mathewhe/aqua_rat huggingface dataset:
Question: The sum of the non-prime numbers between 60 and 70, non-inclusive, is
(A) 387
(B) 429
(C) 457
(D) 499
(E) 536
Rationale: sum of consecutive integers from 61 to 69, inclusive ====> (A1 + An)/2 * # of terms = (61 + 69)/2 * 9 = 65 *9 = 585
sum of non-prime numbers b/w 60 and 70, non inclusive ===> 585 - 128 (i.e., 61 + 67, being the prime #s in the range) =457
Answer: C
Answer: (C) 457
Question: Bag A contains red, white and blue marbles such that the red to white marble ratio is 1:3 and the white to blue marble ratio is 2:3. Bag B contains red and white marbles in the ratio of 1:4. Together, the two bags contain 70 white marbles. How many red marbles could be in bag A?
(A) 1
(B) 3
(C) 4
(D) 6
(E) 14
Rationale: 6 is the answer.
Bag A-
R:W:B = 2:6:9
Let W in bag A be 6K
Bab B -
R:W = 1:4
Let W in bag B be 4k
W = 70 = 6K+4k
=>k=7
Total Red's in bag A will be 2K = 14
E
Answer: (E) 14
Question: If S is the sum of the reciprocals of the consecutive integers from 81 to 90, inclusive, which of the following is less than S?
I. 1/8
II. 1/9
III. 1/10
IV. 1/5
V. 1/8>S >1/9
(A) V
(B) I
(C) II
(D) III
(E) IV
Rationale: Since we summarize the reciprocals from 90 to 81, we can say also that we add ten numbers who are all (with one exception 1/90) greater than 1/90, so that the sum must be greater than 1/9.
On the other side we can say that we add the reciprocals from 91 to 100, so that the sum has to be less than the sum of ten times 1/91.
sum has to be greater than 1/9 and less than 1/8
A
Answer: (A) V
Question: A thief is spotted by a policeman from a distance of 200metres. When the policeman starts the chase, the thief also starts running. If the speed of the thief be 18km/hr and that of the policeman 22km/hr, how far the thief will have run before he is overtaken ?
(A) A)900m
(B) B)500m
(C) C)650m
(D) D)750m
(E) E)800m
Rationale: Relative speed of the policeman = 22-18 = 4 km/hr
time taken by policeman to cover 200m = (200/1000)*(1/4) = 1/20 hr
In 1/20 hr the thief covers a distance of 18/20 km = 9/10 km = 900m
Answer is A
Answer: (A) A)900m
Question: A contest will consist of n questions, each of which is to be answered eithertrueorfalse. anyone who answers all n questions correctly will be a winner. what is the least value of n for which the probability is less than 1/500 that a person who randomly guesses the answer to each question will be a winner?
(A) 5
(B) 10
(C) 50
(D) 100
(E) 1000
Rationale: A contest will consist of n questions, each of which is to be answered eithertrueorfalse. anyone who answers all n questions correctly will be a winner. what is the least value of n for which the probability is less than 1/500 that a person who randomly guesses the answer to each question will be a winner?
A.5
B.10
C.50
D.100
E.1000
Soln: ans is B
Probability that one question is answered right is 1/2.
Now for minimum number of questions needed to take probability less than 1/1000 is
=> (1/2)^n < 1/1000
n = 10 satisfies this.
A
Answer: (A) 5
Question: The faces of a triangular prism are to be painted by 5 different colors. In how many ways can be this be done?
(A) A.720
(B) B.256
(C) C.1
(D) D.120
(E) E.36
Rationale: If I have to paint 5 sides with 5 different colour...
First face can have 5c1 options,
2nd would have 4c1, and subsequent ones would have 3c1, 2c1 and 1 options respectively.
