divelab/Sys2Bench huggingface dataset:
Question: If x is an integer and (x)(x^2)(x^3)(x^6) is positive, which of the following could be negative?
Options:
A)x^4
B)(x)(x^3)
C)(x)(x)
D)x + x^7
E)3x^2
Rationale: A) X^4 - always positive (or 0).
B) X(X^3) = X^4 - Again always positive (or 0).
C) (x)(x) = X^2 - Again always positive (or 0).
D) x+x^7 - Could be -ve if x is -ve.
E) 3X^2 - again always positive (or 0)
Answer D.
Answer: D
Question: A six-sided die is rolled once. What is the probability that the number rolled is greater than 4?
Options:
A)2 / 3
B)2 / 6
C)3 / 3
D)4 / 5
E)2 / 4
Rationale: Only 5 & 6 so, 2 / 6
correct answer B
Answer: B
Question: Sam’s car was fined when he gave Joe and Peter a ride, so they decided to help Sam pay the fine. Joe paid $4 more than 1/4 of the fine and Peter paid $4 less than 1/3 of the fine, leaving pay $5 less than 1/2 the fine to complete the payment. What fraction of the fine did Sam pay?
Options:
A)$30
B)$25
C)$35
D)$40
E)$45
Rationale: Call the fine F. Joe paid (1/4)F + 4 and Peter paid (1/3)F – 4, leaving (1/2)F – 5 left. If we add those three up, they should add up to F.
F = [(1/4)F + 4] + [(1/3)F – 4] + [(1/2)F – 5]
F = (1/4)F + (1/3)F + (1/2)F – 5
Multiply all terms by 12 to clear the fractions.
12F = 3F + 4F + 6F – 60
12F = 13 F – 60
–F = – 60
F = 60
Well, if the fine cost $60, then Sam paid the part not covered by Joe or Peter. Half the fine is $30, and Sam paid $5 less than this: $25.
Answer = B
Answer: B
Question: The product of the first seven positive multiples of three is closest to which of the following powers of 10?
Options:
A)10^9
B)10^8
C)10^7
D)10^6
E)10^5
Rationale: The product will be 3^7 * 1 * 2 * 3 * 4 * 5 * 6 * 7
=3^7 * 5140
= 9^3 * 15420
= ~135000 * 9 * 9
= ~1220000 * 9
= ~11000000 which is very close to 10^7
The correct answer is therefore (C)
Answer: C
Question: Calculate the number of tanks of 50x50x20m size needed to discharge crude oil from a cargo ship of volume 120000 m3 and is 90% full, if the tanks can only be filled up to 95%.
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: Volume of the tank that needed to be filled=50x50x20x0.95=47500
Volume of the crude in ship=120000x0.9=108000
No. of tanks needed to discharge the ship=108000/47500= 2.27
Which is 3 tanks
Answer: C
Answer: C
Question: A bag contains 6 black and 9 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
Options:
A)4
B)4/3
C)4/5
D)4/9
E)3/5
Rationale: Let number of balls = (6 + 9) = 15.
Number of white balls = 9.
P (drawing a white ball) = 9/15=3/5
Hence Answer is E
Answer: E
Question: Average age of boys in a class is 16 years and average age of girls is 15 years, what is the average age of all
Options:
A)15.5
B)15
C)16
D)Cant be computed
E)17
Rationale: Explanation:
As number of girls and boys is not given so result cant be computed
Answer: Option D
Answer: D
Question: The C.P of 10 pens is equal to the S.P of 5 pens. Find his gain % or loss%?
Options:
A)50%
B)40%
C)30%
D)60%
E)20%
Rationale: 10 CP = 5 SP
10 --- 5 CP gain
100 --- ? => 50%(gain)
Answer: A
Answer: A
Question: The first photo shoot takes 3 minutes long and then the following shoots are taken at a rate of 23 seconds/shoot as the model is already at the scene. What is the maximum number of photo shoots taken under 10 minutes ?
Options:
A)13
B)14
C)15
D)16
E)19
Rationale: a must be an integer as it is the number shoots at a rate of 23sec/shoot
3*60 + 23a = 10*60
23a = 420
a = 18
The total number of shoots -->1 +18 = 19 and
20th shoot will be taken at 617 seconds which is above 10 minutes
ANSWER: E
Answer: E
Question: The average age of a group of 10 students is 20 years. If 2 more students join the group, the average age increases by 1 year. The average age of the new students is
Options:
A)23
B)21
C)19.5
D)20
E)22.5
Rationale: Total age of 10 students = 10 * 20 = 200 and the total age of 16 students = 21*15 = 315.
