min",
"10 1/8 min",
"11 1/7 min",
"12 8/7 min",
"11 3/7 min"
] | 1/12 + 1/24 - 1/36
= 7/72
72/7 = 10 2/7
Answer:A
The answer is: A | A |
mathematics | The monthly incomes of A and B are in the ratio 5 : 2. B's monthly income is 12% more than C's monthly income. If C's monthly income is Rs. 15000, then find the annual income of A? | [
"187888",
"276889",
"267777",
"504000",
"297112"
] | B's monthly income = 15000 * 112/100 = Rs. 16800
B's monthly income = 2 parts ----> Rs. 16800
A's monthly income = 5 parts = 5/2 * 16800 = Rs. 42000
A's annual income = Rs. 42000 * 12 = Rs.504000
Answer:D
The answer is: D | D |
mathematics | Two numbers are in respectively 10% and 40% more than a third number. The ratio of the two numbers is? | [
"11:14",
"7:9",
"17:25",
"15:26",
"2:3"
] | Let the 3rd number be x
Then, first number = 110% of x = 110x/100 = 11x/10
second number = 140% of x = 140x/100 = 7x/5
Ratio of first two numbers = 11x/10 : 7x/5 = 11:14
Answer is A
The answer is: A | A |
mathematics | A company conducted a survey about its two brands, A and B. x percent of respondents liked product A, (x – 20) percent liked product B, 23 percent liked both products, and 23 percent liked neither product. What is the minimum number W of people surveyed by the company? | [
"46",
"80",
"W.90",
"W.100",
"200"
] | 100 = x + x - 20 + 23 - 23
x = 60,
So, Product A = 60%, Product B = 40%, Both = 23%, Neither = 23%
23% of the total no. of people should be an integer. So, A,BC are out.
60% of D and 40% of D are both integers. So, D satisfies all conditions.
So, answer is D.
The answer is: D | D |
mathematics | In a rectangular axis system, what is the area of a parallelogram with the coordinates: (5,7), (12,7), (2,3), (9,3) ? | [
"21",
"28.",
"35.",
"49.",
"52."
] | Area of parallelogram = b*h.
Base = Distance in x coordinates between (2,3) and (9,3) = 7
Height = Difference in y coordinates between (5,7) and (2,3) = 3.
Area = 7*3 = 21.
ANSWER:A
The answer is: A | A |
mathematics | How many ways are there to split a group of 6 girls into two groups of 3 girls each? (The order of the groups does not matter) | [
"35",
"10",
"40",
"20",
"25"
] | the combination is 6C3 /2
= 6!/3!*3!*2 = 20/2 =10
B
The answer is: B | B |
mathematics | A person travels from X to Y and vice versa. How long will it take to travel both the ways by bus?
(A) It takes 15 hours in travelling from X to Y by train and returning by bus.
(B) The distance between two places is 360 km.
(C) He can save 3 hrs if he travels both the ways by train. | [
"A and B together",
"B and C together",
"A and C together",
"Any two of them",
"All statements are required"
] | from x to y and y to x it takes 15hrs
let time taken by train be a and by bus be b
so a+b=15
train takes 3 hrs less i.e,
a+a=12
2a=12
a=6
6+b=15
b=9
2b=18hrs
ANSWER:C
The answer is: C | C |
mathematics | From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done? | [
"756",
"800",
"956",
"850",
"650"
] | We may have (3 men and 2 women) or (4 men and 1 woman) or (5 men only).
Required number of ways = (7C3 x 6C2) + (7C4 x 6C1) + (7C5)
= (525 + 210 + 21)
= 756.
