divelab/Sys2Bench huggingface dataset:
Question: X and Y run a 200 m race,where X beats Y by 20 m. To do a favor to Y, X starts 20 m behind the starting line in a second 200 m race. Both run at the same previous speed. Which of the following is true?
Options:
A)X Beats Y by 2m
B)Y Beats X by 10m
C)Y Beats X by 11m
D)Y Beats X by 1m
E)Y Beats X by 11m
Rationale: Let's suppose that the speed of X is 20m/s and that the speed of Y is 18m/s.
So, in the first race, the results are the following:
X crosses the finish line in 10s. In other words, X has run 200m in 10 s.
In 10s, Y has run 180 meters.
Therefore, there is the difference of 20 meters mentioned in the question.
Now, let's review the second race.
In 11 seconds, X can complete the 200 meters race. We have to remember that X is 20 meters behind the starting line.
But in 11 seconds, Y has covered (180+18) =198 meters. Also, it is important to notice that in 11 seconds Y cannot arrive to the finish line.
So, 200 - 198 = 2 meter
Answer: A
Answer: A
Question: If x and y are unique prime integers, which of the following must be odd?
Options:
A)xy^2
B)2x+2y
C)2x−2y
D)2x/2y
E)x−y
Rationale: Any number multiplied by 2 has to be an even number hence
Answer E
Answer: E
Question: Tough and Tricky questions: Combinations.
The product of the digits of the four-digit number h is 48. No two digits of h are identical. How many different numbers are possible values of h?
Options:
A)6
B)12
C)24
D)36
E)42
Rationale: Answer = C = 24
Let number =abcd
Given that a*b*c*d = 48
a,b,c,d can be 1,2,3,8
Number of ways = 4*3*2 = 24
Answer: C
Question: The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %?
Options:
A)18%
B)19%
C)78%
D)48%
E)11%
Rationale: 1500 ---- 270
100 ---- ? => 18%
Answer: A
Answer: A
Question: What is (19^7+19) / 19?
Options:
A)45225766
B)46855821
C)47045882
D)48925947
E)49325989
Rationale: (19^7+19) / 19 =
19*(19^6+1) / 19 =
19^6 + 1
Clearly this is a number which ends with a 2 in the units place.
The answer is C.
Answer: C
Question: 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.87. How much was lent at 5%?
Options:
A)388
B)2998
C)277
D)300
E)271
Rationale: (x*5*1)/100 + [(1500 - x)*6*1]/100 = 87
5x/100 + 90 – 6x/100 = 87
x/100 = 3
=> x = 300.Answer: D
Answer: D
Question: What is the % profit or loss, if the cost price of 4 mangoes is equal to the selling price of 9 mangoes?
Options:
A)75.6%
B)13.6%
C)54.6%
D)55.6%
E)51.6%
Rationale: Let the cost price of 1 mangoes be Rs 1
Cost of 9 mangoes = Rs 9
Selling price of 9 mangoes = 4
Gain/loss = 9 - 4 = 5
%=5/9âˆ—100= 55.6
Answer: D
Answer: D
Question: The sum of two numbers is 30 and their difference is 10. Find their product.
Options:
A)104
B)114
C)315
D)200
E)335
Rationale: Let the numbers be x and y.
Then x + y = 30 and x - y = 10
x = 20; y = 10
xy = 20 * 10 = 200
ANSWER:D
Answer: D
Question: If (x + yi) / i = ( 7 + 9i ) , where x and y are real, what is the value of (x + yi)(x - yi)?
Options:
A)110
B)120
C)130
D)140
E)150
Rationale: (x + yi) / i = ( 7 + 9i )
(x + yi) = i(7 + 9i) = -9 + 7i
(x + yi)(x - yi) = (-9 + 7i)(-9 - 7i) = 81 + 49 = 130
CORRECT ANSWER IS C0130
Answer: C
Question: How many of the following numbers are divisible by 132?