Total options = 5c1 x 4c1 x 3c1 x 2c1 x 1 = 120 distinct ways
Correct answer - D
Answer: (D) D.120
Question: If 9a = 16b what is (4a + 6b)/(15a - 16b)
(A) 3
(B) 4
(C) 5
(D) 59/48
(E) 11
Rationale: 4a + 6b )/( 15a - 16b )
= (4a + 6b)/(15a - 9a) (because 9a = 16b)
= (4a + 6b)/6a
= 2/3 + b/a
= 2/3 + 9/16 (because 9a = 16b, so b/a = 9/16)
= (32+27)/48
= 59/48
ANSWER:D
Answer: (D) 59/48
Question: Conversation between two mathematicians:
First: I have three children. The product of their ages is 36. If you sum their ages, it is exactly same as my neighbor's door number on my left. The second mathematician verifies the door number and says that it is not sufficient. Then the first says "Ok one more clue is that my youngest is really the youngest". Immediately the second mathematician answers. Can you answer the question asked by the first mathematician? What are the children ages?
(A) 6,6, 1
(B) 6,6, 2
(C) 6,5, 1
(D) 6,5, 2
(E) 6,6, 3
Rationale: Possible options for same sum of ages ( 13 here)with product of ages as 36 are
2,2,9
and
6,6,1
but in case of 2,2,9
youngest is not really youngest as two children of age 2 years are twins.
whereas
in case of 6,6,1
youngest is really youngest.
so 6,6, 1 is correct.
ANSWER:A
Answer: (A) 6,6, 1
Question: In the first half of the 20th century, the population of a particular country increased by 200 percent. In the second half of the century , the population increased by 300 percent. What was the percent increase for the 20th century as a whole?
(A)  500%
(B)  600%
(C)  800%
(D)  1100%
(E)  1200%
Rationale: Say initially population was 100.
What is 200% of 100? It is 200 /100 * 100 = 200.
An increase of 200% means the new population became 100 + 200 = 300
What is 300% of 300? It is 300/100 * 300 = 900
An increase of 300% means the new population now is 300 + 900 = 1200
So from 100, the population increased to 1200 i.e. an increase of 1100.
1100 is what percent of 100?
1100 = x/100 * 100
i.e. it is 1100% D
Answer: (D)  1100%
Question: A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. If the smaller wheel has made 49 revolutions, what will be the number of revolutions made by the larger wheel?
(A) 15
(B) 12
(C) 21
(D) 9
(E) 22
Rationale: Explanation:
Let the number of revolutions made by the larger wheel be x
More cogs, less revolutions (Indirect proportion)
Hence we can write as
(cogs) 6 : 14 :: x : 49
â‡’6Ã—49=14 Ã— x
â‡’x = 21
Answer: Option C
Answer: (C) 21
Question: Mr. Thomas investe d an amount of Rs. 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs. 3508, what was the amount invested in scheme B?
(A) Rs.6400
(B) 2878
(C) 2899
(D) 2660
(E) 2701
Rationale: Let the sum invested in scheme A be Rs. x and that in scheme B be Rs. (13900 - x). Then,
(x * 14 * 2)/100 + [(13900 - x) * 11 * 2]/100 = 3508
28x - 22x = 350800 - (13900 = 22)
6x = 45000 => x = 7500
So, sum invested in scheme B = (13900 - 7500) = Rs. 6400.Answer:A
Answer: (A) Rs.6400
Question: A school has 82635 pens to distribute between 9 classes. If split evenly between classes, how many pens would be left over?
(A) 6
(B) 4
(C) 1
(D) 9
(E) 2
Rationale: First add the digits of the total pens. 82635=24. The closest number divisible by 9 is 18. 24-6=18. Therefore 6 pens would need to be removed. Answer A.
Answer: (A) 6
Question: For dinner at a restaurant, there are x +1 choices of appetizers, y main courses, and z +1 choices of dessert. How many total possible choices are there if you choose 1 appetizer, 1 main course, and 1 dessert for your meal?
(A) xyz+xy+yz+y
(B) xyz + xz
(C) xy + z + 1
(D) xyz + 1
(E) xyz + 1/2
Rationale: x appetizers,
y + 1 main courses,
z dessert
Required: 1 appetizer, 1 main course, and 1 dessert
Number of ways possible = yC1*(x+1)C1*(z+1)C1 {NC1 = N! / (N-1)!*1! = N}
Hence, number of ways = y(x+1)(z+1) = (xy + y)(z+1)=xyz+xy+yz+y
Correct Option: A
Answer: (A) xyz+xy+yz+y
Question: A local restaurant recently renovated its dining space, purchasing new tables and chairs to use in addition to the original tables and chairs. The new tables each seat six customers, while the original tables each seat four customers. Altogether, the restaurant now has 40 tables and is capable of seating 216 customers. How many more new tables than original tables does the restaurant have?