Let the average age of 2 new students be x.
Therefore total age of the new students = 2x.
So total age of 12 student =200 +5x=315, x=23
Hence, the correct answer is A.
Answer: A
Question: Three candidates contested in an election and received 6136, 7636, 11628 votes respectively. What is the percentage of the total votes did the winning candidate get?
Options:
A)46%
B)49%
C)57%
D)51%
E)62%
Rationale: Total number of votes polled = 6136+7636+11628 = 25400
Required percentage = 11628*100/25400 = 46%
Answer is A
Answer: A
Question: A sock drawer contains seven socks, each one a different solid color. The colors of the socks are red, orange, yellow, green, blue, indigo, and violet. If the socks are laid next to each other, how many different arrangements of socks could be made?
Options:
A)24
B)240
C)1,024
D)2,520
E)5,040
Rationale: I see no condition for arrangement.
So 7! ways - 5,040
ANS option E is correct answer..
Answer: E
Question: A farming field can be ploughed by 6 tractors in 4 days. When 6 tractors work together, each of them ploughs 120 hectares a day. If two of the tractors were moved to another field, then the remaining 4 tractors could plough the same field in 5 days. How many hectares a day would one tractor plough then?
Options:
A)111
B)184
C)122
D)144
E)166
Rationale: If each of 6 tractors ploughed 120 hectares a day and they finished the work in 4 days, then the whole field is: 120*6*4=720*4=2880hectares. Let's suppose that each of the four tractors ploughed x hectares a day. Therefore in 5 days they ploughed
5*4*x=20*x hectares, which equals the area of the whole field, 2880 hectares.
So, we get 20x=2880
x=2880/20=144. Hence, each of the four tractors would plough 144 hectares a day.
Answer is D.
Answer: D
Question: (1/1*2)+(1/2*3)+(1/3*4)+(1/4*5)+ .............+(1/99*100)=
Options:
A)98/100
B)99/100
C)97/100
D)96/100
E)95/100
Rationale: (1/1*2)+(1/2*3)+(1/3*4)+(1/4*5)+ .............+(1/99*100)= 1-1/100= 99/100
ANSWER:B
Answer: B
Question: The length of a rectangular floor is more than its breadth by 200%. If Rs. 324 is required to paint the floor at the rate of Rs. 3 per sq m, then what would be the length of the floor?
Options:
A)28
B)37
C)18
D)38
E)39
Rationale: Let the length and the breadth of the floor be l m and b m respectively.
l = b + 200% of b = l + 2b = 3b
Area of the floor = 324/3 = 108 sq m
l b = 108 i.e., l * l/3 = 108
l2 = 324 => l = 18.
Answer:C
Answer: C
Question: How many numbers amongst the numbers 5 to 30 are there which are exactly divisible by 6 but not by 4?
Options:
A)Nil
B)1
C)2
D)3
E)More than 3
Rationale: 6,12,18,24,30 are divisible by 6.
12, 24 are divisible by 4 also.
So there are 3 numbers exactly divisible by 6 but not by 4
ANSWER:D
Answer: D
Question: For any positive integer n, n>1, thelengthof n is the number of positive primes (not necessary distinct) whose product is n. For ex, the length of 50 is 4, since 50=2x5x5. What is the greatest possible length of a positive integer less than 1000.
Options:
A)10
B)9
C)8
D)7
E)6
Rationale: you are missing something in your post:
For any positive integer n , n > 1, thelengthof n is the number of positive primes (not distinct) whose product is n. For example, the length of 50 is 3 since 50 = (2)(5)(5)
the lenght of 1000 = (2)(5)(2)(5)(2)(5) = 6
but we need n < 1000
using 2 as the base = (2)(2)(2)(2)(2)(2)(2)(2)(2) = 98 the length of 512.
the answer is C
Answer: C
Question: By selling an shirt for $300, a shop keeper gains 20%. During a clearance sale, the shopkeeper allows a discount of 10% on the marked price. His gain percent during the sale is:
Options:
A)2
B)14
C)8
D)12
E)10
Rationale: C
8%
Marked price = $300
C.P. = 100/120 * 300 = $250
Sale price = 90% of $300 = $270
Required gain % = 20/250 * 100 = 8%.
Answer: C
Question: A car covers a distance of 720 km in 6 hours. Find its speed?
