mathewhe/aqua_rat huggingface dataset:
Question: From a group of 6boys&4girls a Committee of 4 persons is to be formed. In how many different ways can it be done, so that the committee has at least 2 boys?
(A) 126
(B) 138
(C) 185
(D) 198
(E) 200
Rationale: The committee of 4 persons is to be so formed that it has at least 2 men. The different ways that we can choose to form such a committee are:
(i) 2m. 2w in 6C2 x 4 C1=6X5 - 2X1 X 3X3 2X1 =n an (ii) 3m. 1w in 6C3 x 4C1 =6X5X4 3X2X1 X4 _n - a ''''
(iii) 4m in 6C4 -2x1 = 15 Total no. of different ways in which a committee of 4 persons can be formed so that it has at least 2 men. = 90 + 18 + 15 = 185
C
Answer: (C) 185
Question: I bought two books; for Rs.480. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss?
(A) 167
(B) 280
(C) 187
(D) 178
(E) 170
Rationale: x*(85/100)
= (480 - x)119/100
x =280
Answer:B
Answer: (B) 280
Question: Jar Y has 10% more marbles than Jar X . What percent of marbles from Jar Y need to be moved into X so that both jars have equal marbles
(A) 4.54%
(B) 9.09%
(C) 10%
(D) 11%
(E) 12.25 %
Rationale: No; the choices will be approximated only when GMAT question explicitly mentions that;
Here the answer is very close 4.54, not 5.
Jar Y has 10% more marbles than X
Y = 1.1X
If k marbles are taken out of Y. The remaining marbles in Jar Y= 1.1X-k
If k marbles are added to X. The new marbles' count in Jar X= X+k
And we know they are equal;
X+k = 1.1X-k
2k = 0.1X
k= 0.05X
The marbles taken out of Y = 0.05X
Question is: 0.05X is what percent of marbles that was originally there in Y i.e. 1.1X
0.05X1.1X∗1000.05X1.1X∗100
0.05X1.1X∗1000.05X1.1X∗100
5011=4.54¯≈4.545011=4.54¯≈4.54
ANSWER:A
Answer: (A) 4.54%
Question: During the first week of performances of a certain play, 5,400 tickets were sold, all at reduced price. During the remaining weeks of performances, 5 times as many tickets were sold at full price as were sold at reduced price. If the total number of tickets E sold was 25,200, how many of them were sold at full price?
(A) 21,000
(B) 19,800
(C) 16,500
(D) 15,800
(E) 8,700
Rationale: Given:
The question tells us about the number of tickets sold in the first week at reduced price = 5,400. It also tells us that during the remaining weeks, the number of tickets sold at full price was 5 times the no. of tickets sold at reduced price. The total tickets sold was 25,200, and we are asked to find the number of tickets that where sold at full price.
Approach:
The question asks us to find the number of ticket sold at full price. We know that the number of tickets sold at full price was 5 times the no. of tickets sold at reduced price in remaining weeks. Hence, assuming tickets sold at reduced price in remaining weeks to be x would give us the no. of tickets sold at full price to be 5x.
Tickets sold in first week + Tickets sold in remaining weeks = Total no. of tickets soldi.e.
Tickets sold in first week + Tickets sold at full price in remaining weeks + Tickets sold at reduced price in remaining weeks = Total no. of tickets sold
We know the no. of tickets sold during first week and the total no. of tickets sold. We will use this relation to get to our answer.
Working Out:
Tickets sold in first week + Tickets sold at full price in remaining weeks + Tickets sold at reduced price in remaining weeks = Total no. of tickets sold
Substituting values in the equation, we get
5,400 + 5x + x = 25,200
x= 3,300
Tickets sold at full price = 5x = 16,500
Answer: Option C
Answer: (C) 16,500
Question: In an interview , the probability of appointing Husband is 1/5 while that of wife is
¼.find probability that only one of them get selected in interview.
