subject stringclasses 1
value | question stringlengths 3 1.14k | options listlengths 5 5 | solution stringlengths 18 3.7k | answer stringclasses 5
values |
|---|---|---|---|---|
mathematics | A certain sum amounts to Rs.7350 in 2 years and to Rs.8575 in 3 years.find the sum and rate percent | [
"3488",
"7789",
"5400",
"2887",
"1881"
] | Explanation:
Interest for 1 year is the same whether it's simple interest or the compound interest.
Now interest of third year = 8575 - 7350 = 1225; means principal for this interest is 7350 if comound interest is takenIf 7350 is the principal interest = 1225
if 100 is the principal interest =(1225/7350) * 100 = 50/3 %... | C |
mathematics | 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 4 seconds, the speed of each train (in km/hr) is | [
"42",
"36",
"108",
"120",
"124"
] | Explanation:
Distance covered = 120+120 = 240 m
Time = 4 s
Let the speed of each train = v. Then relative speed = v+v = 2v
2v = distance/time = 240/4 = 60 m/s
Speed of each train = v = 60/2 = 30 m/s
= 30×36/10 km/hr = 108 km/hr
Answer: Option C
The answer is: C | C |
mathematics | There are 100 students in 3 sections A, B and C of a class. The average marks of all the three sections was 84. The average of B and C was 87.5 and the average marks of students in A section was | [
"20",
"37",
"28",
"11",
"12"
] | Explanation:
Numbers of students in section A = x
∴ Numbers of students in section B and C = (100 – x)
∴ x 70 + (100 – x) 87.5 = 84 100
=> 70x + 87.5 100 – 87.5x = 8400
=> 8750 – 17.5x = 8400
=> 17.5x = 8750 – 8400 => x = 20.
Answer: A
The answer is: A | A |
mathematics | If the square root of p^2 is an integer, which of the following must be true?
I. p^2 has an odd number of factors
II. p^2 can be expressed as the product of an even number of prime factors
III. p has an even number of factors | [
"I",
"II",
"III",
"I and II",
"II and III"
] | I. p^2 is a perfect square and a perfect square has pairs of factors and '1' with it. The total number of factors is odd
II. If p = 3 then p^2 = 9. The prime factors will always remain even as the p is an integer and the pairs have to come out of square root to make p an integer.
III. This is not true always. Let us sa... | D |
mathematics | Simplify : 5793405 x 9999 | [
"57928256595",
"59278256595",
"57928262559",
"59722422582",
"None of them"
] | 5793405x9999=5793405(10000-1)=57934050000-5793405=57928256595.
Answer is A
The answer is: A | A |
mathematics | Village P’s population is 800 greater than Village Q's population. If Village Q’s population were reduced by 700 people, then Village P’s population would be 7 times as large as Village Q's population. What is Village Q's current population? | [
"910",
"920",
"930",
"940",
"950"
] | P = Q+800.
P=7(Q-700).
7(Q-700)=Q+800.
6Q=5700.
Q=950.
The answer is E.
The answer is: E | E |
mathematics | What is the lowest positive integer that is divisible by 8 through 11, inclusive? | [
"999",
"7811",
"6555",
"9200",
"7920"
] | The integer should be divisible by: 8, 9, 10 and 11. The least common multiple of these integers is LCM=8*9*10*11=7920
Answer: E
The answer is: E | E |
mathematics | A fair red coin with sides marked heads and tails is to be tossed eight times. What is the probability that the coin will land tails side up more than five times? | [
"A)37/256",
"B)56/256",
"C)65/256",
"D)70/256",
"E)81/256"
] | Landing on tails more than 5 times means tails has to hit 6, 7 or 8 times.
8!/6!2! = 7*4 = 28
8!/7!1! = 8
8!/8! = 1
28 + 8 + 1 = 37/256
ans:A
The answer is: A | A |
mathematics | At Company X, senior sales representatives visit the home office once every 18 days, and junior sales representatives visit the home office once every 12 days. The number of visits that a junior sales representative makes in a 2-year period is approximately what percent greater than the number of visits that a senior r... | [
"10%",
"25%",
"33%",
"50%",
"67%"
] | Each 36-day period, senior representatives visit the home office 2 times while junior representatives visit 3 times, thus 50% more.
The answer is D.
The answer is: D | D |
mathematics | A student committee on academic integrity has 72 ways to select a president and vice president from a group of candidates. The same person cannot be both president and vice president. How many candidates are there? | [
"7",
"8",
"9",
"10",
"11"
] | xC1 * (x-1)C1=72
x^2 -x -72 =0
(X-9) (X+8) = 0
X= 9 , -8
-8 can't possible.
C
The answer is: C | C |
mathematics | Find value of X: (422+404)^2−(4×422×404)=X. | [
"234",
"267",
"324",
"356",
"577"
] | Given Equation is in the form (a+b)2−4ab where a=422 and b=404
Hence answer
=(a+b)2−4ab=(a−b)2=(422−404)2=182=324
C
The answer is: C | C |
mathematics | The radius of a circular wheel is 1.75 m, how many revolutions will it make in traveling 1 km? | [
"1000",
"817",
"278",
"268",
"280"
] | 2 * 22/7 * 1.75 * x
= 11000
x = 1000
Answer: A
The answer is: A | A |
mathematics | A set consist of 2k-1 element. What is the number of subsets of this set which contain at most k-1 elements? | [
"2^(2k-2)",
"2^(2k) - 2",
"2^(2k) -1",
"2^(2k)",
"2^(2k-1)"
] | I used k=3, so then we have
5!/2!3! + 5!/4!1! + 5!/0!5!
