mathewhe/aqua_rat huggingface dataset:
Question: The original price of a suit is $200. The price increased 30%, and after this increase, the store published a 30% off coupon for a one-day sale. Given that the consumers who used the coupon on sale day were getting 30% off the increased price, how much did these consumers pay for the suit?
(A) $182
(B) $191
(C) $200
(D) $209
(E) $219
Rationale: Given the foregoing discussion, it may be obvious now the trap-mistake answer is (C). Even if you can’t remember the correct thing to do, at the very least, learn to spot the trap!
The multiplier for a 30% increases is 1 + 0.30 = 1.3, and the multiplier for a 30% decrease is 1 – 0.30 = 0.70, so the combined change is 1.3*0.7 = 0.91, 91% percent of the original, or a 9% decreases. Now, multiply $200*0.91 = $182. Answer = (A).
Answer: (A) $182
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 240 m and they cross each other in 12 sec, then the speed of each train is?
(A) 72
(B) 89
(C) 36
(D) 34
(E) 23
Rationale: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (240 + 240)/12 => x = 20
Speed of each train = 20 m/sec.
= 20 * 18/5 =72 km/hr.
Answer: Option A
Answer: (A) 72
Question: What is the banker's discount if the true discount on a bill of Rs.540 is Rs.90 ?
(A) 108
(B) 120
(C) 102
(D) 106
(E) 105
Rationale: Explanation:
Present Worth, PW = F - TD = 540 - 90 = Rs. 450
Simple Interest on the Present Worth = True Discount
Hence Simple Interest on 450 = 90 ------(Equation 1)
Simple Interest on the face value = Bankers Discount
=> Simple Interest on 540 = Bankers Discount
From Equation 1, Simple Interest on 450 = 90
Hence, Simple Interest on 540 = 90/450×540=540 = Rs. 108
=> Bankers Discount = Rs. 108
Answer: Option A
Answer: (A) 108
Question: Each of the integers from 0 to 8, inclusive, is written on a separate slip of blank paper and the ten slips are dropped into hat. If the slips are then drawn one at a time without replacement, how many must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 10?
(A) 8
(B) 9
(C) 7
(D) 6
(E) 5
Rationale: You should consider the worst case scenario: if you pick numbers 0, 1, 2, 3, 4 and 5 then no two numbers out of these 6 add up to 10.
Now, the next, 7th number whatever it'll be (6,7, or 8) will guarantee that two number WILL add up to 10. So, 7 slips must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 10
Answer: C
Answer: (C) 7
Question: The average weight of 10 men is increased by 1 ½ kg when one of the men who weighs 48 kg is replaced by a new man. What is the weight of the new man?
(A)  80 kg
(B)  63 kg
(C)  70 kg
(D)  75 kg
(E)  85 kg
Rationale: Since the average has increased by 1.5 kg, the weight of the man who stepped in must be equal to 48+10x1.5
48+15=63 Kg
Ans: 'B'
Answer: (B)  63 kg
Question: If an article is sold at 19% profit instead of 12% profit, then the profit would be Rs. 105 more. What is the cost price?
(A) Rs. 1505
(B) Rs. 1510
(C) Rs. 1500
(D) Rs. 1490
(E) None of these
Rationale: Let the cost price of an article be Rs. x.
(19% of x) - (12% of x) = 105
19x/100 - 12x/100 = 105 => 7x = 105 * 100
=> x = 1500
Cost price = Rs. 1500
ANSWER:C
Answer: (C) Rs. 1500
Question: .005/?= .01
(A) .5
(B) .05
(C) .005
(D) .0005
(E) None of them
Rationale: Let .005/x = .01;
Then x = .005/.01
= .5/1
= .5
Answer is A
Answer: (A) .5
Question: 60% of x is greater than 1/3rd of x by 110.what is x?
