mathewhe/aqua_rat huggingface dataset:
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 5, since 50=2x5x5. What is the greatest possible length of a positive integer less than 1000.
(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) = 7 the length of 512.
the answer is (D)
Answer: (D) 7
Question: A is the average (arithmetic mean) of the first 7 positive multiples of 4 and B is the median of the first 3 positive multiples of positive integer n. If the value of A^2 – B^2 is zero, what is the value of n?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Rationale: If A^2 - B^2 = 0, then let's assume that A = B.
A must equal the 4th positive multiple of 4, thus A = 16, which also equals B.
B is the second positive multiple of n, thus n = 16/2 = 8.
The answer is D.
Answer: (D) 8
Question: If x is to be chosen at random from the set {5,6,7,8} and y is to be chosen at random from the set {7,8,9}, what`s the probability that xy will be even?
(A) 1/6
(B) 1/3
(C) 1/2
(D) 5/6
(E) 2/3
Rationale: The product to be even either one or both must be even, so:
P(x=even OR y=even)=P(x=even)+P(y=even)-P(x=even AND y=even)=2/4+1/3-2/4*1/3=2/3;
Or: P(xy=even)=1-P(xy=odd)=1-2/4*2/3=2/3, so basically we find the probability of the product to be odd (which happens when both x and y are odd) and subtract it from 1.
Answer: E.
Answer: (E) 2/3
Question: If 7 spiders make 7 webs in 7 days, then 1 spider will make 1 web in how many days?
(A) 6
(B) 1
(C) 3
(D) 9
(E) 7
Rationale: Let the required number days be x.
Less spiders, More days (Indirect Proportion)
Less webs, Less days (Direct Proportion)
Spiders	1	:	7 :: 7 : x
Webs	7	:	1
:. 1 * 7 * x = 7 * 1 * 7
x = 7.
Answer is E.
Answer: (E) 7
Question: If 7 spiders make 7 webs in 7 days, then 1 spider will make 1 web in how many days?
(A) 8
(B) 6
(C) 7
(D) 5
(E) 1
Rationale: Explanation:
Let the required number days be x.
Less spiders, More days (Indirect Proportion)
Less webs, Less days (Direct Proportion)
{\color{Blue} therefore } 1 x 7 x x = 7 x 1 x 7
=> x= 7
Answer: C
Answer: (C) 7
Question: A fashion designer sold a pair of jeans to a retail store for 40 percent more than it cost to manufacture the pair of jeans. A customer bought the pair of jeans for 40 percent more than the retailer paid for them. The price the customer paid was what percent greater than the cost of manufacturing the jeans?
(A) 65%
(B) 70%
(C) 75%
(D) 85%
(E) 96%
Rationale: find the product of the two increases: (14/10) * (14/10) which is 1.96 and a 96% increase.
E
Answer: (E) 96%
Question: In Town X, 64 percent of the population are employed, and 48 percent of the population are employed males. What percent of the employed people in Town X are females?
(A) 16%
(B) 25%
(C) 32%
(D) 40%
(E) 52%
Rationale: let population be 100
total employed people = 64% of the population = 64
employed males = 48 % of the population = 48
employed females = 16% of the population = 16
employed females % in terms of employed people = (16/64) * 100 = 25%
Answer is B.
Answer: (B) 25%
Question: Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 seconds. The length of each train is ?
(A) 40 meter
(B) 45 meter
(C) 50 meter
(D) 55 meter
(E) None of these
Rationale: Explanation:
Let the length of each train is x meter
Distance will be x+x = 2x
Relative Speed = 46-36 = 10 km/hr
= 10*(5/18) = 25/9 m/sec
Distance = Speed*Time
2x=25/9∗36
2x=100
=>x=50
So length of both the trains are 50 meters
Option C
Answer: (C) 50 meter
Question: The cost of five chairs and three tables is Rs.3110. Cost of one chair is Rs.210 less than cost one table. What is the cost of two tables and two chairs?