10 + 5 + 1 = 16
So our target is 16
Now replace in answer choices
A gives us 2^4 = 16
Hence A is the correct option
Read carefully it says at most so keep in mind that picking a small number such as 3 will help you save time since you have to list fewer outcomes
A... | A |
mathematics | A manufacturer of a certain type of screw rejects any screw whose length is less than 2.47 centimeters or greater than 2.5 + 0.03 centimeters. If k represents the length of a screw, in centimeters, which of the following inequalities specifies all the lengths of screws that are acceptable? | [
"|k + 0.03| > 2.5",
"|k — 0.03| <= 2.5",
"|k — 2.5| > 0.03",
"|k — 2.5| >= 0.06",
"2|k — 2.5| <= 0.06"
] | So, let's go through this step by step:
rejects any screw whose length is less than 2.47 centimeters or greater than 2.5 + 0.03 centimeters.
In other words, any screw that is less than: 2.47 or greater than 2.50 + 0.03 =2.53will be rejected.
If k represents the length of a screw
In other words, K is an acceptable screw... | E |
mathematics | If 1535/1038 = a+1/[b+1 /{c+(d+1/e)}]. Find a*b*c*d*e? | [
"165/2",
"175/2",
"178/3",
"187 by 2",
"197/2"
] | by expanding 1535/1038 make form like a+1/[b+1/{c+(d+ 1/e)}
=1+(497/1038) now a=1
=1+{1/(1038/497)}
=1+{1/(2+42/497)}
=1+{1/(2+1/(497/42)} now b= 2 similarly expand
c=11 d= 1 e=34/8
finally a*b*b*c*d*e
1*2*11*1*34/8
187/2
ANSWER:D
The answer is: D | D |
mathematics | A and B invests Rs.10000 each, A investing for 8 months and B investing for all the 12 months in the year. If the total profit at the end of the year is Rs.45000, find their shares? | [
"s.17000, Rs.2500",
"s.18000, Rs.35059",
"s.16000, Rs.27000",
"s.14000, Rs.25000",
"s.18000, Rs.27000"
] | The ratio of their profits A:B
= 8:12 = 2:3
Share of A in the total profit
= 2/5 * 45000
= Rs.18000 Share of A in the total profit = 3/5 * 45000
= Rs.27000
Answer: E
The answer is: E | E |
mathematics | When E is divided by 5, the remainder is 3. When y is divided by 5, the remainder is 4. What is the remainder when E + y is divided by 5? | [
"0",
"1",
"2",
"3",
"4"
] | In my view the answer should be C
E/5 has Remainder=3 -> E = 5 x Q + 3
Y/5 has a Remainder=4 -> Y = 5 x Q + 3
Combining both
((5 x Q1 + 3) + (5 x Q2 + 3))/5 =
5(Q1+Q2)/5 + 7/5 =
Q1+Q2 + 7/5
7/5 = 1+ 2/5 => Remainder 2
Answer C
The answer is: C | C |
mathematics | Compound interest of Rs.3000 at 10% per annum for 1 l/2years will be (interest compounded half yearly). | [
"Rs.473",
"Rs.374",
"Rs.495",
"Rs.347",
"None of the above"
] | 10% interest per annum will be 5% interest half yearly for 3 terms( 1 1/2 years)
So compound interest=3000[1+(5/100)]^3 - 3000=3000[(21/20)^3 -1]
=3000(9261-8000)/8000
=3*1261/8
=472.8 ~ 473
ANSWER:A
The answer is: A | A |
mathematics | Cara took out a charge account at the General Store and agreed to pay 5% simple annual interest. If she charges $54 on her account in January, how much will she owe a year later, assuming she does not make any additional charges or payments? | [
"$55.70",
"$56.20",
"$56.70",
"$57.20",
"$57.70"
] | 1.05*$54=$56.70
The answer is C.
The answer is: C | C |
mathematics | 9, 16, 18, 25, 36,49 | [
"9",
"16",
"18",
"25",
"36"
] | Each of the numbers except 18, is perfect square.
Answer: Option C
The answer is: C | C |
mathematics | The number 90 can be written as the sum of the squares of 3 different positive integers. What is the sum of these 3 integers? | [
"17",
"16",
"15",
"14",
"13"
] | 7^2+5^2+4^2=49+25+16 = 90
7+5+4 =16
Hence answer is B
The answer is: B | B |
mathematics | From a salary of an officer, 10% is deducted as house rent, 15% of the rest he spend on children's education and 10% of the balance he spends on clothes. Then, he is left with Rs. 4131. Find his total salary? | [
"6000",
"3788",
"9009",
"6788",
"2772"
] | Suppose his total salary be Rs.x, then
90% of 85% of 90% of x = 4131
\inline \Rightarrow \frac{90}{100}\times \frac{85}{100}\times \frac{90}{100}\times x=4131
\inline \therefore x=\frac{4131\times 100\times 100\times 100}{90\times 85\times 90}=6000
Hence , the salary of the officer is Rs.6000
Answer:A
The answer is: A | A |
mathematics | During the second quarter of 1984, a total of 2,976,000 domestic cars were sold. If this was 24% greater than the number sold during the first quarter of 1984, how many were sold during the first quarter ? | [
"714,240",
"2,261,760",
"2,400,000 cars",
"3,690,240",
"3,915,790"
] | Let number of cars sold in 1st quarter = x
Number of cars sold in 2nd quarter = 24% greater than the number sold during the first quarter = (1 + 24/100)x = 1.24 x
1.24 x = 2,976,000
=> x = 2,400,000
So, answer will be C
The answer is: C | C |
mathematics | Charlie, a painter, has 9 jars of paint: 4 are violet, 2 are yellow, and the rest are brown. Charlie will combine 3 jars of paint into a new container to make a new colour, which he will name according to the following conditions:
1) C1, if the paint contains 2 jars of brown paint and no violet paint
2) C2, if the pain... | [
"37/42",
"35/42",
"37/21",
"74/21",
"42/37"
] | the probability that it would be J1 or J2 is same as 1-()probability that it is C1 or C2
For C1-3C2(Brown)*2C1(Yellow)=3*2=6
For C2-3C3(all brown)=1
Total=9C3=84
1-7/84=77/84= 37/42
Answer : A
The answer is: A | A |
mathematics | If a - b = 3 and
a2+b2=29
, then find the value of ab | [
"7",
"8.5",
"10",
"12",
"14"
] | Explanation:
2ab=(a2+b2)−(a−b)2
=> 2ab = 29 - 9 = 20
=> ab = 10
Option C
The answer is: C | C |
mathematics | 5, 11, 17, 25, 33, 43, ? | [
"44",
"26",
"58",
"59",
"53"
] | E
53
The sequence is +6, +6, +8, +8, +10, ....