(A) 100.5
(B) 200.5
(C) 300.5
(D) 350.5
(E) 412.5
Rationale: 6x/10-x/3=110
4x/15=110
x=412.5
ANSWER:E
Answer: (E) 412.5
Question: The grade point average of one third of the classroom is 69; the grade point average of the rest is 60. What is the grade point average of the whole class?
(A) 61.
(B) 63.
(C) 65
(D) 67
(E) It depends how many people are there in the class.
Rationale: Let the number of students in class A be = X1 + X2 + ...... + A1 ( where A1 = remaining students )
Now the remaining avg of the students be A1 / T = 60
A1 = 60T ( we are not sure on the number of students , assuming it as T ).
A = X1 + X2 + ...... + A1 ( First set of students + remaining students).
One third of A students avg is 60.
A / 3 = 69
=> A = 207.
Now X1 + X2 + ...... + A1 = 207.
X1 + X2 + ...... = 207 - 60T.
We are not sure about the number of students in the remaining class + whole class and without that we can't solve this.
Answer: E is correct option.
Answer: (E) It depends how many people are there in the class.
Question: Two trains are running at 40 kmph and 20 kmph respectively in the same direction.Fast train completely passes a man sitting in the slower train in 9 seconds.What is the length of the fast train?
(A) 23 m
(B) 23 2/9 m
(C) 27m
(D) 46 m
(E) 50 m
Rationale: relative speed=20kmph=50/9m/sec
length of the train=50/9*9=50 m
ANSWER:E
Answer: (E) 50 m
Question: The seats in an Engineering college for Computer science, electronics and civil are in the ratio of 5 : 7 :8. There is a proportion to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats ?
(A) 2 : 3 : 4
(B) 6 : 7 : 8
(C) 6 : 8 : 9
(D) 6 : 8 : 7
(E) none of these
Rationale: Originally, let the number of seats for Computer science, electronics and civil are 5x : 7x : 8x respectively.
Number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x)
7x : 21x/2 : 14x = 14x : 21x : 28x = 2 : 3 : 4.
ANSWER:A
Answer: (A) 2 : 3 : 4
Question: The average weight of 4 persons increases by 1.5 kg. If a person weighing 65 kg is replaced by a new person, what could be the weight of the new person?
(A) 71 kg
(B) 77 kg
(C) 76.5 kg
(D) Data inadequate
(E) None of these
Rationale: total weight increases = 4 × 1.5 = 6 kg
so the weight of new person = 65 + 6 = 71 kg
Answer A
Answer: (A) 71 kg
Question: The numerator of a certain fraction is 8 less than the denominator. If 3 is added to the numerator and 3 is subtracted from the denominator, the fraction becomes 3/4. Find the original fraction?
(A) 3/11
(B) 4/11
(C) 5/11
(D) 6/13
(E) 7/13
Rationale: Explanation:
The denominator be P, the numerator will be (P - 8).
The fraction will be (P - 8)/P.
Adding 3 to the numerator and subtracting 3 from the denominator, (P - 8 + 3)/(P - 3) = 3/4.
(P - 5)/(P - 3) = 3/4
P = 20 - 9 => P = 11.
The fraction is: 3/11.
A)
Answer: (A) 3/11
Question: Which of the following leads to the correct mathematical solution for the number of ways that the letters of the word RADAR could be arranged to create a five-letter code?
(A) 5!/(2! x 2!)
(B) 6! − (3! + 2!)
(C) 6! − (3! × 2!)
(D) 6!/(3! + 2!)
(E) 6!/(3! × 2!)
Rationale: Number of letters in word 'RADAR' = 5.
The letters 'A' and 'R' appear 2 times and 2 times respectively in the word 'RADAR'.
Therefore the mathematical solution for number of ways that the letters of the word RADAR can be arranged to create five-letter code
= 5!/(2!*2!)
Answer:A
Answer: (A) 5!/(2! x 2!)
Question: The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 2 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?
(A) 23 years
(B) 22 years
(C) 25 years
(D) 26 years
(E) 27 years
Rationale: EXPLANATION
Let the average age of the whole team by x years.