(A) Rs.1660/-
(B) Rs.1860/-
(C) Rs.2600/-
(D) Cannot be determined
(E) None of these
Rationale: Explanation:
Let ‘x’ be the cost of one chair
Then cost of 1 table = x + 210
Given 5x + 3(x+210) = Rs.3110
8x = 3110 – 630 = 2480
Cost of one chair (x) = 2480/8 = 310
Cost of one table = 310 + 210 = rs.520
:. Cost of 2 tables + 2 chairs = 2x520 + 2x310 = Rs.1660
Answer: Option A
Answer: (A) Rs.1660/-
Question: A man is 22 years older than his son. In two years, his age will be twice the age of his son. The
present age of his son is
(A) 20 years
(B) 21 years
(C) 22 years
(D) 24 years
(E) 26 years
Rationale: Explanation:
Let the son's present age be x years. Then, man's present age = (x + 22) years
=> (x + 22) + 2 = 2(x + 2)
=> x + 24 = 2x + 4
So, x = 20
Answer: Option A
Answer: (A) 20 years
Question: X, Y and Z enter into partnership. X invests some money at the beginning, Y invests double the amount after 6 months, and Z invests thrice the amount after 8 months. If the annual gain be Rs.6000. X's share is?
(A) 2500
(B) 2000
(C) 2100
(D) 2200
(E) 2300
Rationale: x* 12 : 2x* 6: 3x* 4
1:1:1
1/3 * 6000 = 2000
Answer: B
Answer: (B) 2000
Question: It costs Rs. x each to make the first thousand copies of a compact disk and Rs. y to make each subsequent copy. If z is greater than 1,000, how many Rupees will it cost to make z copies of the compact disk?
(A) 1000 x + yz
(B) zx - zy
(C) 1000 (z - x) + xy
(D) 1000 (z - y) + xz
(E) 1000 (x- y) + yz
Rationale: Explanatory Answers
We need to find the total cost to make z copies, z > 1000.
The first 1000 copies will cost Rs.x each. Or the total cost of first 1000 copies = Rs.1000x
The remaining z - 1000 copies will cost Rs.y each.
Or the cost of the z - 1000 = Rs.(z - 1000)y
Therefore, total cost = 1000x + zy - 1000y
= 1000(x - y) + yz
Answer E
Answer: (E) 1000 (x- y) + yz
Question: One hour after Yolanda started walking from X to Y, a distance of 60 miles, Bob started walking along the same road from Y to X. If Yolandaâs walking rate was 5 miles per hour and Bobâs was 6 miles per hour, how many miles had Bob walked when they met?
(A) 40
(B) 25
(C) 28
(D) 30
(E) 30.5
Rationale: Let t be the number of hours that Bob had walked when he met Yolanda. Then, when they met, Bob had walked 4t miles and Yolanda had walked 5(t + 1) miles. These distances must sum to 60 miles, so 6t + 5(t + 1) = 60, which may be solved for t as follows
6t + 5(t + 1) = 60
6t + 5t + 5 = 60
11t = 55
T = 5 (hours)
Therefore, Bob had walked 6t = 6(5) = 30 miles when they met. The best answer is D.
Answer: (D) 30
Question: 1 men takes 37$ to Eat a pizza in restaurant such that it have discount multiple of 4 if u eat more pizza . discount increase by multiple of 4 every pizza u eat. for 1 pizza 0% off. for 2 pizza % off for 3 pizza 8% off. pizza without discount is 10$. How much that man eats the pizza.
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: Solution: B. For 1 pizza 10$. For 2 pizza 10$ +9.6$(4% off)=19.6, For 3 pizza 19.6+9.2(8% off)=28.8, For 4 pizza 28.8+8.8(12% off)=37.6. so he have 37 so he cant eat 4th pizza.
Answer: (B) 3
Question: 150 is increased by 40%. Find the final number.
(A) 200
(B) 210
(C) 180
(D) 190
(E) 220
Rationale: Final number = Initial number + 40%(original number) = 150 + 40%(150) = 150 + 60 = 210.
Answer B
Answer: (B) 210
Question: The probability of rain showers in Barcelona on any given day is 0.7. What is the probability that it will rain on exactly one out of three straight days in Barcelona?