(A) 10
(B) 16
(C) 24
(D) 32
(E) 36
Rationale: If all the tables seated 4, the number of customers could be 4*40 = 160.
216-160 = 56, so 56/2 = 28 tables must be tables seating 6 people.
The number of tables seating 4 people is 40-28 = 12.
The number of new tables is 28-12 = 16 more than the number of old tables.
The answer is B.
Answer: (B) 16
Question: A train running at the speed of 72 km/hr crosses a pole in 9 seconds. Find the length of the train.
(A) 150 meter
(B) 286 meter
(C) 180 meter
(D) 288 meter
(E) 265 meter
Rationale: Speed = 72*(5/18) m/sec
= 20 m/sec
Length of Train (Distance)
= Speed * Time
(20) * 9 = 180 meter
Answer:C
Answer: (C) 180 meter
Question: At a constant Rate of flow, it takes 10 minutes to fill a swimming pool if a large hose is used and 15 minutes if a small hose is Used. At these constant rates, how many minutes will it take to fill the pool when both hoses are used simultaneously?
(A) 6
(B) 12
(C) 15
(D) 25
(E) 50
Rationale: time taken to fill the pool by Large Hose =10 minutes =L or 1/L=1/10 similarly 1/S=1/15
simultaneously it will take 1/L+1/S=1/10+1/15=5/30=6 minutes
Answer : A
Answer: (A) 6
Question: In how many different ways can the letter of the word 'DEIFY' be arranged in such a way that the vowels occupy the odd positions?
(A) 45
(B) 36
(C) 12
(D) 24
(E) 85
Rationale: In the given word there 5 letters in that there are 2 vowels and 3 consonants
no of ways of arranging the vowels=2p2=2
no of ways of arranging the consonants=3p3=6
total number of ways 6*2=12
Answer(C)
Answer: (C) 12
Question: What is the sum of the different positive prime factors of 500?
(A) 10
(B) 7
(C) 15
(D) 16
(E) 18
Rationale: 500
50*10 --> 5*5*2*2*5 --> 5+2=7. Remember its asking for the DIFFERENT positive prime factors of 500.
B
Answer: (B) 7
Question: A sum of the money is distributed among A,B,C,D in the proportion of 5:2:4:3. If C gets $1000 more than D, What is B's share?
(A) 1000
(B) 1500
(C) 2500
(D) 2000
(E) 3200
Rationale: Let the share of A,B,C,D be 5x, 2x, 4x, 3x
then 4x-3x = 1000
x=1000
B's share = 2*1000 = $2000
Answer is D
Answer: (D) 2000
Question: If a = (1/3)b and c = 2a, then which of the following represents the average (arithmetic mean) of a, b, and c, in terms of a ?
(A)  a + 4
(B)  2a
(C)  4a
(D)  (4 1/7)a
(E)  (7 1/4)a
Rationale: Official Answer: B
The average of the three variables isa + b + c/3. However, we need to solve in terms of a, which means we must convert b and c into something in terms of a.
Were told that a =1/3b, which is equivalent to b = 3a. We can plug that in and simplify the average to:a + 3a + c/3
We also know that c = 2a, which we can plug directly into the average expression:
a + 3a + 2a/3
= 6a/3 = 2a, choiceB.
Answer: (B)  2a
Question: If the sides of a triangle are 17.2 cm, 14 cm and 10 cm, what is its area?
(A) 60 cm^2
(B) 70 cm^2
(C) 80 cm^2
(D) 85 cm^2
(E) 90 cm^2
Rationale: The triangle with sides 17.2 cm, 14 cm and 10 cm is right angled, where the hypotenuse is 17.2 cm.