11x â€“ (26 + 28) = 9(x -1)
11x â€“ 9x = 45
2x = 45
x = 22.
So, average age of the team is 22 years.
Answer B
Answer: (B) 22 years
Question: In covering a distance of 30 km, A takes 2 hours more than B. If A doubles his speed, then he would take 1 hour less than B. A's speed is:
(A) 5 km/hr.
(B) 3 km/hr.
(C) 1 km/hr.
(D) 7 km/hr.
(E) 9 km/hr.
Rationale: C
5 km/hr.
Let A's speed be X km/hr.
Then, 30/x - 30/2x = 3
6x = 30
x = 5 km/hr.
Answer: (A) 5 km/hr.
Question: One half of a two digit number exceeds its one third by 8. What is the sum of the digits of the number?
(A) A)3
(B) B)5
(C) C)12
(D) D)9
(E) E)11
Rationale: x/2 – x/3 = 8 => x =48
4 + 8 = 12
ANSWER:C
Answer: (C) C)12
Question: The ages of two persons differ by 16 years. If 5 years ago, the elder one be 5 times as old as the younger one, their present ages (in years) are respectively
(A) 20,20
(B) 20,10
(C) 25,9
(D) 30,10
(E) None of these
Rationale: Explanation:
Let their ages be x and (x + 16) years.
5 (x - 5) = (x + 16 - 5) or 4x = 36 or x = 9.
Their present ages are 25 years and 9 years
Option C
Answer: (C) 25,9
Question: Patrick purchased 90 pencils and sold them at a loss equal to the selling price of 40 pencils. The cost of 90 pencils is how many times the selling price of 90 pencils?
(A)  0.75
(B)  0.8
(C)  1
(D)  1.2
(E)  1.44
Rationale: Say the cost price of 90 pencils was $90 ($1 per pencil) and the selling price of 1 pencil was p.
Selling at a loss: 90 - 90p = 40p --> p = 9/13.
(cost price)/(selling price) = 1/(9/13) = 13/9 = 1.44.
Answer: E.
Answer: (E)  1.44
Question: Mandy drove from point A to point B at 60 Km/h. On her way back she drove at 80 Km/h and therefore her way back lasted one hour less. What is the distance (in Km) between A and B?
(A) 140.
(B) 200.
(C) 240.
(D) 300.
(E) 600.
Rationale: distance=speed*time
d1=s1t1
d2=s2t2
The distance from point A to point B is the same for each trip so,
d1=d2 and
t2=t1-1
thus,
s1t1=s2(t1-1)
60t1=80(t1-1)
t1=4
60*4= 240
Answer: C
Answer: (C) 240.
Question: S is the infinite sequence S1 = 2, S2 = 22, S3 = 222,...Sk = Sk–1 + 2(10k–1). If p is the sum of the first 30 terms of S, what is the eighth digit of p, counting right to left from the units digit?
(A) 1
(B) 2
(C) 4
(D) 6
(E) 9
Rationale: C
Sum of unit digits of first 30 terms = 60
Sum of tens digits of first 30 terms = 58
Sum of thousands digits of first 30 terms = 56
and so on..
p1 = 0
p2 = (6+58) = 4
p3 = (6+56) = 2
p4 = (6+54) = 0
p5 = (6+52) = 8
p6 = (5+50) = 5
p7 = (5+48) = 3
p8 = (5+46) = 1
ANSWER : A
Answer: (A) 1
Question: In a certain apartment building, there are one-bedroom and two-bedroom apartments. The rental prices of the apartment depend on a number of factors, but on average, two-bedroom apartments have higher rental prices than do one-bedroom apartments. Let M be the average rental price for all apartments in the building. If M is $1,000 higher than the average rental price for all one-bedroom apartments, and if the average rental price for all two-bedroom apartments is $9,000 higher that M, then what percentage of apartments in the building are two-bedroom apartments?