ANSWER A
The answer is: A | A |
mathematics | The average marks of Riya,Siya,Lisa was 80. The average marks of Siya,Lisa,Hena was 85. If marks of Hena be 84, what was the mark of Riya? | [
"39",
"69",
"37",
"42",
"None of these"
] | Explanation:
R+S+L=80*3=240
S+L+H=85*3=255
Also, marks of Hena=84
marks of Riya = 240+84-255 = 69
Answer: Option B
The answer is: B | B |
mathematics | Find the value of 80641 x 9999 = m? | [
"807518799",
"806436469",
"807538799",
"806329359",
"817431046"
] | 80641 x 9999 = 80641 x (10000 - 1)
= 80641 x 10000 - 80641 x 1
= 806410000 - 80641
= 806329359
D
The answer is: D | D |
mathematics | Which of the following describes all the values of x for which 8−4x < 18x−18? | [
"x > 5/7",
"x < 5/11",
"5/11 < x",
"x > 13/11",
"13/11 > x"
] | 8−4x < 18x−18
i.e. 8+18 < 18x+4x
i.e. 26 < 22x
i.e. x>26/22
i.e. x>13/11
Answer: Option D
The answer is: D | D |
mathematics | A shopkeeper sold an book offering a discount of 5% and earned a profit of 42.5%. What would have been the percentage of profit earned if no discount was offered? | [
"140",
"120",
"130",
"110",
"150"
] | Let C.P. be $100.
Then, S.P. = $142.50
Let marked price be $x. Then, 95/100 x = 142.5
x = 14250/95 = $150
Now, S.P. = $150, C.P. = $100
Profit % = 50%.
E
The answer is: E | E |
mathematics | The avg weight of A,B & C is 84 kg. If D joins the group, the avg weight of the group becomes 80 kg.If another man E who weights is 7 kg more than D Replaces A, Then the avgof B,C,D&E becomes 79 kg. What is the weight of A? | [
"45",
"65",
"75",
"79",
"90"
] | A + B + C = 3 *84 = 252
A + B + C + D = 4 * 80 = 320 ---- (i)
So, D = 68& E = 68 + 7 = 75
B + C + D +E = 79 * 4 = 316 --- (ii)
From Eq. (i) & (ii)
A-E = 320 – 316 = 4
A = E +4 = 75 + 4 = 79
D
The answer is: D | D |
mathematics | Two stations P and Q are 110 km apart on a straight track. One train starts from P at 7 a.m. and travels towards Q at 20 kmph. Another train starts from Q at 8 a.m. and travels towards P at a speed of 25 kmph. At what time will they meet? | [
"10.30",
"10",
"8.45",
"9.3",
"11"
] | Explanation:
Assume both trains meet after x hours after 7 am
Distance covered by train starting from P in x hours = 20x km
Distance covered by train starting from Q in (x-1) hours = 25(x-1)
Total distance = 110
=> 20x + 25(x-1) = 110
=> 45x = 135
=> x= 3
Means, they meet after 3 hours after 7 am, ie, they meet at 10 a... | B |
mathematics | A company assigns product codes consisting of all the letters in the alphabet.How many product codes are possible if the company uses at most 6 letters in its codes, and all letters can be repeated in any one code? | [
"A.321272406",
"B.308915776",
"C.11881376",
"D.456976",
"E.17576"
] | The no of ways in which the company can make codes of 1 letter : 26
# for 2 letters : 26*26 = 676
# for 3 letters : 26 * 26*26 =17576
# for 4 letters : 26 * 26*26*26 =456976
# for 5 letters : 26 * 26*26*26*26 =11881376
# for 6 letters : 26 * 26*26*26*26*26 =308915776
The total : By adding all of them , 26+676+17576+456... | A |
mathematics | The average (arithmetic mean) of 4 positive integers is 40. If the average of 2 of these integers is 45, what is the greatest possible value that one of the other 2 integers can have? | [
"55",
"69",
"100",
"109",
"115"
] | a + b + c + d =160
a + b = 90
c + d =70
Greatest possible = 69 (Just less than 1)
Answer = B
The answer is: B | B |
mathematics | The average (arithmetic mean) of 27, 32, and 64 is 6 less than the average of 29, 42, and x. What is x? | [
"62",
"64",
"66",
"68",
"70"
] | The average of 27, 32, and 64 is 41.
The average of 29, 42 and x is 47.
Then 29 + 42 + x = 141.
x = 70.
The answer is E.