264, 396, 462, 792, 968, 2178, 5544, 6336
Options:
A)4
B)5
C)6
D)7
E)8
Rationale: A number is divisible by 132, if it is divisible by each one of 11, 3 and 4.
Clearly, 968 is not divisible by 3. None of 462 and 2178 is divisible by 4.
Each one of remaining 5 is divisible by each one of 11, 3 and 4 and therefore, by 132.
ANSWER:B
Answer: B
Question: What decimal fraction is 20 ml of a litre ?
Options:
A).2
B)0.002
C).05
D).02
E)None of these
Rationale: Answer
Required fraction = 20/1000
= 2/100
= .02
Correct Option: D
Answer: D
Question: A crate of mangoes contains one bruised mango for every thirty mango in the crate. If three out of every four bruised mango are considerably unsaleble and there are 10 unsaleable mangoes in the crate then how msny mango are there in the crate?
Options:
A)100 mangoes
B)110 mangoes
C)120 mangoes
D)130 mangoes
E)125 mangoes
Rationale: 100 mangoes
ANSWER:A
Answer: A
Question: A can finish a work in 18 days and B can do same work in half the time taken by A. then working together, what part of same work they can finish in a day
Options:
A)1\5
B)1\6
C)1\7
D)1\8
E)1\9
Rationale: Explanation:
Please note in this question, we need to answer part of work for a day rather than complete work. It was worth mentioning here because many do mistake at this point in hurry to solve the question
So lets solve now,
A's 1 day work = 1/18
B's 1 day work = 1/9 [because B take half time than A]
(A+B)'s one day work =
(1/18+1/9)
=(1+2 /18)=1/6
So in one day 1/6 work will be done.
Option B
Answer: B
Question: A train moves fast a telegraph post and a bridge 264 m long in 8 sec and 20 sec respectively. What is the speed of the train?
Options:
A)22.3 km/hr
B)22.9 km/hr
C)29.2 km/hr
D)79.2 km/hr
E)19.2 km/hr
Rationale: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 8 => x = 8y
(x + 264)/20 = y
y = 22
Speed = 22 m/sec = 22 * 18/5 = 79.2 km/hr.
Answer:D
Answer: D
Question: If Q is a positive integer, and Q/15 = 8.2, what is the remainder when Q is divided by 15?
Options:
A)A.1
B)B.2
C)C.3
D)D.4
E)E.8
Rationale: If Q were a multiple of 15, the quotient Q/15 would be an integer. The fact that it's a decimal tells us that 15 goes into Q eight whole times and some decimal part of a time. This decimal part, 0.2 is the remainder divided by the divisor. Let R be the remainder.
R/15 = 0.2 = 1/5
R = (15)*(1/5) = 3
Answer =(C)
Answer: C
Question: If 2a = 4b = 10, then 40ab =
Options:
A)50
B)100
C)250
D)450
E)500
Rationale: 2a * 4b = 10 * 10 = 100
8 ab = 100
i.e. 40 ab = 500
Answer: Option E
Answer: E
Question: If 35 percent of 400 is 20 percent of x, then x =
Options:
A)200
B)350
C)700
D)900
E)1,400
Rationale: 5/100(400) = 2/10(x)
X = 700..
ANSWER:C
Answer: C
Question: The following sets each have a mean of 10 and the standard deviations are given in variable form.
Set I = {10, 10, 10, 10, 10, 10}, standard deviation = P
Set II = { 7, 8, 9, 11, 12, 13}, standard deviation = R
Set III = {6, 6, 6, 14, 14, 14}, standard deviation = Q
Rank these three standard deviations from least to greatest.
Options:
A)P, Q, R
B)P, R, Q
C)R, Q, P
D)Q, R, P
E)R, Q, P
Rationale: SD is minimum when the terms are closer to the mean.
In set 1, we have all terms equal to mean. hence, its SD is 0.(The Lowest)
Comparing Set 2 and Set 3, Set 2 has terms more closer to mean than set 3. hence, Set 3 Sd is the highest.