(A) 0.189
(B) 0.072
(C) 0.432
(D) 0.72
(E) 0.288
Rationale: IMO This is just for first day! It can rain on 2nd day or 3 rd day (and not rain on other days) in 3 consecutive days!
Hence,
0.7*0.3*0.3 + 0.3*0.7*0.3 + 0.3*0.3*0.7 = 0.189
Option - A
Answer: (A) 0.189
Question: Two trains leave the same train station at 6:00 am and 6:45 am and they travel at 100 kph and 125 kph respectively. How many kilometers from the train station will the two trains be together?
(A) 300
(B) 325
(C) 350
(D) 375
(E) 400
Rationale: At 6:45, the first train is 75 km ahead.
The second train gains 25 km each hour.
The time it takes the second train to catch the first train is 75 / 25 = 3 hours.
In this time, the second train travels 3*125=375 km.
The answer is D.
Answer: (D) 375
Question: The sector of a circle has radius of 21 cm and central angle 135o. Find its perimeter?
(A) 91.5 cm
(B) 91.6 cm
(C) 91.2 cm
(D) 91.3 cm
(E) 91.9 cm
Rationale: Perimeter of the sector = length of the arc + 2(radius)
= (135/360 * 2 * 22/7 * 21) + 2(21)
= 49.5 + 42 = 91.5 cm
Answer: A
Answer: (A) 91.5 cm
Question: What amount does Kiran get if he invests Rs. 18000 at 15% p.a. simple interest for five years?
(A) 31500
(B) 27773
(C) 29989
(D) 28800
(E) 29883
Rationale: Simple interest = (18000 * 5 * 15)/100 = Rs. 13500
Amount = P + I = 18000 + 13500 = Rs. 31500
Answer: A
Answer: (A) 31500
Question: If 2ab - c = 2a(b - 2c), which of the following must be true?
(A)  a=0 and c=0
(B)  a=1/2 and b=2
(C)  b=1 and c=0
(D)  a=1 or b=0
(E)  a=1/4 or c=0
Rationale: 2ab-c = 2a (b-2c)
2ab - c = 2ab - 4ac
c= 4ac
4ac-c = 0
c(4a-1) = 0
Either c = 0; or a = 1/4
E is the answer
Answer: (E)  a=1/4 or c=0
Question: Eric, Nick and Archi make contributions to the Society Of Nature Protection in the ratio of 5:3:2.5. If altogether they contribute 4914 Nis, how much more money does Nick contribute than Archi?
(A) 128 Nis
(B) 212 Nis
(C) 234 Nis
(D) 245 Nis
(E) 288 Nis
Rationale: E:N:A 5:3:2.5
so total = 5x + 3x + 2.5 x = 10.5 x = 4914
so x = 468
Nick Contribution is 0.5 more than Archi so 0.5 x =0.5 * 468 = 234
So C. 234 Nis is the correct answer
Answer: (C) 234 Nis
Question: Two boys starting from the same place walk at a rate of 5kmph and 5.5kmph respectively. What time will they take to be 10km apart, if they walk in the same direction?
(A) 15 hours
(B) 16 hours
(C) 17 hours
(D) 18 hours
(E) 20 hours
Rationale: The relative speed of the boys = 5.5kmph â€“ 5kmph
= 0.5 kmph
Distance between them is 10 km
Time = Distance/Speed
Time= 10km / 0.5 kmph = 20 hrs
answer :E
Answer: (E) 20 hours
Question: The sum of ages of 5 children born 3 years different each is 50 yrs. What is the age of the Elder child?
(A) 7
(B) 9
(C) 16
(D) 18
(E) 21
Rationale: Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.
Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50
5x = 20
x = 4.
x+12= 4+12= 16
C
Answer: (C) 16
Question: A man can row downstream at 18 kmph and upstream at 12 kmph. Find the speed of the man in still water and the speed of stream respectively?
(A) 3
(B) 5
(C) 6
(D) 4
(E) 9
Rationale: Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.
Given x + y = 18 --- (1)
and x - y = 12 --- (2)
From (1) & (2) 2x = 30 => x = 15, y = 3. Answer: A
Answer: (A) 3
Question: If r = 2^3 * 5^2 * 7 and s = 2^3 * 3^2 * 5, which of the following is equal to the greatest common divisor of r and s?