Options:
A)104
B)7778
C)266
D)288
E)120
Rationale: 720/6 = 120 kmph
Answer:E
Answer: E
Question: A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.1 per sq m?
Options:
A)675
B)135
C)320
D)430
E)820
Rationale: Area = (l + b +2d) 2d
= (75 + 55 +2.5 * 2) 2*2.5 => 675
675 * 1 = Rs.675
Answer:A
Answer: A
Question: By investing in 16 2/3% stock at 64, one earns Rs. 1500. The investment made is:
Options:
A)Rs. 5640
B)Rs. 5760
C)Rs. 7500
D)Rs. 9600
E)Rs. 8600
Rationale: To earn Rs.50/3,investment =Rs.64
To earn Rs.1500,investment =(64*1500*3)/50=Rs.5760
ANSWER:B
Answer: B
Question: The balance of a trader weighs 8% less than it should. Still the trader marks up his goods to get an overall profit of 30%. What is the mark up on the cost price?
Options:
A)40%
B)19%
C)25%
D)16.66%
E)9%
Rationale: The most natural way to deal with 'weights' questions is by assuming values.
Say the trader's balance shows 100 gms. It is actually 92 gms because it weighs 8% less. Say, the cost price is $92 ($1/gm). Since he gets a profit of 30%, the selling price must be 92+(30/100)*90 = $119
Since the cost price is actually supposed to be $100 (for 100 gms) and the selling price is $119, the mark up is simply 19%
Ans : B.
Answer: B
Question: All the page numbers from a book are added, beginning at page 1. However, one page number was mistakenly added twice. The sum obtained was 1000. Which page number was added twice?
Options:
A)44
B)45
C)10
D)12
E)11
Rationale: Explanation :
sum of n natural numbers = n (n+1)/2
Here, n( n + 1)/2 = 1000 - x (where x is the number that is added twice)
=> n(n+1) < 2000 - 2x
we need to find max value n can take . We know for a product of two numbers to be max the number should be closest. We need to find out the least number whose square is higher than 2000. For example, 452 = 2025.
So our number is somewhere near to 45. it can't be more than 45 as our required product is less than 2000.
44 * 45 = 1980. So, we can have n = 44.
=> n (n+1) = 44 * 45 = 1980 = 2000 - 2 * 10.
=> x = 10.
Hence, we have 44 pages and page number 10 was added twice.
Answer : C
Answer: C
Question: A lent Rs. 5000 to B for 2 years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs. 2200 in all from both of them as interest. The rate of interest per annum is:
Options:
A)5%
B)10%
C)7%
D)8%
E)9%
Rationale: Explanation :
Let the rate of interest per annum be R%
Simple Interest for Rs. 5000 for 2 years at rate R% per annum +Simple Interest for Rs. 3000 for 4 years at rate R% per annum = Rs.2200
⇒5000×R×2/100+3000×R×4/100=2200
⇒100R + 120R=2200
⇒220R=2200
⇒R=10
i.e, Rate = 10%.
Answer : Option B
Answer: B
Question: Three cubes of metal whose edges are 5, 10 and 15 cm respectively, are melted and one new cube is made. Find the edge of the new cube?
Options:
A)28
B)77
C)66
D)16.5
E)99
Rationale: 53 + 103 + 153 = a3 => a
= 16.5
Answer: D
Answer: D
Question: Cubes with each side one inch long are glued together to form a larger cube. The larger cube's face is painted with red color and the entire assembly is taken apart. 26 small cubes are found with no paints on them . How many of unit cubes have at least one face that is painted red?
Options:
A)64
B)72
C)86
D)98
E)99
Rationale: Use the options.
The options which after getting added to 26 shows a cube of a number could be right.
Here
64+26 = 90
72+26 = 98
86+26 = 112
98+26+124
99+26=125 ---(5*5*5)
So we have 99 as the answer!
E
Answer: E
Question: Fresh grapes contain 85% water by weight and raisins obtained by drying fresh grapes contain 25% water by weight. How many kgs of fresh grapes are needed to get 20kgs of raisins?
Options:
A)75 kgs
B)64kgs
C)100 kgs
D)65 kgs
E)70 kgs
Rationale: The weight of non-water in 20 kg of dried grapes (which is 100-25=75% of whole weight) will be the same as the weight of non-water in x kg of fresh grapes (which is 100-85=15% of whole weight), so 20*0.75 = x*0.15
--> x =100.
Answer: C
Answer: C
Question: Find the probability that the sum of n numbers is divisible by n,assuming n is very large no.