(A) 3/20
(B) 4/20
(C) 5/20
(D) 6/20
(E) 7/20
Rationale: p(H)=1/5
p(w)=1/4
P(H bar)=1-1/5=4/5
p(w bar)=1-1/4=3/4
Required probability=p(H)*p(w bar)+p(w)*p(H bar)
1/5*3/4+1/4*4/5
7/20
ANSWER:E
Answer: (E) 7/20
Question: What is the sum which earned interest?
I. The total simple interest was Rs. 7000 after 7 years.
II. The total of sum and simple interest was double of the sum after 5 years.
(A) I alone sufficient while II alone not sufficient to answer
(B) II alone sufficient while I alone not sufficient to answer
(C) Either I or II alone sufficient to answer
(D) Both I and II are necessary to answer
(E) None of these
Rationale: Explanation:
Let the sum be Rs. x.
I gives, S.I. = Rs. 7000 and T = 7 years.
II gives, Sum + S.I. for 5 years = 2 x Sum Sum = S.I. for 5 years.
Now, S.I. for 7 years = Rs. 7000.
therefore, S.I. for 1 year = Rs. 1000.
Thus, I and II both are needed to get the answer.
Answer: D
Answer: (D) Both I and II are necessary to answer
Question: A is thrice as good a workman as B and therefore is able to finish a job in 40 days less than B. working together, they can do it in
(A) days
(B) ½ days
(C) days
(D) days
(E) days
Rationale: Explanation:
B = 3A
3A – A =40 days
A = 20days
Then, B = 90 days
(A + B) = 20 × 90/ 120 = 20 days .
Answer: Option A
Answer: (A) days
Question: The sum of 36 hours 45 minutes and 12 hours 15 minutes is approximately what percent of a week?
(A)  24%
(B)  approx 29%
(C)  approx 24%
(D)  approx 18%
(E)  approx 12%
Rationale: Since the question is asking for an approximate percentage
36:45+12:15 ~ 49 hours
% of day = (49*100)/(24*7) ~ 29%
Answer is B
Answer: (B)  approx 29%
Question: Positive integer p has n factors; 3p has 3 factors; Which of the following values can n take?
I. 1
II. 2
III. 3
(A) I or II
(B) II or III
(C) only I is true
(D) only II is true
(E) I or III
Rationale: Squares have odd number of factors.The square which is a multiple of 3 is 9.
3 has factors 1,3 .
Therefore 2 factors
Answer D
Answer: (D) only II is true
Question: Sum of the numbers from 1 to 29 is
(A) 400
(B) 430
(C) 435
(D) 405
(E) None of these
Rationale: Explanation: Sum of first n natural numbers = 1 + 2 + 3 + ..... n = n(n+1)/2
Substitute n = 29.
So S20=29Ã—30/2=435
Correct Option: C
Answer: (C) 435
Question: If p is a positive integer and 10p/96 is an integer, then the minimum number of unique prime factors p could have is T:
(A) T=1
(B) T=2
(C) T=3
(D) T=4
(E) T=5
Rationale: 10p/96 should resolve to a integer => 5p/48 should resolve to an integer.
Hence p/48 should resolve to a integer.
48 -- > 2^4 * 3.
Hence p should have atleast 2^4*3 for p/48 to resolve to a int.
The unique prime factors in 2^4 * 3 is 2, 3 and hence the answer is B(2).
Answer: (B) T=2
Question: When 81 is divided by the cube of positive integer z, the remainder is 17. Which of the following could be the value of z?
I.	2
II.	4
III.	8
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II and III
Rationale: 81 divided by z^3 leaves a remainder of 17.
81 = q * 2^3 + 17
64 = q+z^3
Then I tried answer possibilities of 2, 4 and 8.
Only 2^3 = 64 fulfills the equation and yields a remainder of 17.
ANSWER:B
Answer: (B) II only
Question: Magnabulk Corp sells boxes holding d magnets each. The boxes are shipped in crates, each holding c boxes. What is the price charged per magnet, if Magnabulk charges m dollars for each crate?