(A) 50%
(B) 40%
(C) 20%
(D) 30%
(E) 10%
Rationale: Ratio of 2 Bedroom Apartment: 1 Bedroom Apartment = 1000 : 9000 -----> 1 : 9
Let total number of Apartments be X
No. of 2 Bedroom Apartment = (1 / 10) * X
percentage of apartments in the building are two-bedroom apartments ---->
(1/10) * 100 ---> 10%
Answer : E
Answer: (E) 10%
Question: Find the number of square tiles to cover the floor of a room measuring 10 m * 12 m leaving 0.25 m space around the room. A side of square tile is given to be 50 cms?
(A) 277
(B) 476
(C) 437
(D) 257
(E) 212
Rationale: 9 1/2 * 11 1/2 = 1/2 * 1/2 * x => x = 437
Answer:C
Answer: (C) 437
Question: Find the value for x from below equation: x/3=-2?
(A) -6
(B) -4
(C) 4
(D) 5
(E) -5
Rationale: 1. Multiply both sides by 3:
x*3/3= -2/3
2. Simplify both sides:
x = -6
A
Answer: (A) -6
Question: If m=9^(x−1), then in terms of m, 3^(4x−5) must be which of the following?
(A) m/3
(B) 9m
(C) 9m^2
(D) m^2/3
(E) m^2/9
Rationale: m = 9 ^ (X-1)
m = 3 ^ (2x-2)
m^2 = 3 ^ (4x-4)
m^2/3 = 3 ^ (4x-5)
Answer D
Answer: (D) m^2/3
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: Find the least number which when divided by 6, 9, 14, 21 and 24 leaves 1, 4, 9, 16 and 19 as remainders respectively, but when divided by 17 leaves no remainder.
(A) 11277
(B) 1003
(C) 3277
(D) 278
(E) 181
Rationale: LCM of 6, 9, 14, 21 and 24 is 504. Required number = (504 k–5) which is divisible by 17 for the least value of k. (504 k – 5) = (493k + 11k – 5) = (17×29)k + (11k–5) Let k = 1 ⇒ (11×1 – 5) = 7 (not divisible by 17) Let k ⇒ = 2 (11×2 – 5) = 17 (divisible by 17) ∴ (17×29)k + (11k–5) is exactly divisible by 17 for k = 2. ∴ Required Number
= (504)k – 5 = (504×2) – 5 = 1003.
Answer:B
Answer: (B) 1003
Question: The probability that a visitor at the mall buys a pack of candy is 20%. If three visitors come to the mall today, what is the probability that exactly two will buy a pack of candy?
(A) .343
(B) .147
(C) .189
(D) .096
(E) .027
Rationale: One case is: candy - candy - no candy
The probability is 1/5*1/5*4/5 = 4/125
There are 3 such cases, so we should multiply this probability by 3.
P(exactly 2 buy candy) = 4/125 * 3 = 12/125 = 0.096
The answer is D.
Answer: (D) .096
Question: an operation * is defined by the equation:
a*b=a-b/a+b, for all numbers a and b such that a is not equal to -b, if a is not equal to -t and a*t=0, then =?
(A) a) -a
(B) b) -1/a
(C) c) 1/a
(D) d)0
(E) e)a
Rationale: If a*t=0 and a=-t then a-t = o of a=t, so answer E
Answer: (E) e)a
Question: find the average of all the number between 6 and 34 which are divisible by 5.
(A) 18
(B) 20
(C) 24
(D) 30
(E) 32
Rationale: Solution
Average = (10+15+20+25+30/5) =100/2 =20 Answer B
Answer: (B) 20
Question: Kevin purchased a house for Rs.61000 and a site for Rs.29000 respectively, if he sold the house for Rs.77000 and the site for Rs.19000, then find the resultant percentage of gain?
(A) 6.66%
(B) 5.55%
(C) 5.56%
(D) 6.65%
(E) 7.77%
Rationale: Sol.
Total CP = 90000 & total SP = 96000 ⇒ gain = SP/CP = 96000/90000 = 1.0666 = 6.66%.