Options:
A)1
B)1/2
C)3/4
D)None of these
E)Can't be determined.
Rationale: sum of n numbers is n(n+1)/2
case 1)when n is odd take 3
Sum is 3*4/3 it is divisible by 3
we can conclude that n=odd sum of n numbers is divisible by n
case2) when n is even take 4
Sum is 4*5/2=>10 10/4 rem is 2 so not divisible
we can conclude that n=even sum of n numbers is not divisible by n
Total of total 2 cases 1 case is possible
So probability=possible/total=1/2
ANSWER:B
Answer: B
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 120 m and they cross each other in 12 sec, then the speed of each train is?
Options:
A)30
B)35
C)36
D)37
E)38
Rationale: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (120 + 120)/12 => x = 10
Speed of each train = 10 m/sec.
= 10 * 18/5 =- 36 km/hr.
Answer: Option C
Answer: C
Question: An employee’s annual salary was increased 30%. If her old annual salary equals $30,000 , what was the new salary?
Options:
A)$28,000
B)$25,000
C)$20,000
D)$35,000
E)$39,000
Rationale: Old annual salary = $30,000
Salary increase = 30%.
Original salary = $30,000 *30/100
= $9000
new salary = $30,000+$9000
=$39,000
Hence E.
Answer: E
Question: Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
Options:
A)11
B)10
C)8
D)12
E)15
Rationale: Suppose they meet x hours after 7 a.m.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x - 1) hours = 25(x - 1) km.
Therefore 20x + 25(x - 1) = 110
45x = 135
x = 3.
So, they meet at 10 a.m.
Answer: B
Answer: B
Question: For every positive even integer n, the function h(n) is defined to be the product of all the even integers from 4 to n, inclusive. If p is the smallest prime factor of h(100) +4, then p is?
Options:
A)between 4 and 20
B)between 10 and 20
C)between 20 and 30
D)between 30 and 40
E)4
Rationale: h(100) will have 0 in its unit digit because while doing the calculation of the function we are multiplying by 10 (and 100). So h(100)+4 will have 4 in the units digit so smallest prime factor is 4.
Answer: E
Answer: E
Question: Johnny makes $2.35 per hour at his work. If he works 5 hours, how much money will he earn?
Options:
A)$30
B)$54
C)$28.50
D)$12
E)$11.75
Rationale: 2.35*5=11.75. Answer is E.
Answer: E
Question: The number of boys in a class is 2 times the number of girls. Which one of the following numbers cannot represent the total number of children in the class ?
Options:
A)A)47
B)B)44
C)C)42
D)D)40
E)E)38
Rationale: Explanation:
Let number of girls = x and number of boys = 2x.
Then, 2x + x = 3x = total number of students.
Thus, to find exact value of x, the total number of students must be divisible by 3.
Answer: C
Answer: C
Question: On a certain scale of intensity, each increment of 30 in magnitude represents a tenfold increase in intensity. On this scale, an intensity corresponding to a magnitude of 165 is how many times an intensity corresponding to a magnitude of 125?
Options:
A)40
B)100
C)400
D)1000
E)10 000
Rationale: Increase of 40 in magnitude corresponds to 10^4 increase in intensity:
If intensity for 125 is x then for 135 it'll be 10*x, for 145 it'll be 10*10*x=10^2*x, for 155 it'll be 10*10*10*x=10^3*x and for 165 it'll be 10*10*10*10*x=10^2*x.
Answer: B.
Answer: B
Question: The least number which should be added to 720 so that the sum is exactly divisible by 5,6,4 and 3 is :
Options:
A)3
B)13
C)48
D)33
E)43
Rationale: Solution
L.C.M. of 5,6,4 and 3 = 60. on dividing 720 by 60, the remainder is 12.
∴ Number to be added = (60-12) = 48. Answer C
Answer: C
Question: A certain club has 6 members, including Harry. One of the 6 members is to be chosen at random to be the president, one of the remaining 5 members is to be chosen at random to be the secretary, and one of the remaining 4 members is to be chosen at random to be the treasurer. What is the probability that Harry will either be the secretary or the member chosen to be the treasurer?
Options:
A)7/3
B)5/3
C)1
D)2/3
E)1/3
Rationale: Each member out of 6, including Harry, has equal chances to be selected for any of the positions (the sequence of the selection is given just to confuse us). The probability that Harry will be selected to be the secretary is 1/6 and the probability that Harry will be selected to be the treasurer is also 1/6. So, the probability that Harry will be selected to be either the secretary or the the treasurer is 1/6+1/6=2/6.