So, Answer is C
Answer: C
Question: In a race with 20 competitors, the first-place finisher receives a gold medal, the second-place finisher receives a silver medal, and the third-place finisher receives a bronze medal. If there are no ties, in how many different ways may these three medals be awarded?
Options:
A)35
B)120
C)720
D)840
E)6,840
Rationale: Well in this case since there are 3 positions and they can be taken by 3 persons only ,so order matters over here .For gold there are 20 choices ,for silver 19 remain (one who got gold cannot be given silver) and for bronze 18 choices remain.
So total possibilities=20*19*18
Correct answer E=6,840
Answer: E
Question: What percent is 400 gm of 1 kg?
Options:
A)25%
B)40%
C)10%
D)8%
E)12%
Rationale: 1 kg = 1000 gm
400/1000 Ã— 100 = 40000/1000
=40 %
Answer is B
Answer: B
Question: Three photographers, Lisa, Mike and Norm, take photos of a wedding. The total of Lisa and Mikes photos is 70 less than the sum of Mike's and Norms. If Norms photos number 10 more than twice the number of Lisa's photos, then how many photos did Norm Take?
Options:
A)40
B)50
C)60
D)80
E)130
Rationale: L+M=M+N-70 / N=2L+10
70=M+N-L-M
70=N-L
70=2L+10-L
60=L
2(60)+10=130
E
Answer: E
Question: The timing of a college is from 12 p.m to 4.00 p.m. Five lectures are held in the given duration and a break of 5 minutes after each lecture is given to the students. Find the duration of each lecture.
Options:
A)52 minutes
B)45 minutes
C)30 minutes
D)48 minutes
E)44 minutes
Rationale: Explanation:
Total time a student spends in college = 4 hours 00 minutes = 240 minutes
As there are 5 lectures, the number of breaks between lectures is 4. Total time of the break = 20 minutes
Hence, the duration of each lecture is = (240 â€“ 20)/5
= 44 minutes
ANSWER E
Answer: E
Question: If pq = p + q^2 – 2pq, for what value of q is pq equal to p for all values of p?
Options:
A)-2
B)-1
C)1
D)0
E)2
Rationale: C
p + q2 â€“ 2pq = p
=> q2 - 2pq = 0
=> q (q - 2p) = 0
=> q = 0 or q = 2p
im not following the logic you used here.. how did you replace pq with 0 could someone help explain it in MORE DETAI
D
Answer: D
Question: A women sells 3 different size(in kgs) packs of sugar which are multiples of 1.A person who buys sugar should buy all types of packs.4 different people buys 20,21,23,29 kgs .what will the maximum and minimum amounts a person can buy??
Options:
A)22
B)33
C)34
D)54
E)85
Rationale: packet are 11,6 and 7
7+7+6=20
7+7+7=21
6+6+11=23
7+11+11=29
and min 6+6+6=18
and max 11+11+11=33
ANSWER:B
Answer: B
Question: A fence consists of m lengths of fence that are each n feet long. A fence post separates each length of fence by its width of x feet. What is the total length Q of the fence including the fence posts on each end?
Options:
A)mn
B)m(n + x)
C)Q=m(n + x) + x
D)m(n + x) + 2x
E)2mn
Rationale: Notice that since a fence post separates each length of fence, then there will be m+1 posts, for example if there are m=2 fences, then there will be 3 posts: PFPFP. Thus the total length of the posts is (m+1)x.
The total length Q of the fence is mn, therefore the total length of the fence including the fence posts on each end is (m+1)x+mn=mx+x+mn=m(n+x)+x.
Answer: C.
Answer: C
Question: At the end of the month, a certain ocean desalination plant’s reservoir contained 6 million gallons of water. This amount is twice the normal level. If this amount represents 60% of the reservoir’s total capacity, how many million gallons short of total capacity is the normal level?