The answer is: E | E |
mathematics | Winners will be announced the following day at 9 AM Pacific/1 PM Eastern Time.
If A, X, Y, and Z are unique nonzero digits in the equation:
XY
*YX
____
AYZ
And Y > X, the 2-digit number XY = ? | [
"13",
"21",
"23",
"24",
"25"
] | The reasoning is as follows:-
B) can't be answer because Y<X
D) can't be answer because it XY x YX will give 4 digit number. Thus wrong
E) can't be answer because it XY x YX will give 4 digit number. Thus wrong
A) can't be answer because it XY x YX will give 3 digit number but the middle digit will not be equal to Y. T... | A |
mathematics | If w is a positive integer, then 3^w + 3^(w +1) = | [
"4^a",
"3^a − 1",
"3^(2a) + 1",
"3^a*(a − 1)",
"4(3^w)"
] | 3^w + 3^(w +1)
= 3^w + (3^w * 3^1)
= 3^w (1 + 3)
= 3^w(4)
Ans. E) 4(3^w)
The answer is: E | E |
mathematics | The sum of the present ages of a father and his son is 57 years. Six years ago, father's age was four times the age of the son. After 6 years, son's age will be: | [
"17",
"18",
"19",
"20",
"21"
] | Let the present ages of son and father be x and (57 - x) years respectively.
Then, (57 - x) - 6 = 4(x - 6)
51 - x = 4x - 24
x = 15
The son's age after 6 years will be 21.
The answer is E.
The answer is: E | E |
mathematics | 7^6 + 7^6 + 7^6 + 7^6 = | [
"7^7",
"4^6",
"4^8",
"4^9",
"4^12"
] | Hi shakticnb,
Certain Quant questions on the GMAT are just about 'organizing' the information in a specific way. If you find yourself getting confused by a prompt, think about how you might change the way that the information is presented to you.
Here, for example, we're asked for....
7^6 + 7^6 + 7^6 + 7^6 =
Now, the G... | A |
mathematics | The H.C.F of two numbers is 17 and their L.C.M is 5134. If one of the numbers is 289, then the other is? | [
"302",
"304",
"306",
"308",
"310"
] | Other number = (17 * 5134)/289
= 302.
Answer: A
The answer is: A | A |
mathematics | Ayesha’s father was 38 years of age when she was born while her mother was 34 years old when her brother four years younger to her was born. What is the difference between the ages of her parents? | [
"2 years",
"4 years",
"6 years",
"8 years",
"None"
] | EXPLANATION
Mother’s age when Ayesha’s brother was born = 34 years.
Father’s age when Ayesha’s brother was born = (38 + 4) years = 42 years.
Required difference = (42 – 34) years = 8 years.
Answer D
The answer is: D | D |
mathematics | A car averages 55 mph for the first 4 hours of a trip and averages 70 mph for each additional hour. The average speed for the entire trip was 60 mph. How many hours long is the trip? | [
"6",
"8",
"11",
"12",
"14"
] | In 4hr journey = 55*4 = 220mph
Let in the next additional hour journey = 70*x =70x mph
So, (220+70x)/(4+x)= 60
=> 220+70x = 240+60x
=> 10x = 20
=> x = 2h
So the trip is (4+x)=> 6 hours long
ANSWER:A
The answer is: A | A |
mathematics | In a certain company, the ratio of the number of managers to the number of non-managers in any department must always be greater than 7 : 37. In the company, what is the maximum number of non-managers in a department that has 11 managers? | [
"56",
"57",
"58",
"59",
"60"
] | 11/7 * 37 = 58.1
The answer is C.
The answer is: C | C |
mathematics | One man traveled a distance of 61 km in 9hrs. He traveled partly on footat 4 km/hr and partly on bicycle ta 9 km/hr. The distance traveled on foot is? | [
"8 km",
"12 km",
"16 km",
"18 km",
"20 km"
] | Let the distance travelled on foot be x km.
Then, distance travelled on bicycle = (61 -x) km.
So, x + (61 -x) = 9
4 9
9x + 4(61 -x) = 9 x 36
5x = 80
x = 16 km.
C
The answer is: C | C |
mathematics | 3 no.'s A, B & C are in the ratio of 12:15:25. If sum of these no.'s is 312, find the ratio between the difference of B & A & the difference of C & B. | [
"2 : 5",
"3 : 10",
"4 : 5",
"4 : 7",
"5 : 11"
] | We have, a = 12, b = 15, c = 25 and x = 312.
ax_ 12 X 312
a+b+c 12+15+25
— 72,
bx _ 15 X 312 B — — 90 a +b+c 12 + 15+ 25 cx 25 X 312 And, C =
a+b+c 12 + 15+ 25
...B-A=18 andC-B=60
- 150
Thus, their ratio = 18 : 60 or 3 : 10
B
The answer is: B | B |
mathematics | Given that 0 < a < b < c < d, which of the following the largest ? | [
"(c+d) / (a+b)",
"(a+d) / (b+c)",
"(b+c) / (a+d)",
"(b+d) / (a+c)",
"None of these"
] | Explanation :
For the fraction to be largest, denominator should be minimum and numerator should be maximium.