Answer A
Answer: (A) 6.66%
Question: 1, 6, 13, 22, 33, ?
(A) 46
(B) 44
(C) 35
(D) 65
(E) 31
Rationale: A
46
The pattern is + 5, + 7, + 9, + 11,....
Answer: (A) 46
Question: If Scott has earned 15 dollars by working 4 days a week at a constant daily rate for 1 weeks, which of the following represents his daily wage?
(A) 4/15
(B) 1/60
(C) 15/1
(D) 15/3
(E) 15/4
Rationale: Scott total earning = 15
No days he worked = 4
Rate = 1 week
Daily wage = total / (Rate * days)
= 15/(4*1)
E is correct answer...
Answer: (E) 15/4
Question: 8% people of a village in Sri Lanka died by bombardment, 15% of the remainder left the village on account of fear. If now the population is reduced to 3553, how much was it in the beginning?
(A) 2988
(B) 4543
(C) 4400
(D) 2871
(E) 881
Rationale: X * (92/100) * (85/100) = 3553
X = 4543
Answer:B
Answer: (B) 4543
Question: Find the area of the quadrilateral of one of its diagonals is 24 cm and its off sets 9 cm and 6 cm?
(A) 180 cm2
(B) 150 cm2
(C) 168 cm2
(D) 198 cm2
(E) 987 cm2
Rationale: 1/2 * 24(9 + 6)
= 180 cm2
Answer: A
Answer: (A) 180 cm2
Question: On a wedding catering service, An experienced chef can prepare a service for a wedding in 4 hours while an novice chef would finish the preparations in 16 hours.
If the catering service employs the same number of novice and experienced chefs, then how many chefs would it take to prepare a wedding service in 1 hour and 36 minutes?
(A) 2
(B) 3
(C) 4
(D) 6
(E) 8
Rationale: Experienced chefs work = 1 wedding/4 hours
Novice chefs work = 1 wedding/16 hours
Since we don't know the number of experienced or novice chefs but know that there is an equal number each, let the number of chefs for each group equal x
1hr and 36mins = 8/5 an hour
x/4+ x/16 = 1 wedding / (8/5)
x/4 + x/16 = 5/8
x=2
So there are 2 novice chefs and 2 experienced chefs. In total there are 4. The answer is C.
Answer: (C) 4
Question: If 8 parallel lines in a plane is intersected by a family of another 8 parallel lines, how many parallelograms are there in the network thus formed?
(A) 784
(B) 763
(C) 120
(D) 160
(E) 1260
Rationale: parallelogram can formed by 2 horizontal and 2 vertical lines
for horizontal 8c2
for vertical 8c2
total parallelogram is 10 c2*8c2=28*28
=784
ANSWER:A
Answer: (A) 784
Question: A coin is tossed three times. What is the probability that there is at the least one tail?
(A) 7/8
(B) 31/37
(C) 31/18
(D) 31/10
(E) 31/19
Rationale: Let P(T) be the probability of getting least one tail when the coin is tossed three times.
= There is not even a single tail.
i.e. all the outcomes are heads.
= 1/8 ; P(T) = 1 - 1/8 = 7/8
Answer: A
Answer: (A) 7/8
Question: If X+Y = 2X+2Z, X-2Y = 2Z and X+Y+Z = 21, what is the value of Y/Z?
(A) -4.
(B) -2.
(C) -1.7.
(D) 3.
(E) 2.5.
Rationale: X+Y = 2X+2Z
Y= X+2Z---------- 1
X-2Y = 2Z
X-2Z= 2Y--------- 2
Subtracting equation 1 from equation 2
-4Z= Y
Y/Z= -4
A is the answer
Answer: (A) -4.
Question: A, B and C enter into a partnership. A invests 3 times as much as B invests and 2/3 of what C invests. At the end of the year, the profit earned is Rs. 22000. What is the share of C?