Options:
A)15
B)10
C)5
D)20
E)25
Rationale: the Q talks of total capacity, normal level, present level, shortage etc..
so it is all about not going wrong in these terms
6 MG= 60% of Total..
total = 6/.6=10MG..
Normal level= 1/2 of 10=5MG..
shortage of normal level=10-5=5MG..
C
Answer: C
Question: What least no. must be subtracted from 5026 so that remaining no.is divisible by 5?
Options:
A)3
B)4
C)5
D)6
E)1
Rationale: Explanation:
On dividing 5026 by 5 we get the remainder 1, so 1 should be subtracted
Option E
Answer: E
Question: A piece of work can be done by 6 men and 5 women in 6 days or 3 men and 4 women in 10 days. It
can be done by 9 men and 15 women in how many days ?
Options:
A)3 days
B)4 days
C)5 days
D)6 days
E)None of these
Rationale: Explanation:
To calculate the answer we need to get 1 man per day work and 1 woman per day work.
Let 1 man 1 day work =x
and 1 woman 1 days work = y.
=> 6x+5y = 1/6
and 3x+4y = 1/10
On solving, we get x = 1/54 and y = 1/90
(9 men + 15 women)'s 1 days work =
(9/54) + (15/90) = 1/3
9 men and 15 women will finish the work in 3 days
Answer: A
Answer: A
Question: A man can row at 4 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place?
Options:
A)2.4 km
B)2.9 km
C)3.4 km
D)1.9 km
E)5.6 km
Rationale: Explanation:
Speed in still water = 4 kmph
Speed of the current = 1 kmph
Speed downstream = (4+1) = 5 kmph
Speed upstream = (4-1) = 3 kmph
Let the required distance be x km
Total time taken = 1 hour
â‡’ x/5+x/3=1
â‡’3x+5x=15
â‡’8x=15
â‡’x=1.9 km
Answer: Option D
Answer: D
Question: The ‘moving walkway’ is a 300-foot long walkway consisting of a conveyor belt that moves continuously at 3 feet per second. When Bill steps on the walkway, a group of people that are also on the walkway stands 120 feet in front of him. He walks toward the group at a rate of 3 feet per second. Once Bill reaches the group of people, he stops walking and stands with them until the walkway ends. What is Bill’s average rate W of movement for his trip along the moving walkway?
Options:
A)2 feet per second
B)2.5 feet per second
C)3 feet per second
D)4 feet per second
E)5 feet per second
Rationale: A, B, and C don't make ANY sense! we know for some time...(a majority of the 300ft) Bill will walk at a pace of 6ft per second...and then at some later time he will stop and move at 3 ft per second... The average W MUST bebetween3-6 ft per second or the Earth is FLAT!!!.
So we are down to DE, D doesn't make sense on a weighted averages level because we know when Bill gets on the walkway the patrons are already 40% of the way down the 300ft walkway AND they are still moving at half the rate of Bill!! So for Bill to average 4 ft per second he would have had to spend a majority of the 300 ft at 3ft per second because 4 is much closer (when you factor in the size of the values we're dealing with 2 is double 1) to 3 than to 6. We know from the information that isn't possible. Billmust havespent the majority of his time at 6 ft per second before he stopped walking. That leaves only answer E as plausible.
Answer: E
Question: If A = d% of y and B = y% of d, then which of the following is true?
Options:
A)1) A is smaller than B.
B)2) A is greater than B
C)3) Relationship between A and B cannot be determined.
D)4) If x is smaller than y, then A is greater than B.
E)5) None of the above
Rationale: Basically A = B = dy/100
None of the options mentions this; hence E.
Answer: E
Question: A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 64 percent of the distribution lies within one standard deviation d of the mean, what percent of the distribution is less than m + d ?
Options:
A) 16%
B) 32%
C) 48%
D) 82%
E) 92%
Rationale: This is easiest to solve with a bell-curve histogram. m here is equal to µ in the Gaussian normal distribution and thus m = 50% of the total population.