(A) 100cd/m
(B) 100m/(cd)
(C) cd/(100m)
(D) m/(cd)
(E) cd/m
Rationale: crate has = cd magnates
each magnate cost for each crate = m / cd
Ans; D
Answer: (D) m/(cd)
Question: In a group of ducks and cows, the total number of legs are 32 more than twice the number of heads. Find the total number of cows.
(A) A)14
(B) B)12
(C) C)16
(D) D)8
(E) E)6
Rationale: Explanation :
Let the number of ducks be d
and number of cows be c
Then, total number of legs = 2d + 4c = 2(d + 2c)
total number of heads = c + d
Given that total number of legs are 32 more than twice the number of heads
=> 2(d + 2c) = 32 + 2(c + d)
=> d + 2c = 16 + c + d
=> 2c = 16 + c
=> c = 14
i.e., total number of cows = 16
Answer : C
Answer: (C) C)16
Question: If the sum of six numbers is between 135 and 164, then the average (arithmetic mean) of the six numbers could be which of the following?
(A) 15.4.
(B) 20.5
(C) 25.5
(D) 31.25
(E) 32.5.
Rationale: The problem is actually testing the concept of average and Maxima/Minima....
Let all the values be 135 , so the average will be 135/6 => 22.5 ( Minima )
Let all the values be 164, so the average will be 164/6 => 27.3 ( Minima )
Hence answer will be (C) { any number between the maximum and minimum value.... }
Answer: (C) 25.5
Question: 70% of 300 + 25% of 400 - ? = 256
(A) 48
(B) 68
(C) 54
(D) 60
(E) None of these
Rationale: Explanation :
Solution: Let 70% of 300 + 25% of 400 - x = 256.
then, x = (70/100 * 300) + (25/100 * 400) - 256 = 210+100 -256 = 54.
Answer : C
Answer: (C) 54
Question: Indu gave Bindu Rs.6250 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest?
(A) 5
(B) 2
(C) 10
(D) 5
(E) 1
Rationale: 6250
= D(100/4)2
D = 10
Answer: C
Answer: (C) 10
Question: For what value of â€œkâ€ will the equation (2kx2 + 5kx +1)=0 have equal roots?
(A) 2/7
(B) 9/4
(C) 8/25
(D) 7/1
(E) 7/2
Rationale: for a 2nd degree equation ax2+bx_c=0 has equal roots the condition is b2-4ac =0
in the given equation
(5k)^2-4*2k*1=0
by solving this equation
we get k=0, k=8/25
ANSWER:C
Answer: (C) 8/25
Question: In a college, 95 percent of students Passed in math, 97 percent of students Passed in English, 99 percent Passed in French and 92 percent Passed in German.
Can you find out the percentage of students who Passed in all 4 subjects ?
(A) 92%
(B) 90%
(C) 96%
(D) 83%
(E) 89%
Rationale: D
83% of student Passed in all four subjects.
Answer: (D) 83%
Question: A car gets 20 kilometers per gallon of gasoline. How many gallons of gasoline would the car need to travel 120 kilometers?
(A) 8.5 gallons
(B) 5 gallons
(C) 7 gallons
(D) 5.5 gallons
(E) 6 gallons
Rationale: Each 20 kilometers, 1 gallon is needed. We need to know how many 20 kilometers are there in 120 kilometers?
120 / 20 = 4.5 * 1 gallon = 6 gallons correct answer E
Answer: (E) 6 gallons
Question: Three candidates contested an election and received 1130, 7530 and 11620 votes respectively. What percentage of the total votes did the winning candidate get?
(A) 57%
(B) 57.3%
(C) 65%
(D) 90%
(E) 80%
Rationale: total votes are 20280 ( sum of votes obtained by 3 candidates)
percentage of the total votes recd by the winning candidate = 100*11620/20280 = 57.3%
ANSWER:B
Answer: (B) 57.3%
Question: A and B can do a piece of work in 10 days, B and C in 15 days, C and A in 12 days. How long will C take to do it?