Here a and b is minimum which is in denominator of option 1. and c and d is maximum which is also in the numerator of option 1.
Hence 1.) (c+d) / (a+b
Answer : A
The answer is: A | A |
mathematics | In a boat 25 persons were sitting. Their average weight increased one kilogram when One man goes and a new man comes in. The weight of the new man is 70kgs. Find the Weight of the man who is going ? | [
"45",
"66",
"44",
"33",
"61"
] | Weight increased per person is 1 kg. Total increase in weight = 25 kgs Weight of new man is 70 kgs, (Which means his weight is 25 kgs heavier) The weight of the old man was 70 – 25 = 45 kgs
Answer: A
The answer is: A | A |
mathematics | A certain college's enrollment at the beginning of 1992 was 20 percent greater than it was at the beginning of 1991, and its enrollment at the beginning of 1993 was 25 percent greater than it was at the beginning of 1992. The college's enrollment at the beginning of 1993 was what percent greater than its enrollment at ... | [
"47.5%",
"44%",
"50%",
"35%",
"38%"
] | Suppose enrollment in 1991 was 100
Then enrollment in 1992 will be 120
And enrollment in 1993 will be 120*1.25=150
Increase in 1993 from 1991 = 150-100= 50
Answer : C
The answer is: C | C |
mathematics | Two numbers are 30% and 37% are less than a third number .How much percent is the second number less than the first? | [
"10",
"15",
"20",
"30",
"35"
] | I II III
70 63 100
70 -------- 7
100 ------ ? => 10%
ANSWER A
The answer is: A | A |
mathematics | A driver covers a certain distance by car driving at 60 km/hr and returns back to the starting point riding on a scooter at 10 km/hr. What was the average speed for the whole journey? | [
"14.2 km/h",
"17.1 km/h",
"19.3 km/h",
"21.7 km/h",
"23.5 km/h"
] | time 1 = d / 60
time 2 = d / 10
total time = d/60 + d/10 = 7d/60
average speed = total distance / total time = 2d / (7d/60) = 17.1 km/h
The answer is B.
The answer is: B | B |
mathematics | For the positive integers x, x + 2, x + 4, x + 7, and x + 27, the mean is how much greater than the median? | [
"0",
"1",
"2",
"4",
"7"
] | Mean = (x + x+2 + x+4 + x+7 + x+27)/5
=(5x+40)/5
=x+8
Median = x+4
Thus Mean - Median = x+8 - (x+4)
=4
Answer = D
The answer is: D | D |
mathematics | A 180 meter long train crosses a man standing on the platform in 6 sec. What is the speed of the train? | [
"228",
"108",
"1266",
"188",
"211"
] | S = 180/6 * 18/5 = 108 kmph
Answer: B
The answer is: B | B |
mathematics | A certain sum becomes four times itself at simple interest in eight years. In how many years does it become ten times itself? | [
"24",
"55",
"77",
"99",
"01"
] | Let the sum be Rs. x, then it becomes Rs. 4x in eight years Rs. 3x is the interest on x for eight years.
R = (100 * 3x)/(x * 8) = 300/8 %
If the sum becomes ten times itself, then interest is 9x.
The required time period = (100 * 9x)/(x * 300/8) = (100 * 9x * 8)/(x * 300) = 24 years.Answer: A
The answer is: A | A |
mathematics | Kamal obtained 81, 68, 82, 69 and 90 marks(out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks? | [
"65",
"69",
"72",
"75",
"NOne"
] | Sol.
Average
= 81 + 68 + 82 + 69 + 90 / 5)
= (390 / 5)
= 78.
Answer E
The answer is: E | E |
mathematics | Solve for x: 2x – y = (3/4)x + 6. | [
"(y + 6)/5",
"4(y + 6)/5",
"(y + 6)",
"4(y - 6)/5",
"6(y-4)/5"
] | 2x – y = (3/4)x + 6.
or, 2x - (3/4)x = y + 6.
or, (8x -3x)/4 = y + 6.
or, 5x/4 = y + 6.
or, 5x = 4(y + 6).
or, 5x = 4y + 24.
or, x = (4y + 24)/5.
Therefore, x = 4(y + 6)/5
correct answer B
The answer is: B | B |
mathematics | How many integers from 0 to 44, inclusive, have a remainder of 1 when divided by 3 ? | [
"13",
"16",
"17",
"18",
"19"
] | Explanation:
1 also gives 1 remainder when divided by 3, another number is 4, then 7 and so on.
Hence we have an arithmetic progression: 1, 4, 7, 10,..... 43, which are in the form 3n+1.
Now we have to find out number of terms.
tn=a+(n-1)d, where tn is the nth term of an AP, a is the first term and d is the common diff... | A |
mathematics | Find the length of the wire required to go 10 times round a square field containing 53824 m2. | [
"15840",
"9280",
"2667",
"8766",
"66711"
] | a2 = 53824 => a = 232
4a = 928
928 * 10 = 9280
Answer: B
The answer is: B | B |
mathematics | If e is a positive integer and 10^e – 74 in decimal notation has digits whose sum is 440, what is the value of e? | [
"40",
"44",
"45",
"46",
"50"
] | Answer E = 50
We have (10^e)-74, where the sum of the digits is 440.
100-74 = 26, so we already have 2+6 = 8 from the 440.
Because we have a power of 10, we will have numbers like 100, 1000, 10000 and so on. This minus 74 rests 26 and a lot of 9s. E.g: 1000-74 = 9926.