Area of the triangle
= 1/2 * 14 * 10
= 70 cm^2
Answer: B
Answer: (B) 70 cm^2
Question: A sum of money becomes triple itself in 5 years at simple interest. How many years will it become six times at the same rate?
(A) 12 1/2 years
(B) 12 1/7 years
(C) 12 8/2 years
(D) 13 1/2 years
(E) 22 1/2 years
Rationale: 100 ---- 200 ---- 5
200 ---- 5
100 ---- 2 1/2
------------------
600 ---- 12 1/2 years
Answer: A
Answer: (A) 12 1/2 years
Question: In what time a sum of money double itself at 8% per annum simple interest?
(A) 33 1/8%
(B) 33 1/3%
(C) 33 7/3%
(D) 32 1/3%
(E) 12 1/2%
Rationale: P = (P*8*R)/100
R = 12 1/2%
Answer: E
Answer: (E) 12 1/2%
Question: A sum of Rs.1000 at simple interest amounts to Rs. 1192 in 4 years. The S.I. for 1 year is:
(A) Rs. 45
(B) Rs. 70
(C) Rs. 39
(D) Rs. 72
(E) Rs. 48
Rationale: S.I. for 4 years = Rs. (1192 - 1000) = Rs. 192.
S.I. for 1 year = Rs. 192/4 = Rs. 48.
Answer: Option E
Answer: (E) Rs. 48
Question: In an office in Singapore there are 60% female employees. 50 % of all the male employees are computer literate. If there are total 62% employees computer literate out of total 1600 employees, then the no. of female employees who are computer literate ?
(A) 690
(B) 674
(C) 672
(D) 960
(E) None
Rationale: Solution: Total employees,
= 1600
Female employees, 60% of 1600.
= (60 *1600) /100 = 960.
Then male employees,
= 640
50 % of male are computer literate,
= 320 male computer literate.
62 % of total employees are computer literate,
= (62 *1600) /100 = 992 computer literate.
Thus, Female computer literate = 992 - 320
= 672.
Answer: Option C
Answer: (C) 672
Question: A man can row 10 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. How far is the place?
(A) 5.02
(B) 4.92
(C) 4.82
(D) 4.72
(E) 4.61
Rationale: M = 10
S = 1.2
DS = 10 + 1.2 = 11.2
US = 10 - 1.2 = 8.8
x/11.2 + x/8.8 = 1
x = 4.92.Answer: B
Answer: (B) 4.92
Question: Joseph has 3/4 number of books as that of Ron. If each of them add 5 books, what will be the ratio of these two new books numbers ?
(A) 3/4
(B) 8/9
(C) 18/19
(D) 23/24
(E) It cannot be determined from the information given
Rationale: 3/4 = 3x/4x
we need to find out (3x+5)/(4x+5) off course we cannot solve this to arrive at any rational number hence E.
Answer: (E) It cannot be determined from the information given
Question: A car is traveling 68 kilometers per hour. How many meters does the car travel in one minute?
(A) 1250m/min
(B) 1133.33m/min
(C) 2560m/min
(D) 1670m/min
(E) 1890m/min
Rationale: Convert hour into minutes ( 1 hour = 60 minutes) and kilometers into meters (1 km = 1000 m) and simplify
68 kilometers per hour = 68 km/hr
= (68 × 1000 meters) / (60 minutes) = 1,133.33 meters / minute
correct answer is B)1133.33m/min
Answer: (B) 1133.33m/min
Question: what should be the length of rope which is tied to one end to cow and other end to holder.so,that cow can graze 9856 sq.m?
(A) 56 m
(B) 64 m
(C) 88 m
(D) 168 m
(E) 102 m
Rationale: πr^2=9856
r^2=[7/22*9856]=[448*7]=[64*49]=[8*7]^2=56^2
r=56 m
answer A
Answer: (A) 56 m
Question: Which of the following is equal to 2(1/5)%?
(A) 0.012/100
(B) 0.12/100
(C) 2.2/100
(D) 12/100
(E) 12/10
Rationale: This notation may be confusing for some, since it looks like we're multiplying 2 and 1/5
How about adding a space:Which of the following is equal to (2 1/5)%
(2 1/5)% = 2.2% = 2.2/100
Answer:
C
Answer: (C) 2.2/100
Question: If 3/p=5 & 3/q=15 then p-q=?