(A) 70 days
(B) 55 days
(C) 24 days
(D) 40 days
(E) 11 days
Rationale: 2c = 1/15+ 1/12– 1/10 = 1/20
c = 1/40 => 40 days
Answer: D
Answer: (D) 40 days
Question: C, D and E invested Rs.4500, Rs.9500 and Rs.11000 respectively, in a partnership business. Find the share of E in profit of Rs.25000 after a year?
(A) 10000
(B) 11000
(C) 12000
(D) 13000
(E) 14000
Rationale: Explanation:
4500:9500:11000
9:19:22
22/50 * 25000 = 11000
B)
Answer: (B) 11000
Question: If 0 < a < b and k = (2a + 9b)/b , which of the following must be true?
(A) k < 2
(B) k < 7
(C) k < 9
(D) k > 9
(E) k > 11
Rationale: Please follow posting guidelines (link in my signature) especially writing the correct topic title. Also do mention the source of the question if you select the tag:Source-Other Please Specify.
As for your question, it is very simple and straightforward with number plug in.
Assume a=1 and b=2 as a<b, you get k = (2+14)/2 = 10. This eliminates all but option D , making it the correct answer.
Answer: (D) k > 9
Question: There are A girls in a class, and their average height is M inches. In the same class, there are B boys with an average height of N inches. What is the average height of all the students in the class?
(A) (X + Y)/(M + N)
(B) (M + N)/(X + Y)
(C) (AM + BN)/(A + B)
(D) (XM + YN)/(X + Y)
(E) MN/XY
Rationale: Total height = AM+BN
No of students = A+B
Avg = (AM+BN)/(A+B)
Answer is C
Answer: (C) (AM + BN)/(A + B)
Question: In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?
(A) 80
(B) 90
(C) 15
(D) 209
(E) 105
Rationale: We may have (1 boy and 3 girls) or (2 boys and 2 girls) or (3 boys and 1 girl) or (4 boys).
Required number
of ways	= (6C1 x 4C3) + (6C2 x 4C2) + (6C3 x 4C1) + (6C4)
= (6C1 x 4C1) + (6C2 x 4C2) + (6C3 x 4C1) + (6C2)
= (24 + 90 + 80 + 15)
= 209.
ANSWER D 209
Answer: (D) 209
Question: 85% of a number is added to 24, the result is the same number. Find the number?
(A) 228
(B) 267
(C) 277
(D) 160
(E) 882
Rationale: (85/100) * X + 24 = X
3X = 480
X = 160
Answer: D
Answer: (D) 160
Question: Which of the following cannot be true if the sum of k consecutive integers is 0?
I. The product of the k integers is positive
II. The smallest of the k integers is zero
III. The largest of the k integers is negative
(A) I only
(B) II only
(C) III only
(D) I and III
(E) I, II and III
Rationale: For the sum of k consecutive integers to be 0 we must have one of the following cases: {0}, {-1, 0, 1}, {-2, -1, 0, 1, 2}, ..., {..., -3, -2, -1, 0, 1, 2, 3, ...}.
I. The product of the k integers is positive. As you can see the product of the integers in either of these sets is always 0, thus I cannot be true.
II. The smallest of the k integers is zero. If the set is {0}, then it's possible.
III. The largest of the k integers is negative. As you can see the largest of the integers is always more than or equal to zero, thus III cannot be true.
Answer: D.
Answer: (D) I and III
Question: The population of a town increases by 10% per annum for two years then decreases by 10% per annum for the next two years, if the population of the town four year ago was 10000, what would it be today?
(A) 9500
(B) 9801
(C) 10100
(D) 9000
(E) None of these
Rationale: Explanation :
Increase of population = (100+10)% = 110% = 1.1
Reduction of population = (100 -10)% = 90% = 0.9
Total effect = 1.1 X 1.1 X 0.9 X 0.9 = 0.9801,
Population = 10000 X 0.9801 = 9801
Answer : B
Answer: (B) 9801
Question: Which of the following options is the correct value of z if the greatest common divisor of (z-1)!,(z+2)!, and (z+4)! is 120.