So dividing the 432/9 = 48, that`s the number of 9s... | E |
mathematics | A boat moves upstream at the rate of 1 km in 20 minutes and down stream 1 km in 15 minutes. Then the speed of the current is : | [
"1 kmph",
"0.5 kmph",
"3 kmph",
"2.5 kmph",
"3.5 kmph"
] | Rate upstream = (1/20 *60) = 3 kmph
Rate down stream = 1/15 * 60 = 4 kmph
Rate of the current = ½ (4-3) = 0.5 kmph
ANSWER:B
The answer is: B | B |
mathematics | The value of (4x10^7)(7x10^8) is closest to which of the following? | [
"10^15",
"10^12",
"10^13",
"10^14",
"10^17"
] | multiplying these we get,
28 x 10^7 x 10^8
= 2.8x 10^16
which is closer to 10^17
Answer: E
The answer is: E | E |
mathematics | In how many ways can 5 different candies be distributed in 4 identical baskets? | [
"120",
"51",
"24",
"5^4",
"4^5"
] | 5-N-N-N : 5C5 = 1 - OK
4-1-N-N : 5C4 *1C1 = 5 - OK
3-2-N-N : 5C3*2C2 = 10 - OK
3-1-1-N : 5C3*2C1*1C1 = 20 - NO - only 10, once you decide to split the remaining two after choosing the 3 before, no factor of 2 needed
2-2-1-N : 5C2*3C2*1C1 = 30 - NO - it is 15 = 30/2; baskets being identical, doesn't matter which group o... | B |
mathematics | What is x if x + 3y = 10 and y = 3? | [
"1",
"2",
"3",
"4",
"5"
] | Substitute y by 3 in x + 3y = 10
x + 3(3) = 10
x + 9 = 10
If we substitute x by 1 in x + 9 = 10, we have 1 + 9 = 10. Hence
x = 1 correct answer A
The answer is: A | A |
mathematics | Linda spent 4/5 of her savings on furniture and the rest on a TV. If the TV cost her $100, what were her original savings? | [
"$900",
"$300",
"$500",
"$700",
"$800"
] | If Linda spent 4/5 of her savings on furniture, the rest
5 / 5 - 4 / 5 = 1 / 5 on a TV
But the TV cost her $100. So 1 / 5 of her savings is $100. So her original savings are 5 times $100 = $500
correct answer C
The answer is: C | C |
mathematics | If 15 machine can finish a job in 36 days, then how many more machines would be needed to finish the job in one -fourth less time? | [
"a. 5",
"b. 8",
"c. 10",
"d. 12",
"e. 16"
] | You might think of this in a management context - we can use the principle of 'person-hours' to solve any problem where we have identical workers. So, using simpler numbers, suppose you know that 6 identical employees, working simultaneously, would finish a job in 5 hours. Then that job requires 6*5 = 30 total hours of... | A |
mathematics | Pipes A and B can fill a tank in 2 and 3 hours. Pipe C can empty it in 6 hours. If all pipes are opened together, then the tank will be filled in? | [
"3/2hr",
"1/2hr",
"1hr",
"9/7hr",
"5/3hr"
] | Net part filled in 1 hour = 1/2 + 1/3 - 1/6 = 2/3
The tank will be full in 3/2 hr
Answer is B
The answer is: B | B |
mathematics | What is the sum of all 3 digit numbers that leave a remainder of '2' when divided by 3? | [
"897",
"164,850",
"164,749",
"149,700",
"156,720"
] | Explanatory Answer
Step 1: Identify the series
The smallest 3 digit number that will leave a remainder of 2 when divided by 3 is 101.
The next couple of numbers that will leave a remainder of 2 when divided by 3 are 104 and 107.
The largest 3 digit number that will leave a remainder of 2 when divided by 3 is 998.
It is... | B |
mathematics | In a barrel of juice there is 20 liters; in a barrel of beer there are 80 liters. If the price ratio between barrels of juice to a barrel of beer is 3:4, what is the price ratio between one liter of juice and one liter of beer? | [
"3:2.",
"2:1.",
"3:1.",
"4:3.",
"3:4"
] | Price of 20 L juice= 3x
1L= 3x/20
Price of 80 L beer= 4x
1L= 4x/80
Ratio of 1 L price = 3x/20/4x/80= 3:1
C is the answer
The answer is: C | C |
mathematics | If money is invested at r percent interest, compounded annually, the amount of investment will double in approximately 70/r years. If Pat's parents invested $ 7000 in a long term bond that pays 8 percent interest, compounded annually, what will be the approximate total amount of investment 18 years later, when Pat is r... | [
"$28000",
"$15000",
"$12000",
"$10000",
"$9000"
] | Since investment doubles in 70/r years then for r=8 it'll double in 70/8=~9 years (we are not asked about the exact amount so such an approximation will do). Thus in 18 years investment will double twice and become ($7,000*2)*2=$28,000 (after 9 years investment will become $7,000*2=$14,000 and in another 9 years it'll ... | A |
mathematics | A clock store sold a certain clock to a collector for 45 percent more than the store had originally paid for the clock. When the collector tried to resell the clock to the store, the store bought it back at 25 percent of what the collector had paid. The shop then sold the clock again at a profit of 55 percent on its bu... | [
"$149.55",
"$134.56",
"$175.43",
"$158.65",
"$255.45"
] | Now, in the question above, lets say the original cost of the clock to store was C$ and then it sold the same to the collector at 45% profit.
This means the clocks' selling price was C (1.45) and this becomes cost price for the collector.