(A) 2 * 5
(B) 2^3 * 5
(C) 2^3 * 5^2
(D) 2*3*5*7
(E) 2^3 * 3^2 *5^2 * 7
Rationale: GCD = product of prime factors raised to the least power = 2^3 * 5
The answer is B.
Answer: (B) 2^3 * 5
Question: What is the square root of 36, divided by 6?
(A) 9
(B) 36
(C) 122
(D) 6
(E) 1
Rationale: Square root is a number times itself
Square root of 36=6, 6/6=1
(E)1
Answer: (E) 1
Question: In 10 years,A will be twice as old as B was 10 years ago.If A is now 9 years older than B,the present age of B is :
(A) 19 Years
(B) 29 Years
(C) 39 Years
(D) 49 Years
(E) 59 Years
Rationale: Solution
Let B's present age = x years.Then,A's present age =(x +9) years.
∴ (x + 9)+ 10 = 2 (x - 10) ⇔ x + 19 = 2x- 20 ⇔ x = 39.Answer C
Answer: (C) 39 Years
Question: The H.C.F. and L.C.M. of 0.63, 1.05 and 2.1
(A) (i)0.20(ii)6.31
(B) (i)0.21(ii)5.30
(C) (i)0.21(ii)6.30
(D) (i)1.21(ii)6.50
(E) None of these
Rationale: Explanation :
Making the same number of decimal places, the given numbers are 0.63, 1.05 and 2.10.
Without decimal places, these numbers are 63, 105 and 210.
Now, H.C.F. of 63, 105 and 210 is 21.
H.C.F. of 0.63, 1.05 and 2.1 is 0.21.
L.C.M. of 63, 105 and 210 is 630.
L.C.M. of 0.63, 1.05 and 2.1 is 6.30.
ANSWER IS C
Answer: (C) (i)0.21(ii)6.30
Question: I flew my tiny seaplane to visit my mother. On the flight up, I flew at 140 mph. On the way home, I flew 88 mph. What was my average speed for the trip?
(A) 114 mph
(B) 110 mph
(C) 88 mph
(D) 100 mph
(E) 99 mph
Rationale: (140 mph +88 mph)/2= 114 mph
Correct answer is: A
Answer: (A) 114 mph
Question: Pradeep has to obtain 25% of the total marks to pass. He got 185 marks and failed by 25 marks. The maximum marks are
(A) 840
(B) 600
(C) 800
(D) 1000
(E) 900
Rationale: Explanation :
Let their maximum marks be x.
Then, 25% of x = 185 + 25
=>25/100x= 210
x = (210100/25)
x= 840.
Answer : A
Answer: (A) 840
Question: On what sum will the compound interest for 2 1⁄2 years at 10% amount to Rs. 31762.5?
(A) Rs.5000
(B) Rs.30000
(C) Rs.25000
(D) Rs.20000
(E) Rs.30000
Rationale: Explanation:
P(1+10/100)2 × (1+(1/2×10)/100) = 31762.5
P(11/10)2 × (21/20) = 31762.5
P = (31762.5 × 20 × 10 × 10)/(21 × 11 × 11)
= (1512.5 × 20 × 10 × 10)/(11 × 11)
= (137.5 × 20 × 10 × 10)/11
= 12.5 × 20 × 10 × 10 = Rs. 25000
Answer: Option C
Answer: (C) Rs.25000
Question: A and B are two stations 390 km apart. A train starts from A at 10 a.m. and travels towards B at 65 kmph. Another train starts from B at 11 a.m. and travels towards A at 35 kmph. At what time do they meet?
(A) 2.15 pm
(B) 2.15 am
(C) 3.15 pm
(D) 3.15 am
(E) None of them
Rationale: Suppose they meet x hours after 10 a.m. Then,
(Distance moved by first in x hrs) + [Distance moved by second in (x-1) hrs]=390.
65x + 35(x-1) = 390 => 100x = 425 => x =	17/4
So, they meet 4 hrs.15 min. after 10 a.m i.e., at 2.15 p.m.
Answer is A.