The answer is: E | E |
mathematics | Number of prime numbers between 10 and 20 is | [
"4",
"5",
"6",
"7",
"9"
] | total 4=1, 13, 17, 19
ANSWER:A
The answer is: A | A |
mathematics | A survey of n people in the town of Eros found that 50% of them preferred Brand A. Another survey of 100 people in the town of Angie found that 60% preferred Brand A. In total, 55% of all the people surveyed together preferred Brand A. What is the total number of people surveyed? | [
"50",
"100",
"150",
"200",
"250"
] | It is simply a weighted average question. Since the given average of 50% and 60% is 55% (right in the middle), it means the number of people surveyed in Eros (n) is same as the number of people surveyed in Angie.
So n = 100
Total = 100 + 100 = 200
Answer (D)
The answer is: D | D |
mathematics | The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is: | [
"127 m",
"277 m",
"245 m",
"217 m",
"219 m"
] | Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30 = 25/2 => 2(130 + x) = 750 => x = 245 m.
Answer: C
The answer is: C | C |
mathematics | A team has to design a flag. The team has four yellow strips of cloth and five green strips of cloth that they must use as is to make the flag. How many different flags can the team design with the materials at hand? | [
"24",
"120",
"126",
"140",
"156"
] | The # of permutations of total 4+5=9 strips where 4 are identical yellow and 5 are identical green is 9!/(4!*5!)=126 (note that they must use all the materials at hand, also I guess that the strips must be either only vertical or only horizontal).
Answer: C.
The answer is: C | C |
mathematics | In how many ways can the letters of the word SPHERICAL be arranged such that all the vowels always appear together? | [
"9!*6!",
"9!",
"7!*3!",
"9!*3!",
"6!*3!"
] | The 9 letters can be grouped into 6 consonants and one set of 3 vowels.
The number of ways to arrange 7 units is 7!
Then, for each arrangement, the 3 vowels can be arranged in 3! ways.
The total number of arrangements is 7!*3!
The answer is C.
The answer is: C | C |
mathematics | Kathleen can paint a room in 4 hours, and Anthony can paint an identical room in 5 hours. How many hours would it take Kathleen and Anthony to paint both rooms if they work together at their respective rates? | [
"8/15",
"40/9",
"15/8",
"9/4",
"15/4"
] | (1/4 + 1/5)t=2
t= 40/9
Answer: B
The answer is: B | B |
mathematics | The probabilities of solving a question by 3students A, B & C are 1/2,1/3 &1/4, respectively. The probability that the problem will be solved is? | [
"1/3",
"3/4",
"3/5",
"3/7",
"4/7"
] | Sol. First, we find the probability of not solving the problem x PTO x = (1 — D x - D x - D
1 2 3 1 =iXiX71=4;
1 3 Required probability 3/4
B
The answer is: B | B |
mathematics | Ashwin rented a power tool from a rental shop. The rent for the tool was $25 for the first hour and $10 for each additional hour. If Ashwin paid a total of $125, excluding sales tax, to rent the tool, for how many hours did she rent it? | [
"11",
"12",
"15",
"18",
"16"
] | 25 + 10n = 125
n = 10
Total time = n+1 hrs = 10+1 hrs = 11 hrs
Answer : A
The answer is: A | A |
mathematics | The curved surface of a sphere is 64 π cm2. Find its radius? | [
"9",
"8",
"4",
"5",
"6"
] | 4 πr2 = 64 => r = 4
Answer:C
The answer is: C | C |
mathematics | The average of four consecutive odd numbers is 24. Find the largest number. | [
"25",
"27",
"29",
"31",
"32"
] | Explanation:
Let the numbers are x, x+2, x+4, x+6, then
=>x+(x+2)+(x+4)+(x+6)4=24
=>4x+12)4=24
=>x+3=24=>x=21
So largest number is 21 + 6 = 27
Answer: Option B
The answer is: B | B |
mathematics | Suppose son name is 120,his brother name is 150 and his mother name is 230.find out his father's name??? | [
"190",
"210",
"230",
"240",
"260"
] | since difference between all name is =30
so father's name will be 230+30=260.