(A) 9
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: GCD of (z-1)!,(z+2)!, and (z+4)! is 120. Find z.
Best way to find n is substitute each of the answer and find out the correct one.
Only option C gave the correct answer.
Option C: 6 and find GCD or 5!, 8! and 10!. 5! itself is 120 and 5! which is contained in the other two factorials. This satisfies the condition, hence answer is 6.
Answer is C.
Answer: (C) 6
Question: The speed of a bus including stoppages is 35 kmph and excluding stoppages is 70 kmph. Of how many minutes does the train stop per hour?
(A) 7
(B) 15
(C) 25
(D) 30
(E) 35
Rationale: Explanation:
T = 35/70 * 60 = 30
Answer: Option D
Answer: (D) 30
Question: 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?
(A) 20
(B) 80
(C) 160
(D) 220
(E) 250
Rationale: 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*5/10*2/10*2/10*2/10=160/9000
E. 250
Answer: (E) 250
Question: A number when divided by 45, gives 432 as quotient and 0 as remainder. What will be the remainder when dividing the same number by 21
(A) A)15
(B) B)3
(C) C)4
(D) D)6
(E) E)7
Rationale: Explanation:
P ÷ 45 = 432
=> P = 432 * 45 = 19440
P / 31 = 19440 / 21 = 925, remainder = 15
Answer: Option A
Answer: (A) A)15
Question: A certain no. whendivided by 35leaves a remainder 25, what is the remainder if the same no.be dividedby 15?
(A) 2
(B) 4
(C) 7
(D) 8
(E) 9
Rationale: Explanation:
35 + 25 = 60/15 = 4 (Remainder)
B
Answer: (B) 4
Question: How many S ways are there of placing 6 marbles in 4 bowls, if any number of them can be placed in each bowl?
(A) 6C4
(B) 6P4
(C) 4^6
(D) 6^4
(E) 6!
Rationale: Each marble has 4 options, so there are total of S= 4*4*4*4*4*4=4^6 ways.
Answer: C.
The total number of ways of dividing n identical items among r persons, each one of whom, can receive 0,1,2 or more items is (n+r -1)C(r-1).
Answer: (C) 4^6
Question: A and B can do a piece of work in 8 days. With the help of C they finish the work in 5 days. C alone can do that piece of work in?
(A) 30 DAYS
(B) 35 DAYS
(C) 40 DAYS
(D) 8 DAYS
(E) 3 DAYS
Rationale: C = 1/5 – 1/8= 1/40 => 40 days
Answer:C
Answer: (C) 40 DAYS
Question: A starts a business with a capital of Rs. 9,000. B joins in the business with Rs.18,000 after some time. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1?
(A) 2 months
(B) 6 months
(C) 7 months
(D) 8 months
(E) None of these
Rationale: Explanation :
Let B joins for x months. Then
A:B = 9000*12 : x* 18000 = 3 : 1
=> 9*12 : 18x= 3 : 1
=> 9*12/ 18x = 3/1 = 3
=> 9*4 /18x = 1
=> 2/x = 1
=> x = 2. Answer : Option A
Answer: (A) 2 months
Question: The sum of five consecutive odd numbers of set p is 435. What is the sum of five consecutive numbers of another set q. Whose largest number is 45 more than the largest number of set p?
(A) 530
(B) six hundred seventy
(C) 730
(D) 770
(E) None of these
Rationale: Let the five consecutive odd numbers of set p be 2n - 3, 2n - 1, 2n + 1, 2n + 3, 2n + 5.
Sum of these five numbers
= 2n - 3 + 2n - 1 + 2n + 1 + 2n + 3 + 2n + 5
= 10n + 5 = 435 => n = 43
Largest number of set p = 2(43) + 5 = 91
The largest number of set q = 91 + 45 = 136
=> The five numbers of set q are 132, 133, 134, 135, 136.