(A) 5/24
(B) 6/24
(C) 2/15
(D) 8/24
(E) 9/24
Rationale: p=3/5 , q=3/15=>q=1/5
therefore
p-q=(3/5)-(1/5)=2/15
ANSWER:C
Answer: (C) 2/15
Question: An entrepreneurship competition requires registering teams to have 3 team members, at least one of which must be a technology co-founder. If all team members must come from the auditorium during the meet and greet event which has 4 technologists and 6 businessmen, how many possible team submissions are possible?
(A) 76
(B) 100
(C) 162
(D) 198
(E) 202
Rationale: We have 3 scenarios here:
1) 1 tech2 businessmen: 4C1 x 6C2 = 60
2) 2 tech1 businessman: 4C2 x 6C1 = 36
3) 3 tech0 businessmen: 4C3 = 4
Total: 60+36+4 = 100
Answer: B
Answer: (B) 100
Question: After allowing a discount of 15% on the marked price, the selling price is Rs. 6800 for an article. If it was sold at marked price, there would have been a profit of 60%. The cost price of the article is?
(A) 2999
(B) 1689
(C) 5000
(D) 2789
(E) 2675
Rationale: Given SP = Rs. 6800
Marked price = [SP(100)]/(100 - d%) = (6800 * 100)/(100 - 15)
= Rs. 8000
If SP = Rs. 8000, profit = 60%
CP = [SP(100)]/(100 + 60) = (8000 * 100)/160
= Rs.5000
Answer: C
Answer: (C) 5000
Question: If the farmer sells 75 of his chickens, his stock of feed will last for 20 more days than planned, but if he buys 100 more chickens, he will run out of feed 15 days earlier than planned. If no chickens are sold or bought, the farmer will be exactly on schedule. How many chickens does the farmer have?
(A) 60
(B) 120
(C) 240
(D) 275
(E) 300
Rationale: Let V denote the volume of feed one chicken consumes per day. Then the total volume of feed in stock will be V∗D∗C where D is the number of days the feed will last if the number of chickens does not change and CC is the current number of chickens. From the question it follows that
V(D+20)(C−75)=VDC
V(D−15)(C+100)=VDC
The first equation simplifies to 20C−75D=1500. The second equation simplifies to (−15)C+100D=1500 After dividing everything by 5 we get the linear system:
4C−15D=300
(−3)C+20D=300
Solving it we get C=300 D=60
Answer: E
Answer: (E) 300
Question: A bowl was filled with 100 ounces of milk, and 0.004 ounce of the milk evaporated each day during a 90-day period. What percent of the original amount of milk evaporated during this period?
(A) A)0.0036%
(B) B)0.36%
(C) C)3.6%
(D) D)36%
(E) E)42%
Rationale: Total amount of milk evaporated each day during a 90-day period = .004 * 90
= .36
percent of the original amount of milk evaporated during this period = (0.36/100) * 100%
= 0.36 %
Answer B
Answer: (B) B)0.36%
Question: what is the next no. 4 12 84
(A) 632
(B) 732
(C) 832
(D) 850
(E) 902
Rationale: 3^0 + 3 = 4
3^2 + 3 = 12
3^4 + 3 = 84
3^6 + 3 = 732
ANSWER:B
Answer: (B) 732
Question: There are 12 slate rocks, 17 pumice rocks, and 8 granite rocks randomly distributed in a certain field. If 2 rocks are chosen at random and without replacement, what is the probability that both rocks will be slate rocks?
(A) 5/36
(B) 7/64
(C) 9/83
(D) 11/111
(E) 13/135
Rationale: 12/37*11/36 = 11/111
The answer is D.