ANSWER:E
The answer is: E | E |
mathematics | The consumption of diesel per hour of a bus varies directly as square of its speed. When the bus is travelling at 70 kmph its consumption is 1 litre per hour. if each litre costs $70 and other expenses per hous is $ 70, then what would be the minimum expenditure required to cover a distance of 700 Km? | [
"1000",
"1500",
"1240",
"1630",
"1400"
] | 70 kmph consumption is 1 lt/hr
so 700 km will take 10 hrs and the consumption is 10 lt for entire distance.
1 lt costs $70
so 10 lt costs $700
extra expenses for 1 hr - $70
10 hrs - $700
total expense - $700 + $700 = $1400
Answer : E
The answer is: E | E |
mathematics | Two trains are running in opposite directions with the same speed. If the length of each train is 240 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is: | [
"68 km/hr.",
"32 km/hr.",
"34 km/hr.",
"35 km/hr.",
"72 km/hr."
] | Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (240 + 240 )/12
2x = 40
x = 20.
Speed of each train = 10 m/sec = 20 x 18/5 km/hr = 72 km/hr.
answer :E
The answer is: E | E |
mathematics | Aaron will jog from home at 5 miles per hour and then walk back home by the same route at 10 miles per hour. How many miles from home can Aaron jog so that he spends a total of 3 hours jogging and walking? | [
"15",
"18",
"10",
"12",
"14"
] | xyt/(x+y)
x= 5, y=10, t= 3
5*10*3/5+10 = 150/50 = 10
Answer : C
The answer is: C | C |
mathematics | A palindrome is a number that reads the same forward and backward, such as 464. How many odd five-digit numbers are palindromes? | [
"40",
"400",
"500",
"5,000",
"100,000"
] | 5th digit 1,3,5,7,9
4th digit 0 through 9
3rd digit 0 through 9
i.e 10*10*5 = 500 numbers
first and second digit is going to be same as 4th and 5th. so it would still be 400 numbers.
Answer is C.
The answer is: C | C |
mathematics | In a certain store, the profit is 150% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit? | [
"30%",
"70%",
"100%",
"50%",
"120%"
] | Let C.P. = Rs. 100. Then, profit = Rs. 150, S.P. = Rs. 250
New C.P. = 125% of Rs. 100 = Rs. 125.
New S.P. = Rs. 250
Profit = 250 - 125 = Rs. 125
Required percentage = 125/250 * 100 = 50%
ANSWER:D
The answer is: D | D |
mathematics | A train sets off at 2 p.m. at the speed of 70 kmph. Another train starts at 3:30 p.m. in the same direction at the rate of 85 kmph. At what time the trains will meet? | [
"10.18 p.m",
"10.29 p.m",
"10.30 p.m",
"10.38 p.m",
"10.32 p.m"
] | D = 70 * 1 ½ = 105 km
RS = 85 – 70 = 15
T = 105/15 = 7 h
3.30 + 7 h = 10.30 p.m.
Answer:C
The answer is: C | C |
mathematics | The bus uses 80 gallons of fuel to fly 320 miles. At this rate, how many gallons of fuel are needed for a 800 mile bus? | [
"100",
"300",
"150",
"200",
"50"
] | Number of gallons of fuel per mile = 320 /80 = 4 gallons per mile
Number of gallons of fuel for a 800 mile bus = 800/4= 200
ANSWER:D
The answer is: D | D |
mathematics | The area of sector of a circle whose radius is 12 metro and whose angle at the center is 42° is? | [
"52.5",
"52.9",
"52.8",
"52.1",
"52.2"
] | 42/360 * 22/7 * 12 * 12 = 52.8 m2
Answer: C
The answer is: C | C |
mathematics | Sebastian bought a meal at a restaurant
and left a 15% tip. With the tip, he paid
exactly $36.11. How much did the meal cost without the tip? | [
"$28.98",
"$29.91",
"$30.40",
"$30.60",
"$30.85"
] | The tip is a percent increase of 15%, which is 115%. Let x equal the price before the tip.