Sum of above numbers = 132 + 133 + 134 + 135 + 136 = 670.
ANSWER:B
Answer: (B) six hundred seventy
Question: Length of a rectangular plot is 20 mtr more than its breadth. If the cost of fencin gthe plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr?
(A) 50 m
(B) 60 m
(C) 65 m
(D) 70 m
(E) 75 m
Rationale: Let breadth = x metres.
Then, length = (x + 20) metres.
Perimeter = 5300 m = 200 m.
26.50
2[(x + 20) + x] = 200
2x + 20 = 100
2x = 80
x = 40.
Hence, length = x + 20 = 60 m
B
Answer: (B) 60 m
Question: Find the one which does not belong to that group ?
(A) 23776
(B) 28287
(C) 84284
(D) 28278
(E) 83484
Rationale: Explanation:
42624, 37573, 74347 and 93339 are palindromes but not 84284.
Answer: C
Answer: (C) 84284
Question: In a certain pond, 50 fish were caught, tagged, and returned to the pond. A few days later, 50 fish were caught again, of which 8 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what is the approximate number of fish in the pond?
(A)  400
(B)  625
(C)  1,250
(D)  2,500
(E)  312
Rationale: total fish = x
percentage of second catch = (8/50)*100 = 16%
so, x * 16% = 50
x = 312 ans.E
Answer: (E)  312
Question: What is the sum of all remainders obtained when the first 100 natural numbers are divided by 8?
(A) 397
(B) 401
(C) 403
(D) 405
(E) 399
Rationale: A positive integer can give only the following 9 remainders when divided by 9: 1, 2, 3, 4, 5, 6, 7, 8, and 0.
1 divided by 9 gives the remainder of 1;
2 divided by 9 gives the remainder of 2;
...
8 divided by 9 gives the remainder of 8;
9 divided by 9 gives the remainder of 0.
We'll have 11 such blocks, since 99/9=11. The last will be:
91 divided by 9 gives the remainder of 1;
92 divided by 9 gives the remainder of 2;
...
98 divided by 9 gives the remainder of 8;
99 divided by 9 gives the remainder of 0.
The last number, 100, gives the remainder of 1 when divided by 9, thus the sum of all remainders will be:
11(1+2+3+4+5+6+7+8+0)+1=401.
Answer: B.
Answer: (B) 401
Question: A thief goes away with a SANTRO car at a speed of 35 kmph. The theft has been discovered after half an hour and the owner sets off in a bike at 100 kmph when will the owner over take the thief from the start?
(A) 12/3 hours
(B) 2/7 hours
(C) 7/13 hours
(D) 1/3 hours
(E) 2/5 hours
Rationale: -----------35--------------------|
100 35
D = 35
RS = 100 â€“ 35 = 65
T = 35/65 = 7/13 hours
ANSWER:C
Answer: (C) 7/13 hours
Question: Three numbers are in the ratio 3:5:7. The largest number value is 42. Find difference between Smallest & largest number is?
(A) 20
(B) 22
(C) 24
(D) 26
(E) 28
Rationale: == 3:5:7
Total parts = 15
= The largest number value is 42
= The largest number is = 7
= Then 7 parts -----> 42 ( 7 * 6 = 42 )
= smallest number = 3 & Largest number = 7
= Difference between smallest number & largest number is = 7 - 3 = 4
= Then 4 parts -----> 24 (4 * 6 = 24)
C
Answer: (C) 24
Question: If X^y denotes x raised to the power y, then find last two digit of
1507^3381+1457^3757
(A) 64
(B) 65
(C) 66
(D) 75
(E) 84
Rationale: 1507^3381+1457^3757
=> 07^3381+57^3757
49^1690×7 + 49^1878 × 57
=> (100-51)^1690 ×7 + ( 100-51)^1878×57
=> 51^1690 × 7 + 51^1878×57
=> 07+57=64
ANSWER:A
Answer: (A) 64
Question: A car dealer purchased new cars at 80% of their list price and sold them for 90% of their list price. What is his percent gain?