Answer: (D) 11/111
Question: what is the remainder when 46! is divided by 47
(A) 46
(B) 47
(C) 45
(D) 44
(E) 43
Rationale: when 2!/3 remainder is 2
4!/5 remainder is 4
6!/7 remainder is 6
so when the number is prime in the divisor then the remainder is (no.-1)
46 will be the remainder
ANSWER:A
Answer: (A) 46
Question: A BAG CONTAINS 6 WHITE AND 4 BLACK BALLS .2 BALLS ARE DRAWN AT RANDOM. FIND THE PROBABILITY THAT THEY ARE OF SAME COLOUR.
(A) 4/78
(B) 7/15
(C) 15/7
(D) 5/8
(E) 3/7
Rationale: LET S BE THE SAMPLE SPACE
THEN N(S)=NO OF WAYS OF DRAWING 2 BALLS OUT OF (6+4)=10C2=(10*9)/(2*1)=45
LET E=EVENT OF GETTING BOTH BALLS OF SAME COLOUR
THEN N(E)=NO OF WAYS(2 BALLS OUT OF SIX) OR(2 BALLS OUT OF 4)
=(6C2+4C2)=(6*5)/(2*1)+(4*3)/(2*1)=15+6=21
P(E)=N(E)/N(S)=21/45=7/15
Ans: B
Answer: (B) 7/15
Question: There is 60% increase in an amount in 6years at SI. What will be the CI of Rs. 16,000 after 3 years at the same rate?
(A) 2372
(B) 2572
(C) 4542
(D) 2343
(E) 5296
Rationale: Let P = Rs. 100. Then, S.I. Rs. 60 and T = 6 years.
R = 100 x 60 = 10% p.a.
100 x 6
Now, P = Rs. 16000. T = 3 years and R = 10% p.a.
C.I.
= Rs. 16000 x 1 +	10 3	- 1
100
= Rs. 16000 x	331
1000
= 5296.
E
Answer: (E) 5296
Question: 21 ball numbered 1 to 21. A ballis drawn and then another ball is drawn without replacement.
(A) 7/41
(B) 3/41
(C) 9/42
(D) 4/51
(E) 5/13
Rationale: The probability that first toy shows the even number,
=1021=1021
Since, the toy is not replaced there are now 9 even numbered toys and total 20 toys left.
Hence, probability that second toy shows the even number,
=920=920
Required probability,
=(1021)×(920)=(1021)×(920)
=9/42
C
Answer: (C) 9/42
Question: 0.99999 + 0.11111 = ?
(A) 1
(B) 1.0001
(C) 1.0021
(D) 1.111
(E) 1.1111
Rationale: 0.99999 + 0.00001 = 1
0.1111 + 1 = 1.1111
Correct answer is E.
Answer: (E) 1.1111
Question: A train 300 m long can cross an electric pole in 15 sec and then find the speed of the train?
(A) 65 Kmph
(B) 70 Kmph
(C) 72Kmph
(D) 75 Kmph
(E) 78 Kmph
Rationale: Length = Speed * time
Speed = L/T
S = 300/15
S = 20 M/Sec
Speed= 20*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 72 Kmph
ANSWER:C
Answer: (C) 72Kmph
Question: In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 4 boys when a boy gets any no. of prizes?
(A) 55
(B) 60
(C) 64
(D) 59
(E) 67
Rationale: Ans.(C)
Sol. In this case, repetitions are allowed, so all the three prizes can be given in 4 ways, i.e. (4 x 4 x 4) ways = 43 ways = 64 ways Or nr ways = 43 ways = 64 ways
Answer: (C) 64
Question: If 3 and 5 are prime numbers, which of the following CANNOT be the sum of 3 and 5?
(A) 9
(B) 11
(C) 13
(D) 8
(E) 19
Rationale: ans : A
Answer: (A) 9
Question: At a certain university, the ratio of the number of teaching assistants to the number of students in any course must always be greater than 3:85. At this university, what is the maximum number of students possible in a course that has 4 teaching assistants?
(A) 111
(B) 112
(C) 113
(D) 114
(E) 115
Rationale: (4/3)*85=113 plus remainder
The answer is C.
Answer: (C) 113
Question: In 2005, 30 percent of the math department’s 40 students were female, and in 2007, 40 percent of the math department’s 65 students were female. What was the percent increase from 2005 to 2007 in the number of female students in the department?