Answer: (A) 2.15 pm
Question: 2 no's are respectively 40% & 60% more than 3rdnumber. Find the ration of two numbers ?
(A) 4 : 5
(B) 5 : 7
(C) 7 : 8
(D) 7 : 9
(E) 7 : 11
Rationale: Step 1: Let the third number is A
Then first number is 140% of A = 140 x A / 100 = 7A / 5 and second number is 160% of B = 160 x B / 100 = 8B /5.
Step 2: now ratio of first and second number is 7A / 5 : 8B / 5 = 35A : 40B = 7 : 8.
C
Answer: (C) 7 : 8
Question: A five-digit number divisible by 3 is to be formed using numerical 0, 1, 2, 3, 4 and 5 without repetition. The total number of ways this can be done is:
(A) 122
(B) 210
(C) 216
(D) 217
(E) 225
Rationale: First step:
We should determine which 5 digits from given 6, would form the 5 digit number divisible by 3.
We have six digits: 0, 1, 2, 3, 4, 5. Their sum=15.
For a number to be divisible by 3 the sum of the digits must be divisible by 3. As the sum of the six given numbers is 15 (divisible by 3) only 5 digits good to form our 5 digit number would be 15-0={1, 2, 3, 4, 5} and 15-3={0, 1, 2, 4, 5}. Meaning that no other 5 from given six will total the number divisible by 3.
Second step:
We have two set of numbers:
1, 2, 3, 4, 5 and 0, 1, 2, 4, 5. How many 5 digit numbers can be formed using these two sets:
1, 2, 3, 4, 5 --> 5! as any combination of these digits would give us 5 digit number divisible by 3. 5!=120.
0, 1, 2, 4, 5 --> here we can not use 0 as the first digit, otherwise number won't be any more 5 digit and become 4 digit. So, desired # would be total combinations 5!, minus combinations with 0 as the first digit (combination of 4) 4! --> 5!-4!=4!(5-1)=4!*4=96
120+96=216
Answer: C.
Answer: (C) 216
Question: A single discount equivalent to the discount series of 10%, 10% and 5% is?
(A) 23.05
(B) 31.95
(C) 21.65
(D) 23.45
(E) 23.15
Rationale: 100*(90/100)*(90/100)*(95/100) = 76.95
100 - 76.95 = 23.05
Answer: A
Answer: (A) 23.05
Question: What is the value of n if the sum of the consecutive odd intergers W from 1 to n equals 169?
(A) 47
(B) 25
(C) 37
(D) 33
(E) 29
Rationale: Before you tackle this question you must first understand that the question is comprised of two key parts, 1st is finding out how manytermsis in that sequence and 2nd whatactual number valuethat term is. In an arithmetic progression, in this case consecutive odd integers 1, 3, 5, ...., there are two set of rules.
Rule #1 (Arithmetic Sequence): xn = a + d(n-1) Identifies what the actual # in the sequence would be. Each number in the sequence has a term such as 1(is the first term), 3(is the second term) and so on. So if I were to ask you to find out what the 10th term is of that sequence you would use that formula to find that value.
a=1 (first term)
d=2 (the common difference) remember in the sequence 1, 3, 5, 7 the common difference is always 2
*On a side note we use n-1 because we don't have d in the first term, therefore if we were solving for the first term we would get 0 as n-1 and 0 times d would give us 0, leaving only the first term. This works regardless what your first term is in any sequence.
But remember the question asksWhat is thevalueof n if the sum of the consecutive odd integers from 1 to n equals 169?which means we first need a consecutive sequence that sums up to 169 and than find what the value of the n is, in this case it would be the last number in that sequence. In order to find that we first need to knowhow many terms(how many of the n there is) in order to be able to plug n in this formula given we know what the sum is. For that to happen we need to use Rule #2.
Rule #2 (Summing an arithmetic series): 169 = n/2(2a+(n-1)d). Given the question gives us what the sum is (169 in this case) we would simply use this formula to solve for n. Once we solve for n (13 in this case) we can simply plug n into the first formula (rule 1) and find the value.