Now, when the collector tries to sell the same clock to the store, the store buys... | D |
mathematics | Find the odd man out. 49, 65, 81, 144, 169, 225, 441 | [
"49",
"65",
"81",
"144",
"169"
] | Explanation :
Each of the given numbers except 65 is a perfect square
Answer : Option B
The answer is: B | B |
mathematics | The value of a laptop depreciates at the rate of 30% every year. It was purchased 2 years ago. If its present value is Rs. 3430, its purchase price was | [
"6000",
"6500",
"7000",
"7500",
"8000"
] | Explanation:
= Rs.7000
Answer: C
The answer is: C | C |
mathematics | One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 39 minutes, then the slower pipe alone will be able to fill the tank in | [
"144 mins",
"140 mins",
"136 mins",
"156 minw",
"None of these"
] | Explanation:
Let the slower pipe alone fill the tank in x minutes
then faster will fill in x/3 minutes.
Part filled by slower pipe in 1 minute = 1/x
Part filled by faster pipe in 1 minute = 3/x
Part filled by both in 1 minute =
1/x+3/x=1/39
=>4/x=1/39
x=39∗4=156 mins
Option D
The answer is: D | D |
mathematics | A cyclist bikes x distance at 8 miles per hour and returns over the same path at 10 miles per hour. What is the cyclist's average rate for the round trip in miles per hour? | [
"8.1",
"8.9",
"8.6",
"8.3",
"9.0"
] | Distance = d1 = x miles
Speed = s1 = 8 miles per hour
Time = t1 = Distance/ Speed = x/8
2. Going from B to A
Distance = d2 = x miles
Speed = s2 = 10 miles per hour
Time = t2 = Distance/ Speed = x/10
3. Average Speed = Total Distance/Total Time
Total Distance = x + x = 2x
Total Time = x/10 + x/8 = x (1/10 + 1/8) = =9x/4... | B |
mathematics | The no. of girls in a class are seven times the no. of boys, which value cannever be the of total students? | [
"3",
"5",
"8",
"9",
"11"
] | Let the boys are X, then girls are 7X, total = X+7X = 8X
So it should be multiple of 8, 30 is not a multiple of 8.
C
The answer is: C | C |
mathematics | How long does a train 165 meters long running at the rate of 90 kmph take to cross a bridge 660 meters in length? | [
"33",
"72",
"55",
"82",
"62"
] | Explanation:
T = (660 + 165)/90 * 18/5
T = 33
Answer: Option A
The answer is: A | A |
mathematics | Two brothers took the GMAT exam, the higher score is X and the lower one is Y. If the difference between the two scores is equal to their average, what is the value of X/Y ? | [
"3.",
"2.",
"1/2.",
"1/3.",
"There isn't enough data to answer the question."
] | Answer is A : 3
X - Y = (X + Y)/2
Solving for X/Y =3
The answer is: A | A |
mathematics | In a certain lottery drawing, two balls are selected at random from a container with 50 balls, numbered from 1 to 50, inclusive. If the winner of the lottery is awarded a cash prize in the amount of $1,000 times the product of the numbers on the two selected balls, which of the following is a possible amount of the cas... | [
"$9.85 x 10^6",
"$2.45 x 10^6",
"$1.00 x 10^7",
"$1.05 x 10^7",
"$9.90 x 10^7"
] | The max product of any two balls can be 49 * 50 = 2450 = 2.45 * 10^3
If you multiply it by $1000 the max amount will be 2.45 * 10^6.
B
The answer is: B | B |
mathematics | A sum of money deposited at compound interest (compounded yearly) amounts to $1210 in 2 years and to $1452 in 3 years. What is the interest rate? | [
"20%",
"10%",
"60%",
"70%",
"30%"
] | 1452 - 1210 = 242
242 / 1210 = 0.2 = 20%
The answer is A.
The answer is: A | A |
mathematics | An analysis of the monthly incentives received by 5 salesmen : The mean and median of the incentives is $7000. The only mode among the observations is $12,000. Incentives paid to each salesman were in full thousands. What is the difference between Q the highest and the lowest incentive received by the 5 salesmen in the... | [
"$4000",
"$5000",
"$9000",
"$11,000",
"$13,000"
] | Break down the question in to steps:
Step #1: incentives received by 5 salesmen -->abcde
Step #2: mean and median of the incentives is $7000: via number properties --> total incentives = 7,000 * 5 = 35, 000ab7,000de
Step #3: only mode among the observations is $12,000: mode is the value that appears most often in a set... | D |
mathematics | If b/x = 7/4 and b/y =7/ 5, then (y -x) = | [
"b/2",
"b/7",
"2b",
"3b/7",
"b"
] | Ratio 1:
4b = 7x
Ratio 2:
5b = 7y
y -x = b/7
Answer is B
The answer is: B | B |
mathematics | Of the three-digit positive integers whose three digits are all different and nonzero, how many are odd integers greater than 700? | [
"84",
"91",
"100",
"105",
"243"
] | Number of combinations for type 1 : 1*7*4 = 28
Number of combinations for type 2: 1*7*5 = 35
Number of combinations for type 3 : 1*7*4 = 28
Thus, total numbers possible = 28+35+28 = 91.
B is thus the correct answer
The answer is: B | B |
mathematics | A person has to cover a distance of 10km in 1hour. If he covers one half of the distance in half of the total time; to cover the remaining distance in the remaining time, his speed must be? | [
"5km/hr",
"8km/hr",
"10km/hr",
"12km/hr",
"15km/hr"
] | Remaining distance = 5km
Remaining time = 1/2 * 60 = 30min = 1/2 hour
Required speed = 5*2 = 10km/hr
Answer is C
The answer is: C | C |
mathematics | The arithmetic mean of the set S = {5, K, 4, 10, M, 5} is 6. If K and M are integers, and K ≠ M, what is the median of the numbers in the set? | [
"4",
"4.5",
"5",
"5.5",
"6"
] | The sum of the numbers is 6*6 = 36
K+M = 36 - 10 - 5 - 5 - 4 = 12
Since K ≠ M, K and M do not equal 6.