So, if 64% is one st.Dev, then on either side of m we have 64/2 = 32%. So, 32% are to the right and left of m (= 50%). In other words, our value m + d = 50 + 32 = 82% goingfrom the mean m, to the right of the distributionin the bell shaped histogram.. This means that 82% of the values are below m + d.
Like I said, doing it on a bell-curve histogram is much easier to fullygethow this works, or you could apply GMAT percentile jargon/theory to it
D
Answer: D
Question: If |x + 10| = 10 what is the sum of all the values of x.
Options:
A)20
B)40
C)-20
D)0
E)-40
Rationale: There will be two cases
x+10 = 10 and x+10 = -10
Solve for x => x=10-10=> x=0 or x= -10 - 10 => x= -20
The sum of both values will be 0 + -20 =-20
Answer is C
Answer: C
Question: Machine A produces 100 parts twice as fast as Machine B does. Machine B produces 100 parts in 80 minutes. If each machine produces parts at a constant rate, how many parts does Machine A produce in 20 minutes?
Options:
A)60
B)80
C)70
D)40
E)50
Rationale: Machine B produces 100 part in 80 minutes. Machine A produces 100 parts twice as fast as B, so Machine A produces 100 parts in 80/2=40 minutes.
Now, Machine A produces 100 parts in 40 minutes which is 100/40 = 10/4 parts/minute.
10/4 parts X a total of 20 minutes = 10/4 * 20 =50
E
Answer: E
Question: How many positive integers Q less than 10,000 are such that the product of their digits is 210?
Options:
A)24
B)30
C)48
D)54
E)72
Rationale: 210 is the answer when 2, 3, 5 and 7 are multiplied. 210 can also be arrive using 5,6 and 7 and 1, 5, 6 and 7.
So sum of arrangements of 2357, 567 and 1567. This translates to 4! +3! + 4!, this equals to 24 + 6 + 24 = 54, D is the answer.
Answer: D
Question: A 50 ml after-shave lotion at 30% alcohol is mixed with 30 ml of pure water. What is the percentage of alcohol in the new solution?
Options:
A)16.75%
B)17.75%
C)18.75%
D)19.75%
E)None of these
Rationale: The amount of the final mixture is given by
50 ml + 30 ml = 80 ml
The amount of alcohol is equal to the amount of alcohol in pure water ( which is 0) plus the amount of alcohol in the 30% solution. Let x be the percentage of alcohol in the final solution. Hence
0 + 30% 50 ml = x (80)
Solve for x
x = 0.1817 = 18.75%
Answer C
Answer: C
Question: We have 5 people and 3 chairs. In how many ways chairs can be occupy?
Options:
A)58
B)42
C)60
D)72
E)80
Rationale: no. of ways they can be occupy = 5*4*3 = 60
Answer is C
Answer: C
Question: Find four consecutive even integers so that the sum of the first two added to twice the sum of the last two is equal to 760.
Options:
A)120 ,122 , 124 ,126
B)120 ,122 , 124 ,128
C)120 ,121 , 122 ,123
D)123 ,125 , 127 ,129
E)None of these
Rationale: Let x, x + 2, x + 4 and x + 6 be the four integers. The sum of the first two
x + (x + 2)
twice the sum of the last two is written as
2 ((x + 4) + (x + 6)) = 4 x + 20
sum of the first two added to twice the sum of the last two is equal to 760 is written as
x + (x + 2) + 4 x + 20 = 760
Solve for x and find all four numbers
x = 123 , x + 2 = 125 , x + 4 = 127 , x + 6 = 129
Answer D
Answer: D
Question: The value of a machine depreciates at 20% per annum. If its present value is Rs. 1,50,000, at what price should it be sold after two years such that a profit of Rs. 25,000 is made?