It feels very confusing and difficult at first, but once you identify the steps all you need to do is plug and play. We have the sum (169) of a sequence, the number of terms in that sequence is (unknown). Rule #2 tells us how many numbers there are in that sequence and Rule #1 gives us what that last term is.
Answer: (B) 25
Question: The average age of the district level hockey team of eleven is 22 years.The average age gets increased by 1 year when the coach age is also included.what is the age of the coach ?
(A) 22 yrs
(B) 34 yrs
(C) 27 yrs
(D) 28 yrs
(E) 19 yrs
Rationale: Total age of players in team = 22 x 11 = 242
When coach is included, total members = 12, Avg age increases by one becomes 23
Total age when coach is included = 23x12 = 276
Age of coach = 276-242 = 34 yrs.
Answer: B
Answer: (B) 34 yrs
Question: An aircraft is flying at a height of 3000m from the ground at an average speed of 400 km/hr while descending. It has to travel 5 kms before it can touch down the runway and start operating its break system. It will take less than 10 seconds to reach the touch down point. How far it is from the touch down point if it had been on they ground.
(A) 5 kms
(B) 4 kms
(C) 3 kms
(D) 6 kms
(E) none of these
Rationale: answer is 4
simple Pythagoras theorem
ANSWER:B
Answer: (B) 4 kms
Question: At what rate percent on simple interest will a sum of money double itself in 30 years?
(A) 3 1/9%
(B) 3 7/3%
(C) 7 1/3%
(D) 5 1/3%
(E) 1 1/3%
Rationale: P = (P*30*R)/100
R = 3 1/3%
Answer: A
Answer: (A) 3 1/9%
Question: How many three digit numbers can having only two consecutive digits identical is
(A) 153
(B) 162
(C) 168
(D) 163
(E) None of these
Rationale: When 0 is the repeated digit like
100, 200, ...., 9 in number
When 0 occurs only once like
110, 220, ....., 9 in number
When 0 does not occur like
112,211, ....., 2 × (8 × 9) = 144 in number.
Hence, total = 9 + 9 + 144 = 162.
Answer B
Answer: (B) 162
Question: If m^2-8m+1=0,then m^3+m^(-3)= ?
(A) 487
(B) 488
(C) 489
(D) 457
(E) 495
Rationale: here from equation 1 we will get
m^2-8m+1=0
m^2=8m-1
m=(8m-1)/m.........(1)
m=8-1/m
so m+1/m=8
now in equation 2
m^3+1/m^3
(m+1/m)(m^2 - m*1/m + 1/m^2)
(m+1/m)(m^2 - 1 + 1/m^2)
(m+1/m)(m^2 + 1/m^2 - 1)
(m+1/m){(m+1/m)^2 - 2m*1/m - 1} {since a^2+b^2=(a+b)^2-2ab}
(m+1/m){(m+1/m)^2 - 2-1}
now putting the value of m from equation 1
8(8^2-2-1)
8(64-3)
=488
ANSWER:B
Answer: (B) 488
Question: The ratio of the radius of two circles is 2: 7, and then the ratio of their areas is?
(A) 1:7
(B) 2:9
(C) 1:9
(D) 4:49
(E) 3:4
Rationale: r1: r2 = 2: 7
Î r1^2: Î r2^2
r1^2: r2^2 = 4:49
Answer: D
Answer: (D) 4:49
Question: A girl was asked to multiply a certain number by 43. She multiplied it by 34 and got his answer less than the correct one by 1215. Find the number to be multiplied.
(A) 130
(B) 132
(C) 135
(D) 136
(E) 138
Rationale: Let the required number be x. Then,
43x – 34x = 1215 or 9x = 1215 or x = 135.
Required number = 135
ANSWER:C
Answer: (C) 135
Question: A certain football coach allows his quarterback to call three plays in a row. If the quarterback can choose from 3 passing plays, 4 running plays, and 2 trick plays, how many different arrangements of plays can be run, if the same play can’t be run more than once?
(A) 24
(B) 125
(C) 243
(D) 504
(E) 729
Rationale: P=3, R=4, and T=2.
There are following cases possible:
1. Different kinf of plays:
PRT (Any combination) = 3*4*2*3!=144.