Answer: E.
Answer: E
Question: In a class, there are 15 boys and 10 girls. Three students are selected at random. The probability that 1 girl and 2 boys are selected, is:
Options:
A)21/46
B)25/117
C)1/50
D)3/25
E)2/25
Rationale: Let S be the sample space and E be the event of selecting 1 girl and 2 boys.
Then, n(S)	= Number ways of selecting 3 students out of 25
= 25C3 `
=	(25 x 24 x 23)/(3 x 2 x 1)
= 2300.
n(E)	= (10C1 x 15C2)
= (10 x	(15 x 14)/(2 x 1))
= 1050.
P(E) =	n(E)	/n(S)	=	1050/2300	=	21/46	.
Answer:A
Answer: A
Question: By selling a house for Rs.45000, it was found that 1/8 of the outlay was gained, what ought the selling to price to have been in order to have lost 5 p.c?
Options:
A)33377
B)38000
C)27999
D)2776
E)198712
Rationale: CP + CP/8 = 45000
CP = 40000
SP = 40000*(95/100) = 38000
Answer:B
Answer: B
Question: A number is decreased by 10% and then increased by 10%. The number so obtained is 10 less than the original number. What was the oiginal number ?
Options:
A)1000
B)3899
C)1028
D)1039
E)1002
Rationale: Explanation:
Let the original number be x.
Final number obtained = 110% of (90% of x)
Answer: A) 1000
Answer: A
Question: Number of ways in which the letters of word GARDEN can be arranged with vowels in alphabetical order, is
Options:
A)360
B)240
C)120
D)480
E)None
Rationale: Solution
Order of vowels of fixed
∴ required number of ways are 6!/2!
Answer A
Answer: A
Question: If the remainder is 16 when the integer n is divided by 30, what is the remainder when 2n is divided by 15?
Options:
A)0
B)2
C)4
D)6
E)8
Rationale: n = 30k+16
2n = 2(30k+16) = 4k*15 + 32 = 4k*15 + 2*15 + 2 = 15j + 2
The answer is B.
Answer: B
Question: Find the one which does not belong to that group ?
Options:
A)35
B)77
C)28
D)19
E)11
Rationale: Explanation:
48, 75, 84 and 57 are divisible by 3 but not 35.
Answer:A
Answer: A
Question: A student has 8 trousers and 12 shirts. In how many different ways can the student select a trouser and a shirt?
Options:
A)84
B)96
C)108
D)120
E)132
Rationale: The student can select one trouser in 8 ways.
The student can select one shirt in 12 ways.
The number of ways to select one trouser and one shirt is 8 * 12 = 96 ways
The answer is B.
Answer: B
Question: The diagonals of a rhombus are 15 cm and 20 cm. Find its area?
Options:
A)158
B)129
C)150
D)123
E)117
Rationale: 1/2 * 15 * 20 = 150
Answer:C
Answer: C
Question: Calculate the mean of each data set {9,10,11,7,13}
Options:
A)4
B)5
C)8
D)9
E)10
Rationale: mean of Data set A = (9+10+11+7+13)/5 = 10
mean of Data set B = (10+10+10+10+10)/5 = 10
mean of Data set C = (1+1+10+19+19)/5 = 10
Option E
Answer: E
Question: Two highways start from a point P and meet again at the point Q. Between P and Q there are 5 subways, joining the highways at 5 different places. How many different routes are possible for a journey from P to Q?
Options:
A)12
B)16
C)24
D)32
E)64
Rationale: If one starts its journey from point P, one has 2 options ( to go via either highway)... When he reaches 1st subway point he has again, 2 options, to continue on the highway or to go through subway., When he reaches next subway, he will have same two options, of course we are considering that he doesn't return from any point.
Since, there are 5 subways, he has the option of choosing from 2 choices 6 times (one when he just starts his journey). So, total ways he can reach is destination is 2^6 = 64.
ANSWER:E
Answer: E
Question: If m and n are positive integers and m^2 + n^2 = 89, what is the value of m^3 + n^3?
Options:
A)72
B)224
C)320
D)512
E)637
Rationale: You need to integers which squared are equal 89.
Which could it be ? Let's start with the first integer:
1^2 = 1
2^2 = 4
3^2 = 9
4^2 = 16
5^2 = 25
6^2 = 36
7^2 = 49
8^2 = 64
Stop. The integers can't be greater than 8 or we will score above 89.
The second integer need to be picked up the same way.