Thus, 115% of this price equals $36.11:
1.15x = 36.11
Divide both sides by 1.15:=>x=36.11/1.15=31.40
correct answer C)$31.40
The answer is: C | C |
mathematics | John distributes his pencil among his 4 friends Rose, Mary, Ranjan, and Rohit in the ratio 1/1 : 1/3 :1/4:1/5 . What is the minimum no. of pencils that the person should have? | [
"45",
"65",
"98",
"107",
"198"
] | Rakesh : Rahul : Ranjan : Rohit = 1 / 1 : 1 / 3 : 1 / 4 : 1 / 5
Step 1: At First we need to do is LCM of 2,3,4 and 5 is 60.
Step 2: Then pencil are distributed in ratio among friends,
Rakesh = ( 1 / 1 x 60 ) = 60.
Rahul = ( 1 / 3 x 60 ) = 20.
Ranjan = ( 1 / 4 x 60 ) = 15.
Rohit = ( 1 / 5 x 60 ) = 12.
Step 3: Total numb... | D |
mathematics | Three table runners have a combined area of 204 square inches. By overlapping the runners to cover 80% of a table of area 175 square inches, the area that is covered by exactly two layers of runner is 24 square inches. What is the area of the table that is covered with three layers of runner? | [
"18 square inches",
"20 square inches",
"24 square inches",
"28 square inches",
"30 square inches"
] | Total = a + b + c - (sum of EXACTLY 2-group overlaps) - 2*(all three) + Neither
80%*175 = 204 - 24 - 2*(all three) + 0
2*(all three) = 204 - 24 - 140
all three = 20
Answer: B
The answer is: B | B |
mathematics | What is the sum of the odd integers from 25 to 55, inclusive? | [
"495",
"550",
"555",
"600",
"640"
] | The mean is 40.
Sum=Mean(# of elements)
There are 16 odd numbers between 25-55 inclusive. 16*40=640
E
The answer is: E | E |
mathematics | A car averages 45 mph for the first 4 hours of a trip and averages 75 mph for each additional hour. The average speed for the entire trip was 65 mph. How many hours long is the trip? | [
"12",
"11",
"10",
"9",
"8"
] | Let the time for which car averages 75 mph = t
65*(t+4)= 45*4 + 75 t
=>10 t= 80
=> t = 8
Total duration of the trip = 8+4=12
Answer A
The answer is: A | A |
mathematics | The average age of 6 men increases by 3 years when two women are included in place of two men of ages 24 and 26 years. Find the average age of the women? | [
"37",
"26",
"34",
"18",
"11"
] | Explanation:
24 + 26 + 6 * 3 = 68/2 = 34
Answer: C
The answer is: C | C |
mathematics | Convert the 13/54 m/s into kilometers per hour? | [
"1.7",
"1.5",
"0.86",
"1.1",
"1.2"
] | 13/54 m/s = 13/54 * 18/5 = 13/15
= 0.86 kmph.
Answer: C
The answer is: C | C |
mathematics | If the price of 50 toys is 1000, then what will the price of 20 toys ? | [
"400",
"361",
"117",
"287",
"112"
] | One toy price = 1000/50 = 20
20 toy price = 20 * 20 = 400
Answer : A
The answer is: A | A |
mathematics | After allowing a discount of 15% on the marked price, the selling price is Rs. 6800 for an article. If it was sold at marked price, there would have been a profit of 60%. The cost price of the article is? | [
"Rs. 6400",
"Rs. 5600",
"Rs. 5000",
"Rs. 4800",
"None of these"
] | Given SP = Rs. 6800
Marked price = [SP(100)]/(100 - d%) = (6800 * 100)/(100 - 15) = Rs. 8000
If SP = Rs. 8000, profit = 60%
CP = [SP(100)]/(100 + 60) = (8000 * 100)/160 = Rs. 5000
ANSWER:C
The answer is: C | C |
mathematics | Ice-ColdIce-cream factory produces only tricolor ice-cream products, where each ice-cream has three stripes of different colors. The factory uses the colors pink, purple, orange, silver, blue and GREEN. How many different ice-cream products have at least one stripe out of the following colors: pink, purple or orange (a... | [
"12",
"14",
"18",
"19",
"20"
] | IMO: D - 19
There are 6C3 = 20 ways to create different colored ice cream products. Out of these 20, only 1 (Silver, Blue, GREEN) will not contain at least one of the colors pink, purple, or orange. 20 - 1 = 19.