(A) Rs. 2250
(B) Rs. 3375
(C) Rs. 6000
(D) Rs. 5625
(E) None of these
Rationale: Explanation:
Let the investment of C be Rs. x.
The inverstment of B = Rs.(2x/3)
The inverstment of A = Rs. (3 × (2/3)x) = Rs. (2x)
Ratio of capitals of A, B and C = 2x : 2x/3 : x = 6 : 2 : 3
C's share = Rs. [(3/11) × 22000] = Rs. 6000
Answer: Option C
Answer: (C) Rs. 6000
Question: Three photographers, Lisa, Mike and Norm, take photos of a wedding. The total of Lisa and Mikes photos is 60 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?
(A) 40
(B) 50
(C) 60
(D) 110
(E) 80
Rationale: L+M=M+N-60 / N=2L+10
60=M+N-L-M
60=N-L
60=2L+10-L
50=L
2(50)+10=110
D
Answer: (D) 110
Question: In a camp,there is a meal for 120 men or 200 children.If 110 children have taken the meal,how many men will be catered to with the remaining meal ?
(A) 20
(B) 30
(C) 40
(D) 50
(E) 54
Rationale: Solution
There is a metal for 200 children. 110 children have taken the meal.
Remaining meal is to be catered to 90 children.
Now, 200 children = 120 men
90 children =( 120/200x90)men= 54 men. Answer E
Answer: (E) 54
Question: How many keystrokes are needed to type numbers from 1 to 1000?
(A) 3001
(B) 2893
(C) 2704
(D) 2890
(E) None of these
Rationale: Explanatory Answer
While typing numbers from 1 to 1000, there are 9 single digit numbers: from 1 to 9.
Each of these numbers requires one keystroke.
That is 9 key strokes.
There are 90 two-digit numbers: from 10 to 99.
Each of these numbers requires 2 keystrokes.
Therefore, 180 keystrokes to type the 2-digit numbers.
There are 900 three-digit numbers: from 100 to 999.
Each of these numbers requires 3 keystrokes.
Therefore, 2700 keystrokes to type the 3-digit numbers.
1000 is a four-digit number which requires 4 keystrokes.
Totally, therefore, one requires 9 + 180 + 2700 + 4 = 2893 keystrokes.
Choice B
Answer: (B) 2893
Question: A man invests in a 16% stock at 128. The interest obtained by him is
(A) 22.5%
(B) 42.5%
(C) 12.5%
(D) 62.5%
(E) 82.5%
Rationale: By investing Rs 128, income derived = Rs. 16
By investing Rs. 100, income derived = = Rs.12.5
Interest obtained = 12.5%
Answer: C
Answer: (C) 12.5%
Question: The product of two natural numbers is 17. Then, the sum of the reciprocals of their squares is:
(A) 1/289
(B) 289/290
(C) 290/289
(D) 289
(E) None of these
Rationale: Let the numbers be a and b. Then,
ab = 17, a = 1 and b = 17
So, 1/a2 + 1/b2 = (a2 + b2)/a2 b2
= (12 + 172)/(1 * 17)2 = 290/289
ANSWER:C
Answer: (C) 290/289
Question: In the island of Hanoi is trapped a princess. To rescue her, the prince has to transfer a set of rings
numbered 1 to 7 from tower A to tower C. The rings are stacked one over the other in an order, with 1 at the top and 6 at the bottom, and have to be stacked in the same fashion on tower C. The prince can move only one ring at a time, and can store the rings in a stack, temporarily, in another tower B.Minimum how many moves of rings, between the towers, will it take the prince to arrange the rings in tower C ?
(A) 13
(B) 14
(C) 15
(D) 16
(E) 17
Rationale: As a total of 7 rings are to be transferred, it is mentioned that only 6 rings are present in Tower A. So, either 1 ring is present separately or there are 7 rings itself in tower A. In both cases, answer should be "13".