(A) 11
(B) 12.5
(C) 15
(D) 16
(E) 20
Rationale: Cost = 80% of List Price = .8*LSale = 90% of List Price = .9*LGain Ratio = (Sale - Cost) / Cost = (.9*L - .8*L) / .8*L = .1*L / .8*L = .125Gain Percent = 100 * Gain Ratio = 100 * .125 = 12.5% = Answer B
Answer: (B) 12.5
Question: A goods train leaves a station at a certain time and at a fixed speed. After ^hours, an express train leaves the same station and moves in the same direction at a uniform speed of 90 kmph. This train catches up the goods train in 4 hours. Find the speed of the goods train.
(A) 24 kmph
(B) 36 kmph
(C) 56 kmph
(D) 32 kmph
(E) 46 kmph
Rationale: Let the speed of the goods train be x kmph.
Distance covered by goods train in 10 hours= Distance covered by express train in 4 hours
10x = 4 x 90 or x =36.
So, speed of goods train = 36kmph.
Ans: B
Answer: (B) 36 kmph
Question: Out of 10 persons working on a project, 6 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them?
(A) 29/7
(B) 29/3
(C) 29/1
(D) 29/30
(E) 29/20
Rationale: P(at least one graduate) = 1 - P(no graduates)
= 1 - 4C₃/¹⁰C₃ = 1 - (4*3*2)/(10 * 9 * 8)
= 29/30
Answer: D
Answer: (D) 29/30
Question: How much time will it take for an amount of 1000 to yield 100 as interest at 5% per annum of simple interest?
(A) 3 years
(B) 4 years
(C) 2 years
(D) 5 years
(E) 7 years
Rationale: Time = (100 x 100)/(1000 x 5) years = 2 years.
answer C
Answer: (C) 2 years
Question: In the quiet town of "Nothintodo" there are 600 inhabitants, 400 are unemployed and 300 are somnambulists. If half of the somnambulists are unemployed, how many are employed and are not somnambulists?
(A) 50.
(B) 100
(C) 150
(D) 200
(E) 300
Rationale: 400 are unemployed and 300 are somnambulists. So 200 are employed and 300 are Non-somnambulists.
Half of the somnambulists are unemployed = 150. So employed somnambulists = 300 -150 = 150.
Employed and not somnambulists = 200 - 150 = 50.
Hence the answer is A.
Answer: (A) 50.
Question: There are two positive numbers in the ratio 2:7. If the larger number exceeds the smaller by 30, then find the larger number?
(A) 42
(B) 38
(C) 44
(D) 36
(E) 46
Rationale: Let the two positive numbers be 2x and 7x respectively.
7x - 2x = 30
5x = 30 => x = 6
=> Larger number = 7x = 42.
Answer: A
Answer: (A) 42
Question: Four of the five parts numbered (a), (b), (c), (d) and (e) are exactly equal. Which of the parts is not equal to the other four? The number of that part is the answer.
(A) (a + b)(a – 2b)
(B) a2 – b(a + 2b)
(C) a2 + b2 – ab – 3b2
(D) (a + b)(a – b) + ab
(E) (a – b)2 + b(a – 3b)
Rationale: Others equal a2 – ab – 2b2 whereas (d) equals a2 + ab – b2 .
Answer D
Answer: (D) (a + b)(a – b) + ab
Question: In six successive games, a baseball team scored 2 runs once, 8 runs twice, and 12 runs three times.
What was the average (arithmetic mean) number of runs the team scored per game over the six-game period?
(A) 9
(B) 7
(C) 6
(D) 5
(E) 4
Rationale: 2 runs once (one game)
8 runs twice (two game)
12 runs three times (three games)
SO we have (2*1 + 8*2 + 12*3)/6 = 54/6 = 9.
ANS: A.
Answer: (A) 9