Options:
A)Rs. 1,10,000
B)Rs. 1,20,000
C)Rs. 1,24,000
D)Rs. 1,21,000
E)None of these
Rationale: The value of the machine after two years = 0.8 * 0.8 * 1,50,000 = Rs. 96,000
SP such that a profit of Rs. 25,000 is made = 96,000 + 25,000 = Rs. 1,21,000
ANSWER:D
Answer: D
Question: The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number?
Options:
A)3
B)4
C)9
D)11
E)None of these
Rationale: Answer: Option B
Let the ten's digit be x and unit's digit be y.
Then, (10x + y) - (10y + x) = 36
9(x - y) = 36
x - y = 4.
Answer: B
Question: A factory has a fixed cost of $44,000 a month, and a cost of $2.5 for every item produced. If the selling price of a single item is $5, what is the number of items must be sold monthly for the factory to cover its cost exactly?
Options:
A)9,000
B)14,000
C)17,600
D)22,500
E)27,000
Rationale: selling price - Cost price = 2.5 so per unit profit =2.5
cost to recover =44000
no of items required = 44000/2.5 = 17600
Answer: C
Answer: C
Question: What is the twenty-fifth decimal to the right in the fraction 10/11?
Options:
A)1
B)3
C)5
D)7
E)9
Rationale: 10/11 = 0.9090909090...
The odd-numbered decimal places are 9.
The answer is E.
Answer: E
Question: Distance between two stations A and B is 778 km. A train covers the journey from A to B at 84 km per hour and returns back to A with a uniform speed of 56km per hour. Find the average speed of the train during the whole journey?
Options:
A)67.0 km /hr
B)67.2 km /hr
C)69.0 km /hr
D)69.2 km /hr
E)None
Rationale: Solution
Required average speed	=(2xy / x+y)km/hr
= 2 x 84 x 56 /(84 + 56)
= (2 x 84 x 85 /140)
= 67.2 km/hr.
Answer B
Answer: B
Question: If the numerator of a fraction be increased by 20% and its denominator be diminished by 10%, the value of the fraction is 20/21. Find the original fraction ?
Options:
A)1/2
B)3/5
C)4/7
D)5/7
E)7/9
Rationale: Let the original fraction be x/y
Then, 120% of x/90% of y = 20/21
120x/90y = 20/21
x/y = 5/7
Answer is D
Answer: D
Question: The average of runs of a cricket player of 10 innings was 42. How many runs must he make in his next innings so as to increase his average of runs by 4?
Options:
A)87
B)86
C)28
D)76
E)80
Rationale: Average after 11 innings = 46
Required number of runs
= (46* 11) - (42* 10) = 506 - 420
= 86.
Answer: B
Answer: B
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are picked at random, what is the probability that they are either red or green?
Options:
A)53/105
B)43/105
C)42/105
D)32/105
E)46/105
Rationale: given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability that both marbles are red = 4Câ‚‚/Â¹âµCâ‚‚ = (3 * 2)/(15 * 14) = 3/21
Probability that both are green = 6Câ‚‚/Â¹âµCâ‚‚ = (2 * 1)/(15 * 14) = 1/105
Probability that one red and other is green = (4Câ‚ * 6Câ‚)/Â¹âµCâ‚‚ = (2 * 3 * 2)/(15 * 14) = 27/105
Required probability = 3/21 + 1/105 + 27/105
= 43/105
Answer:B
Answer: B
Question: The area of one square is x^2 + 12x + 36 and the area of another square is 4x^2 − 12x + 9. If the sum of the perimeters of both squares is 64, what is the value of x?
Options:
A)0
B)4.3
C)2.5
D)4.67
E)10
Rationale: spotting the pattern of equations both are in form of (X+C)^2 so
A1= (x+6)^2A2= (2x-3)^2
L1= x+6 L2= 2x-3
P1 = 4( x+6)P2=4(2x-3)
P1+P2=64
4( x+6) +4(2x-3)=64..............> X=4.3
Answer: B
Answer: B
Question: By how much is 70% of 120 greater than 35% of 200.