As a temporary stack can be used, therefore transfer top 6 rings of Tower A(or all 6 rings in case 7th ring is present separately) to Tower B in "Last in first out" order one ring at a time, so that the 6th ring is at the top of the stack in Tower B. .................-> 6 Moves made
Now, place the seventh ring at the bottom of the stack in Tower C.....1 move made here, so total moves till now= 6+1 =7
Again start transferring all 6 rings from Tower B to Tower C keeping the 6th ring above 7th ring n 1st ring at the top. ...........6 moves made here. Total moves made till now= 7+6 =13
ANSWER:A
Answer: (A) 13
Question: In how many ways a committee consisting of 5 women and 6 men can be formed from 8 women and 10 men?
(A) A)12540
(B) B)11450
(C) C)11760
(D) D)13250
(E) E)12450
Rationale: Required number of ways = 8C5*10C5 = 8C3*10C4 = 11760
Answer is C
Answer: (C) C)11760
Question: Paul's income is 40% less than Rex's income, Quentin's income is 20% less than Paul's income, and Sam's income is 40% less than Paul's income. If Rex gave 60% of his income to Sam and 40% of his income to Quentin, Quentin's new income would be what fraction of Sam's new income?
(A) 11/12
(B) 13/17
(C) 13/19
(D) 12/19
(E) 11/19
Rationale: Let Rex's income = 100, then:
Rex = 100
Paul = 60
Quentin = 48
Sam = 36
Rex gives 60 dollars to sam, so now sam has 96 dollars
Rex gives 40 dollars to Quentin, so now Quentin has 88 dollars
The fraction Q/S = 11/12
ANSWER:A
Answer: (A) 11/12
Question: Ayesha's father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
(A) 2 years
(B) 4 years
(C) 6 years
(D) 8 years
(E) 10 years
Rationale: Mother's age when Ayesha's brother was born = 36 years.
Father's age when Ayesha's brother was born = (38 + 4) = 42 years.
Required difference = (42 - 36) = 6 years.
ANSWER:C
Answer: (C) 6 years
Question: 12 points lie on a circle. How many cyclic quadrilaterals can be drawn by using these points?
(A) 990
(B) 495
(C) 1980
(D) none
(E) Cannot be determined
Rationale: Explanation :
For any set of 4 points we get a cyclic quadrilateral. Number of ways of choosing 4 points out of 12 points is 12C4=495Therefore, we can draw 495 quadrilaterals.
Answer : B
Answer: (B) 495
Question: A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 36 sec. What is the length of the platform?
(A) 389 m
(B) 350 m
(C) 289 m
(D) 299 m
(E) 25 m
Rationale: Speed = 300/36= 25/3 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/39 = 25/3
=> x = 25 m.
Answer:E
Answer: (E) 25 m
Question: The numbers in which of the following pairs do NOT have a pair of distinct prime divisors in common?
(A) 10 and 20
(B) 12 and 18
(C) 20 and 16
(D) 21 and 63
(E) 22 and 88
Rationale: 16 has only the prime 2 (16=2^4) in its prime factorization, so it can not have a PAIR of distinct prime divisors in common with ANY of the numbers.
The answer is C.
Answer: (C) 20 and 16
Question: Find the value of 15 + 2 â€¢ (8 â€“ 3)
(A) 25
(B) 13
(C) 17
(D) 24
(E) 15
Rationale: 15 + 2 â€¢ (8 â€“ 3)
= 15 + 2 (5)
= 15 + 2 *5
= 15 + 10
= 25
correct answer A
Answer: (A) 25
Question: 5 blue marbles, 3 red marbles and 4 purple marbles are placed in a bag. If 4 marbles are drawn without replacement, what is the probability that the result will not be 2 blue and 2 purple marbles?
(A) 4/33
(B) (5/36)^2
(C) 1/2
(D) (31/36)^2
(E) 29/33
Rationale: Answer is 29/33.
The probability of 2 blue and 2 purple marbles selected is 5C2.4C2/12C4 =4/33.
Subtracting the above from 1 we get 29/33 E
Answer: (E) 29/33