Thus one of the two numbers is 5 or less and one is 7 or more.
Then middle two numbers in the set are 5 and 5.
The median is 5.
The answer is C.
The answer is: C | C |
mathematics | The sum of two numbers is 65. Their difference is 5. The bigger number is | [
"20",
"25",
"30",
"35",
"45"
] | X + Y = 65
X - Y = 5
Adding 2X = 70 ==> X = 35 and Y = 65 - 35 = 30
Bigger number is X = 35
Answer D.
The answer is: D | D |
mathematics | A wire in the form of a circle of radius 3.5 m is bent in the form of a rectangule, whose length and breadth are in the ratio of 6 : 5. What is the area of the rectangle? | [
"17 cm2",
"30 cm2",
"18 cm2",
"19 cm2",
"15 cm2"
] | The circumference of the circle is equal to the permeter of the rectangle.
Let l = 6x and b = 5x 2(6x + 5x) = 2 * 22/7 * 3.5
=> x = 1
Therefore l = 6 cm and b = 5 cm Area of the rectangle
= 6 * 5
= 30 cm2
Answer: B
The answer is: B | B |
mathematics | Cereal A is 11% sugar by weight, whereas healthier but less delicious Cereal B is 2% sugar by weight. To make a delicious and healthy mixture that is 4% sugar, what should be the ratio of Cereal A to Cereal B, by weight? | [
"2:5",
"1:3",
"2:7",
"3:4",
"1:5"
] | 2% is 2%-points below 4% and 11% is 7%-points above 4%.
The ratio of A:B should be 2:7.
The answer is C.
The answer is: C | C |
mathematics | In a division sum, the quotient is 120, the divisor 456 and the remainder 333, find the dividend? | [
"23504",
"34545",
"55053",
"23434",
"23456"
] | Explanation:
120 * 456 + 333 = 55053
C
The answer is: C | C |
mathematics | At the end of the first quarter, the share price of a certain mutual fund was 30 percent higher than it was at the beginning of the year. At the end of the second quarter, the share price was 75 percent higher than it was at the beginning of the year. What was the percent increase in the share price from the end of the... | [
"20%",
"25%",
"30%",
"34.6%",
"40%"
] | Another method is to use the formula for 2 successive percentage changes:
Total = a + b + ab/100
75 = 30 + b + 30b/100
b = 34.6
Answer (D)
The answer is: D | D |
mathematics | The mass of 1 cubic meter of a substance is 200 kg under certain conditions. What is the volume in cubic centimeters of 1 gram of this substance under these conditions? (1 kg =1,000 grams and 1 cubic meter = 1,000,000 cubic centimeters) | [
"1",
"2",
"3",
"4",
"5"
] | 200 kg - 1 cubic meter;
200,000 g - 1 cubic meter;
200,000 g - 1,000,000 cubic centimeters;
1 g - 1,000,000/200,000 = 10/2 = 5 cubic centimeters.
Answer: E.
The answer is: E | E |
mathematics | How many terms are there in 2,4,8,16……1024? | [
"10",
"14",
"16",
"18",
"20"
] | Clearly 2,4,8,16……..1024 form a GP. With a=2 and r = 4/2 =2.
Let the number of terms be n . Then
2 x 2n-1 =1024 or 2n-1 =512 = 29.
n-1=9 or n=10.
ANSWER A 10
The answer is: A | A |
mathematics | Express a speed of 72 kmph in meters per second? | [
"10 mps",
"76 mps",
"20 mps",
"97 mps",
"16 mps"
] | 72 * 5/18
= 20 mps
Answer:C
The answer is: C | C |
mathematics | Find the length of the wire required to go 12 times round a square field containing 104976 m2. | [
"15840",
"3388",
"2667",
"8766",
"15552"
] | a2 = 104976 => a = 324
4a = 1296
1296 * 12 = 15552
Answer: E
The answer is: E | E |
mathematics | Kelly and Jody packed boxes with books. If Jody packed 40% of the total number of boxes, what was the ratio of the number of boxes Kelly packed to the number that Jody packed? | [
"1 to 6",
"1 to 4",
"2 to 5",
"3 to 5",
"3 to 2"
] | Explanation:
If Jody packed 40% of the boxes then Kelly packed 60%. The ratio of the number of boxes Kelly packed to the number Jody packed is thus 60%/40%=3/2
Answer: Option E
The answer is: E | E |
mathematics | Mary can do a piece of work in 11 days. Rosy is 10% more efficient than Mary. The number of days taken by Rosy to do the same piece of work is? | [
"10",
"15",
"20",
"25",
"30"
] | Ratio of times taken by Mary and Rosy = 110:100 =11:10
Suppose Rosy takes x days to do the work.
11:10 :: 11:x => x= 10 days.
Hence, Rosy takes 10 days to complete the work.
Answer: A
The answer is: A | A |
mathematics | A and B are two multiples of 14, and Q is the set of consecutive integers between A and B, inclusive. If Q contains 12 multiples of 14, how many multiples of 7 are there in Q? | [
"20",
"21",
"22",
"23",
"24"
] | Halfway between the multiples of 14, there will be another multiple of 7.
The total number of multiples of 7 is 12+11 = 23.
The answer is D.
The answer is: D | D |
mathematics | If x and y are positive integers and y ≠ 1, then xy(y −1) is | [
"Always even",
"Always odd",
"Odd only when x is odd",
"Even only when y is even",
"Odd only when xy is odd"
] | Expression is xy(y-1). We can ignore x and only work with y.
If y = even -> entire expression is even since anything multiplied by even is even
If y = odd, y-1 -> even -> entire expression is even since anything multiplied by even is even
Hence, entire expression will always be even.
Answer (A).