1^2 = 1
2^2 = 4
3^2 = 9
4^2 = 16
5^2 = 25
6^2 = 36
7^2 = 49
8^2 = 64
The only pair that matches is 8^2 + 5^2 = 89.
So 8^3 + 5^3 = 637.
Answer E.)
Answer: E
Question: There are 9 people and 7 chairs. In how many different ways people can occupy the chairs?
Options:
A)405
B)504
C)404
D)505
E)506
Rationale: number of ways = 9*8*7 = 504
Answer is B
Answer: B
Question: Canister C is 1/2 full of water and canister D, which has twice the capacity of canister C, is 1/3 full of water. If the water in canister D is poured in canister C until canister C is completely full of water, canister D will still contain what fraction of its capacity of water?
Options:
A)0
B)1/36
C)1/12
D)1/6
E)1/4
Rationale: Say canister C has a capacity of 6 liters. It's half full, thus there can be poured 3 liters of water.
Canister B is 12 liters and there are 4 liters of water. We can pour 3 liters from D to C and 1 liter will still be left in D, which is 1/12 of its total capacity.
Answer: C.
Answer: C
Question: A cistern 10 meters long and 4 meters wide contains water up to a depth of 1 meter 25 cm. What is the total area of the wet surface?
Options:
A)45
B)55
C)65
D)75
E)85
Rationale: Area of the wet surface = [2(lb + bh + lh) - lb]
= 2(bh + lh) + lb
= [2 (4 x 1.25 + 10 x 1.25) + 10 x 4]
= 75
The answer is D.
Answer: D
Question: If set A={2,2,2,....,n times} , set B={4,4,4,4....m times} and set C={11,11,11...k time} , then in terms of m,n and k , how many possible subsets from sets A,B, and C can be created ?
Options:
A)a) k(n+m+mn)+ k
B)b) k^2(mn+n/m)
C)c) (1+n+m+mn)(k+1)
D)d) kmn(k+m+n)
E)e) None of the above.
Rationale: a) how many 2's are included?
b) how many 3's are included?
and
c) how many 11's are included?
For the number of 2, we could have zero 2's, or one 2, or two 2's, all the way up to n 2's. That's (n + 1) possibilities for the 2's. Similarly, (m + 1) possibilities for the 3's and (k + 1) possibilities for the 11's. We simply multiply these three numbers.
NOTICE that one set, the set that includes no 2's, no 3's, and no 11's, is included. This is known in mathematics as thenull set, sometimes called the empty set, a set with no members. Technically, this is a subset of every possible set, but that's a technical detail of set theory that goes well beyond what the GMAT would expect students to know. Even the the calculation is not that difficult, some of the technical aspects of this question are not in line with the GMAT's expectations.
The number of subsets is (m + 1)(n + 1)(k + 1). The answer is not given in that form. Instead, the first two factors have been FOILed together:
(mn + m + n + 1)(k + 1).
Mike
C
Answer: C
Question: Two persons A and B can complete a piece of work in 30 days and 45 days respectively. If they work together, what part of the work will be completed in 2 days?
Options:
A)2/5
B)1/6
C)1/4
D)1/9
E)2/6
Rationale: A's one day's work = 1/30
B's one day's work = 1/45
(A + B)'s one day's work = 1/30 + 1/45 = 1/18
The part of the work completed in 2 days = 2 (1/18) = 1/9.
ANSWER D
Answer: D
Question: A woman named Susila started a business investing Rs. 25,000. Roja joined him after six months with an amount of Rs. 50,000 and Sachin joined them with Rs. 75,000 after another six months. The amount of profit earned should be distributed in what ratio among Susila , Roja and Sachin respectively, 3 years after Aman started the business ?
Options:
A)7:6:10
B)12:15:16
C)42:45:56
D)3 : 5 : 6
E)12:15:18
Rationale: Explanation :
Akash : Roja : Sachin = (25,000 x 36) : (50,000 x 30) : (75,000 x 24)
= 36 : 60 : 72 => 3 : 5 : 6
Answer : D
Answer: D
Question: Tough and Tricky questions: Combinations.
Four students - 2 boys and 2 girls - are to sit side by side for a makeup exam. How many ways could they arrange themselves given that no two boys and no two girls can sit next to one another?
Options:
A)8
B)36
C)72
D)240
E)720
Rationale: We can have 2 arrangements:
BGBG or GBGB
2!*2!*2 = 2*2*2 = 8 ways.
Ans. A) 8
Answer: A