(A) 15%
(B) 116%
(C) 136%
(D) 155%
(E) 160%
Rationale: Female students in 2005 = 30% of 40 = 12
Female students in 2007 = 40% of 65 = 26
Percentage increase = [(26 - 12)/12] *100 % = 116%
Correct Option: B
Answer: (B) 116%
Question: 7^6n -1^ 6n When n is an integer > 0 is divisible by
(A) 119
(B) 127
(C) 131
(D) 132
(E) 134
Rationale: 127
B
Answer: (B) 127
Question: How many different ways can 2 students be seated in a row of 7 desks, so that there is always at least one empty desk between the students?
(A)  2
(B)  3
(C)  30
(D)  6
(E)  12
Rationale: 15 ways to seat the students:
with two empty seats between
1 empty w/ one student on the left most
1 empty....right most
two students can be interchanged
15x2=30
C
Answer: (C)  30
Question: A 300 m long train crosses a platform in 54 sec while it crosses a signal pole in 18 sec. What is the length of the platform?
(A) 287
(B) 350
(C) 600
(D) 277
(E) 122
Rationale: Speed = 300/18 = 50/3 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/54 = 50/3
3x + 900 = 2700 => x = 600 m.
Answer: C
Answer: (C) 600
Question: How many even four-digit integers smaller than 2000 are there such that all their digits are different?
(A) 190
(B) 212
(C) 224
(D) 240
(E) 280
Rationale: Case 1: Numbers starting with 1 followed by an EVEN number
The hundreds digit can take 5 numbers (0,2,4,6,8) so 5 ways
The unit digit can take remaining 4 EVEN numbers left after using 1, to be EVEN so 4 ways.
The tens digit can take remaining 7 numbers left after using 3 numbers so 7 ways.
Total = 5*4*7=140
Case 2: Numbers starting with 1 followed by an ODD number
The hundreds digit can take 4 numbers (3,5,7,9) so 4 ways
The unit digit can take 5 numbers (0, 2, 4, 6, 8) to be EVEN, so 5 ways.
The tens digit can take remaining 7 numbers left after using 3 numbers so 7 ways.
Total = 4*5*7 = 140
Hence 140+140=280, correct answer is E
Answer: (E) 280
Question: What is the largest number of four digits which is divisible by 15, 25, 40 and 75 ?
(A) 9600
(B) 5200
(C) 362
(D) 958
(E) 258
Rationale: Explanation:
Largest number of four digits = 9999
LCM of 15, 25, 40 and 75 = 600
9999 ÷ 600 = 16, remainder = 399
Hence,Largest number of four digits which is divisible by 15, 25, 40 and 75
= 9999 - 399 = 9600
Answer:A
Answer: (A) 9600
Question: If x+y=20, x-y=10, for integers of x and y, x=?
(A) 15
(B) 20
(C) 25
(D) 13
(E) 42
Rationale: x+y =20
x-y = 10
2x = 30
x = 15
Answer is A
Answer: (A) 15
Question: What is the difference between the largest number and the least number written with the figures 3, 4, 7, 0, 3?
(A) 94983
(B) 49198
(C) 43983
(D) 41288
(E) 43981
Rationale: Explanation:
74330 Largest
30347 Smallest
-------------
43983
Answer: C
Answer: (C) 43983
Question: Mary's income is 60% more Than Tim's income and Tim's income is 10% less than Juan's income.What % of Juan's income is Mary's income.
(A) 144%
(B) B.120%
(C) 96%
(D) 80%
(E) 64%
Rationale: Even I got 96%
J = 100
T = 100*0.9 = 90
M = 90*1.6 = 144
If Mary's income is x percent of J
M = J*x/100
x = M*100/J = 144*100/100 = 144
Ans:A
Answer: (A) 144%
Question: Find large number from below question The difference of two numbers is 1500. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder
(A) 1797
(B) 1250
(C) 1540
(D) 1600
(E) 1635
Rationale: Let the smaller number be x. Then larger number = (x + 1365).
x + 1500= 6x + 15
5x = 1485
x = 297
Large number = 297+1365 = 1797
A
Answer: (A) 1797