The answer is: A | A |
mathematics | What is the rate percent when the simple interest on Rs.800 amount to Rs.400 in 2 Years? | [
"5%",
"6%",
"2%",
"25%",
"1%"
] | Interest for 2yrs = 400
Interest for 1yr = 200
Interest rate = 200/800 x 100 = 25%
Answer : D
The answer is: D | D |
mathematics | If Yury has been writing programming code for 16 hours at a rate of 5 lines of code per 20 seconds, how many lines of code has he written? | [
"126(10^2)",
"126(10^3)",
"144(10^2)",
"1.26(10^7)",
".126(10^9)"
] | 5 LINES IN 20 SECONDS
SO FOR 1 MINUTE ( 5 X 3 = 15 LINES )
I HOUR = 60 MINUTES
15 X 60 = 900 LINES IN AN HOUR
16 HOURS = 900 X 16 = 144(10^2)
ANSWER C
The answer is: C | C |
mathematics | Rs.1500 is divided into two parts such that if one part is invested at 6% and the other at 5% the whole annual interest from both the sum is Rs.85. How much was lent at 5%? | [
"399",
"700",
"288",
"500",
"211"
] | (x*5*1)/100 + [(1500 - x)*6*1]/100 = 85
5x/100 + 90 – 6x/100 = 85
x/100 = 5
=> x = 500
Answer: D
The answer is: D | D |
mathematics | In doing a division of a question with zero remainder, a candidate took 12 as divisor instead of 21. The quotient obtained by him was 35. The correct quotient is | [
"0",
"12",
"13",
"20",
"None"
] | Sol.
Dividend = (12 x 35) = 420.
Now, dividend = 420 and divisor = 21.
∴ Correct quotient = 420 / 21 = 20.
Answer D
The answer is: D | D |
mathematics | The average weight of 20 persons sitting in a boat had some value. A new person added to them whose weight was 45 kg only. Due to his arrival, the average weight of all the persons decreased by 5 kg. Find the average weight of first 20 persons? | [
"55",
"56",
"57",
"58",
"60"
] | 20x + 45 = 21(x – 5)
X=60
ANSWER:E
The answer is: E | E |
mathematics | Hariprasad and Madhusudan started a business, investing sums in the ratio of 2 : 3. If Hariprasad had invested an additional amount of 10,000 the ratio of Hariprasad's investment to Madhusudan's investment would have been 3 : 2. What was the amount invested by Hariprasad? | [
"8000",
"12000",
"9000",
"Data inadequate",
"None of these"
] | Let the initial investments of Hariprasad and Madhusudan be 2x and 3x,respectively.
From the question,
2x+10000/3x=32
or, 4x + 20000 = 9x
\ x = 4000
\ Amount invested by Hariprasad = 2x = 8000
Answer A
The answer is: A | A |
mathematics | what is the value of y if the greatest common divisor of (y-4)!,(y+1)!, and (y+2)! is 720. | [
"12",
"10",
"9",
"7",
"8"
] | GCD of (y-4)!,(y+1)!, and (y+2)! is 720. Find y.
Best way to find n is substitute each of the answer and find out the correct one.
Only option B gave the correct answer.
Option B: 10 and find GCD or 6!, 11! and 12!. 6! itself is 720 and 6! which is contained in the other two factorials. This satisfies the condition, he... | B |
mathematics | Consider there is an elevator and you are at the upside and coming down using elevator. You walk 20 steps and then you stop, then you reach to the ground in 10 minutes. If you walk 10 steps and then stop, then you reach to the ground in 20 minutes. What is the speed of the elevator and How many steps are there?? | [
"1 step/min",
"2 step/min",
"3 step/min",
"4 step/min",
"5 step/min"
] | Let e be the speed of the elevator, n be the no. of steps
n = 20 + 10*e = 10+20*e
e=1
n=30
No. of steps : 30
Speed : 1 step/min
ANSWER:A
The answer is: A | A |
mathematics | The greatest number of four digits which is divisible by 15, 25, 40 and 75 is: | [
"9000",
"9400",
"9600",
"9800",
"9200"
] | Greatest number of 4-digits is 9999.
L.C.M. of 15, 25, 40 and 75 is 600.
On dividing 9999 by 600, the remainder is 399.
Required number (9999 - 399) = 9600.
Answer: Option C
The answer is: C | C |
mathematics | In a certain fish pond, 1 out of every 120 bass are caught. If 3 out of every 4 caught bass are fried for dinner, and there are 9 fried bass for dinner, how many bass total are there in the pond? | [
"5,000",
"700",
"500",
"1,222",
"1,440"
] | Proportions: Let B = bass, and Bc = bass caught, and Bcf = caught fried bass.
9Bcf/xBc = 3Bcf/4Bc
xBc = 12Bc
12Bc/yB = 1Bc/120B
yB = 1,440B
Answer: E
The answer is: E | E |
mathematics | If an amount of Rs 42,240 is distributed equally
amongst 22 persons, how much amount would each
person get? | [
"Rs 1905",
"Rs 1920",
"Rs 745",
"Rs 765",
"None"
] | Required amount =42240/22 = Rs 1920
Answer B
The answer is: B | B |
mathematics | The population of a town is 8000. It decreases annually at the rate of 20% p.a. What will be its population after 2 years? | [
"4300",
"4500",
"5120",
"5230",
"5366"
] | Formula :
( After =100 denominator
Ago = 100 numerator)
8000 × 80/100 × 80/100 = 5120
C
The answer is: C | C |
mathematics | The length of the bridge, which a train 130 m long and traveling at 45 km/hr can cross in 30 sec is? | [
"227",
"268",
"245",
"299",
"271"
] | Speed = 45 * 5/18 = 25/2 m/sec.
Time = 30 sec
Let the length of bridge be x meters.
Then, (130 + x)/30 = 25/2
x = 245 m.
Answer:C:
The answer is: C | C |
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