Options:
A)15
B)14
C)13
D)16
E)17
Rationale: (70/100) * 120 â€“ (35/100) * 200
84 - 70 = 14
Answer: B
Answer: B
Question: Evaluate: |6 - 8(3 - 12)| - |5 - 11| = ?
Options:
A)40
B)50
C)72
D)70
E)80
Rationale: According to order of operations, inner brackets first. Hence
|6 - 8(3 - 12)| - |5 - 11| = |6 - 8*(-9)| - |5 - 11|
According to order of operations, multiplication within absolute value signs (which may be considered as brackets when it comes to order of operations) next. Hence
= |6 + 72| - |5 - 11|
= |78| - |-6|
= 78 - 6 = 72
correct answer C)72
Answer: C
Question: A vendor purchases binder clips at 12 for rs60.How many clips should he sell for rs60 to earn a profit of 20%?
Options:
A)5
B)8
C)6
D)10
E)12
Rationale: Profit of 20% means he should sell the 12 clips for 72 Rs
so for 60 Rs he should sell 10 clips
ANSWER:D
Answer: D
Question: Before being simplified, the instructions for computing income tax in Country R were to add 2 percent of one's annual income to the average (arithmetic mean) of 100 units of Country R's currency and 1 percent of one's annual income. Which of the following represents the simplified formula for computing the income tax, in Country R's currency, for a person in that country whose annual income is X?
Options:
A)50X/200
B)50+3X/100
C)50+X/40
D)100+X/50
E)100+3X/100
Rationale: 50+X/40=C
Answer: C
Question: 35 percent of the women in a college class are science majors, and the non-science majors make up 70% of the class. What percentage of the men are non-science majors if 40% of the class are men?
Options:
A)37.5
B)27.5
C)77.5
D)87.5
E)93.5
Rationale: 3.5/k + 2/m = 6/t
Assuming total # is 100 :
[Science - Women] will have -> 0.35 * 60 = 21
[Non-Science-Women] will have -> 39
[Science-Men] will have = 30-21 = 9
[Non-Science-men] will have - 31
S0 31/40 * 100 = 77.5%
Answer -C
Answer: C
Question: During a particular equestrian competition, the rider and his horse have 5 fences to jump. If the rider falls off during a jump, the rider is disqualified. The probability of the rider falling off on a jump is 12/35. What is the least number of fences that the rider can jump before the probability of falling off at least once is more than 50%.
Options:
A)1
B)5
C)4
D)2
E)3
Rationale: Rule of Subtraction: P(A) = 1 - P(A')
Rule of Multiplication: P(A ∩ B) = P(A) P(B)
The probability that the rider falls at least once in 2 jumps is 1- (23/35)^2 = 1 - 529/1,225 = 696/1,225 < 50%.
The probability that the rider falls at least once in 3 jumps is 1- (23/35)^3 = 1 - 12,167/42,875 = 30,708/42,875 > 50%.
Answer: E
Answer: E
Question: Xavier, Yvonne, and Zelda each try independently to solve a problem. If their individual probabilities for success are 1/5, 1/2 and 5/8, respectively, what is the probability that Xavier and Yvonne, but not Zelda, will solve the problem?
Options:
A)11/8
B)3/80
C)9/64
D)5/64
E)3/64
Rationale: P(Xavier will solve)=1/5
P(Yvonne will solve)=1/2
P(Zelda will NOT solve) = 1- 5/8 = 3/8.
Now, we need to multiply all this Ps to find an answer:
p= (1/5)*(1/2)*(3/8) = 3/80.
Ans. B.
Answer: B
Question: A and B put in Rs.300 and Rs.400 respectively into a business. A reinvests into the business his share of the first year's profit of Rs.210 where as B does not. In what ratio should they divide the second year's profit?
Options:
A)39:40
B)39:48
C)39:43
D)39:46
E)39:42
Rationale: 3: 4
A = 3/7*210 = 90
390: 400
39:40
Answer: A
Answer: A