The other way would be to calculate the number of ice cream products that contain at least one of the colors... | D |
mathematics | We give the following information about a race hedge.
There are 10 hurdles. The distance between consecutive two lines (that is to say which follow) is 9.14 m. There are 13.72 m between the starting line and the first line and the last hurdle between 14.02 m and line arrival. Each hurdle measures 106 cm in height.
What... | [
"14060cm.",
"12060cm.",
"15060cm.",
"11060cm.",
"None"
] | Solution:
[13.72+(9.14*9)+14.02+[(106÷100)*10]] =>L=[13.72+82.26+14.02+10.6] =>L=120.6m = 12060cm.
Answer B
The answer is: B | B |
mathematics | If y is an integer, then the least possible value of |23 - 8y| is | [
"5",
"2",
"3",
"4",
"1"
] | We know that 8y is a multiple of 8, so let’s first look at the multiples of 8 closest to 23. We have “16” and “24”. Let’s subtract both of these from 23 and see which one produces the smallest result. When 2y = 16, y is 2 and when 3y = 24, y is 5. Let’s start with letting y = 4.
|23-8(2)|
|23-16|
|7| = 7
Next, let’s le... | E |
mathematics | A train 1200 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is? | [
"288 m",
"256 m",
"100 m",
"278 m",
"287 m"
] | Speed = 78 * 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (1200 + x)/60
= 65/3
x = 500 m.
Answer:C
The answer is: C | C |
mathematics | In a consumer survey, 85% of those surveyed liked at least one of three products: 1, 2, and 3. 50% of those asked liked product 1, 30% liked product 2, and 20% liked product 3. If 6% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three ... | [
"5",
"9",
"15",
"20",
"25"
] | Use the forumla ;
Total = Group1 + Group2 + Group3 - (sum of 2-group overlaps) - 2*(all three) + Neither
100 = 50 + 30 + 20 - ( sum of 2) -2(6) +15
100 = 103-( sum of 2)
3 = sum of 2
so more than 1 = 9
B
The answer is: B | B |
mathematics | What is the smallest no. that should be added to 31110 to make it exactly divisible by 9? | [
"1",
"3",
"5",
"6",
"9"
] | If a number is divisible by 9, the sum of its digits must be a multiple of 9.
Here, 3+1+1+1+0=6, the next multiple of 9 is 9.
3 must be added to 31110 to make it divisible by 9
B
The answer is: B | B |
mathematics | If the personal income tax rate is lowered from 42% to 32%, what is the differential savings for a tax payer having an annual income before tax to the tune of $42400? | [
"$3500",
"$5000",
"$4240",
"$7000",
"$10000"
] | Saving = (42-32)% of 42400 = 4240.
Answer:C
The answer is: C | C |
mathematics | At a local supermarket, a box of cereal usually costs 18 dollars. This week, the supermarket sells the box of cereal for 12 dollars. How much money will you save if you buy this cereal at this supermarket? | [
"5 dollars",
"3 dollars",
"6 dollars",
"2 dollars",
"4 dollar"
] | Solution:
In this situation, there is a decrease in the price.
Saving = 18 - 12 = 6 dollars
Option C
The answer is: C | C |
mathematics | Insert the missing number. 34, 7, 37, 14, 40, 28, 43, (...) | [
"31",
"42",
"46",
"56",
"68"
] | Explanation :
We have two series here
34, 37, 40, 43, ... (Increase by 3)
7, 14, 28, ... (Multiply by 2)
Hence, next term is 28 × 2 = 56
Answer : Option D
The answer is: D | D |
mathematics | In the city of San Durango, 60 people own cats, dogs, or rabbits. If 36 people owned cats, 40 owned dogs, 10 owned rabbits, and 12 owned exactly two of the three types of pet, how many people owned all three? | [
"2",
"4",
"7",
"12",
"32"
] | Total = C + D + R - (CD + DR + CR) - 2CDR
60 = 36 + 40 + 10 - (12) - 2x
x = 7
So, answer will be C
The answer is: C | C |
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