2. Two same kind of plays and one from other kind of play:
PPR (Any combination. Notice that the two P's here must be different) = C23∗4∗3!=72C32∗4∗3!=72;
PPT = C23∗2∗3!=36;
RRP = C24∗3∗3!=108
RRT = C24∗2∗3!=72
TTP = C22∗3∗3!=18
TTR = C22∗4∗3!=24
3. All three plays are of the same kind:
PPP = C^3_3*3!=6
RRR = C^3_4*3!=24
TTT is not possible because we have only two T's.
Total = 144 + 72 + 36 + 108 + 72 + 18 + 24 + 6 + 24 = 504.
Answer: D.
Answer: (D) 504
Question: 3889 + 16.952 - ? = 3854.002
(A) 51.95
(B) 49.75
(C) 45.97
(D) 47.59
(E) 45.79
Rationale: Let 3889 + 16.952 - x = 3854.002.
Then x = (3889 + 16.952) - 3854.002
= 3905.952 - 3854.002
= 51.95.
Answer is A
Answer: (A) 51.95
Question: A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train?
(A) 299
(B) 180
(C) 288
(D) 127
(E) 122
Rationale: Length of the train be ‘X’
X + 120/15 = X + 180/18
6X + 720 = 5X + 900
X = 180m
Answer: B
Answer: (B) 180
Question: 8597 - ? = 7429 - 4358
(A) 5426
(B) 5706
(C) 5526
(D) 5476
(E) None of these
Rationale: Explanation:
7429 Let 8597 - x = 3071
-4358 Then, x = 8597 - 3071
---- = 5526
3071
----
Answer: C
Answer: (C) 5526
Question: Rajan got married 8 years ago. His present age is 6/5 times his age at the time of his marriage. Rajan's sister was 10 years younger to him at the time of his marriage. The age of Rajan's sister is
(A) 32 years
(B) 36 years
(C) 38 years
(D) 40 years
(E) None
Rationale: Solution
Let Rajan's present age be x years. Then, his age at the time of marriage	=(x-8) years.
Therefore	x= 6/5(x-6)
5x = 6x-48
x=48.
Rajan's sister's age at the time of his marriage=(x-8)-10	=(x-18)=30
Rajan's sister's present age	=(30+8)
= 38 years.
Answer C
Answer: (C) 38 years
Question: Which of the following is closer to (20!+19!)/(20!-19!)?
(A) 11
(B) 13
(C) 1
(D) 3
(E) 7
Rationale: Notice that 20! = (20)(19!),
(20!+19!)*(20!-19!)=[19!(20+1)]*[19!(20-1)]
= 21/19
≈ 1
Answer: C
Answer: (C) 1
Question: Let X be the smallest positive integer such that 28 and 42 are factors of 678 - X, so the value of X is:
(A) 28
(B) 48
(C) 6
(D) 62
(E) 34
Rationale: You can simply check which of the possible values for X will make 678-X divisible by 28 and 42 simultaneously.
The only possible value is X = 6 (because 678 - 6 = 672 = 28*24 = 42*16).
Answer C
Answer: (C) 6
Question: If |8y−3|=|2y+7|, which of the following could be a value of y?
(A) 1
(B) 5/3
(C) 2/5
(D) -2/3
(E) -1
Rationale: 8y − 3 = 2y + 7 or 8y − 3 = -2y - 7
6y = 10 or 10y = -4
y = 5/3 or y = -2/5
Answer: B
Answer: (B) 5/3
Question: A sum fetched total simple interest of 4016.25 at the rate of 10 p.c.p.a. in 5 years. What is the sum?
(A) 8925
(B) 8032.5
(C) 4462.5
(D) 8900
(E) None of these
Rationale: Let the sums be P.
Now, 50% of P = 4016.25
or, P = 8032.5
Answer B
Answer: (B) 8032.5
Question: The least number of complete years in which a sum of money put out at 20% compound interest will be more than doubled is:
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Explanation:
P(1+20/100)n>2P =>(6/5)n>2.
Now,(6/5x6/5x6/5x6/5)>2.
So, n=4years.
ANSWER IS B
Answer: (B) 4