mathewhe/aqua_rat huggingface dataset:
Question: To produce an annual income of Rs. 1200 from a 15 % stock at 90,the amount of stock needed is :
(A) s. 10,000
(B) s. 10,800
(C) s. 14,400
(D) s. 16,000
(E) s. 46,000
Rationale: Solution
For an income of Rs. 15, stock needed = Rs. 100.
For an income of Rs. 1500, stock needed = Rs. 10/12x15000=10,000
Answer A
Answer: (A) s. 10,000
Question: The boys in the class have an average height of 140 cm and the girls in the class have an average height of 150 cm. If the overall class average height is 144 cm, what is the ratio of boys to girls in the class?
(A) 1/2
(B) 3/2
(C) 3/4
(D) 4/3
(E) 4/5
Rationale: (150G + 140B) / (G+B) = 144
150G + 140B = 144(G+B)
6G=4B
B/G = 3/2
The answer is B.
Answer: (B) 3/2
Question: Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:
(A) 3:5
(B) 4:5
(C) 5:5
(D) 4:3
(E) 2:1
Rationale: third no is x
first no - 120% of x = 6x/5
second no = 150x/100= 3x/2
ration of first nos = 6x/5:3x/2 = 12x:15x
= 4:5
ANSWER B
Answer: (B) 4:5
Question: One-fourth of the students at a nursery school are 5 years old or older. If 15 students have not yet reached their fourth birthday, and a total of 25 students are not between 4 years old and 5 years old, how many children are in the nursery school?
(A) 20
(B) 25
(C) 30
(D) 35
(E) 40
Rationale: x/4 students are > 5 yrs
15 students are < 4 yrs
x/4+15 = 25
x/4 = 10
x = 40
Answer: E
Answer: (E) 40
Question: Find the HCF of
2/3,4/6,8/27
(A) 2/27
(B) 8/3
(C) 2/3
(D) 2/27
(E) 1/7
Rationale: Explanation:
Whenever we have to solve this sort of question, remember the formula.
HCF =
HCF of Numerators/LCM of Denominators
So answers will be option 1
Option A
Answer: (A) 2/27
Question: A can do a piece of work in 20 days. B in 15 days A and C in 12 days. In how many days can A finish the work if he is assisted by B on one day and C on the next, alternately?
(A) 2 days
(B) 5 days
(C) 8 days
(D) 7 days
(E) 9 days
Rationale: C
8 days
A + B = 1/20 + 1/15 = 7/60
A + C = 1/20 + 1/12 = 8/60
7/60 + 8/60 = 15/60 = 1/4
4 days * 2 = 8 days
Answer: (C) 8 days
Question: what are the total number of divisors of 600?
(A) 24
(B) 40
(C) 16
(D) 20
(E) 30
Rationale: The prime factorization of 600
600 = (2^3)(3^1)(5^2)
The number of divisors (including 1 and the number itself) is the product of one plus the exponents.
(3+1)(1+1)(2+1) = 24
ANSWER:A
Answer: (A) 24
Question: In Solution P, the proportion of water to alcohol is 3:1. In Solution Q, the proportion of water to alcohol is 2:1. If the two solutions are combined, what is the concentration of alcohol in the new solution if the original solutions were mixed in equal amounts?
(A) 25%
(B) 29%
(C) 33%
(D) 37%
(E) 41%
Rationale: Let V be the total volume of the new solution.
The amount of alcohol added from Solution P is (1/4)*V/2=(1/8)*V
The amount of alcohol added from Solution Q is (1/3)*V/2=(1/6)*V
The total amount of alcohol in the new solution is (1/8+1/6)*V=(7/24)*V
The alcohol concentration is 7/24=29% (approximately)
The answer is B.
Answer: (B) 29%
Question: Eddy and Freddy start simultaneously from city A and they travel to City B and City C respectively. Eddy takes 3 hours and Freddy takes 4 hours to complete the journey. If the distance between City A and City B is 600 kms and City A and City C is 360 kms. What is the ratio of their average speed of travel? (Eddy: Freddy)
(A) 8/3
(B) 3/8
(C) 8/5
(D) 5/8
(E) 20/9
Rationale: Distance traveled by Eddy = 600 km
Time taken by Eddy = 3 hours
Average speed of Eddy = 600/3 = 200 km/hour
Distance traveled by Freddy = 360 km
Time taken by Freddy = 4 hours
Average speed of Freddy = 360/4 = 90 km/hour
Ratio of average speed of Eddy to Freddy = 200/90 = 20/9
Answer E
Answer: (E) 20/9
Question: A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 48 years now, the son's age 4 years back was:
(A) 12 years.
(B) 14 years.
(C) 17 years.
(D) 20 years.
(E) 19 years.
Rationale: Let the son's present age be x years. Then, (48 - x) = x
2x = 48.
x = 24
Son's age 4 years back (24- 4) = 20 years.
ANSWER :D
Answer: (D) 20 years.
Question: The average age of 36 students in a group is 18 years. When teacher's age is included to it, the average increases by one. What is the teacher's age in years ?
(A) 35 years
(B) 55 years
(C) 51 years
(D) 54 years
(E) None of these
Rationale: Explanation:
Age of the teacher = (37 * 19 - 36 * 18) years = 55 years. Answer: B
Answer: (B) 55 years
Question: For which of the following values of n is (100+n)/n NOT an integer?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: This problem is easiest solved by plugging in each answer choice.
A) (100 + 1)/1 = 101/1 = 101
Answer choice A yields an integer.
B) (100 + 2)/2 = 102/2 = 51
Answer choice B yields an integer.
C) (100 + 3)/3 = 103/3 = 34, remainder 2
Answer choice C DOES NOT yield an integer.
Although we believe answer choice C is correct, we should still test the other answer choices.
D) (100 + 4)/4 = 104/4 = 26
Answer choice D yields an integer.
E) (100 + 5)/5 = 105/5 = 21
Answer choice E yields an integer.
Thus, the correct answer is answer choice C.
Answer: (C) 3
Question: How many different ways can you select a pilot and a co pilot if you have 80 people to choose from?
(A) 199
(B) 200
(C) 398
(D) 4950
(E) 6320
Rationale: 1) PERMUTATION:-
since it is selection, we have to find permutation..
80P2= 80!/(80-2)!=6320
ANS:E
Answer: (E) 6320
Question: Prints a page 64 pg per min .If the printed for 3 hours except 10 min.Where there was an paper jam,how many page did it print
(A) 11,700
(B) 2860
(C) 11,684
(D) 12,140
(E) 10,880
Rationale: 3 hrs =180 min
10 min delay so 180-10=170 min
=170*64=10880 pages
ANSWER:E
Answer: (E) 10,880
Question: (17)3.5 x (17)? = 178
(A) 2.29
(B) 2.75
(C) 4.25
(D) 4.5
(E) None of these
Rationale: Solution
let (17)3.5 * (17)x = 178. then, (17)3.5 + x = (17)8.
∴ 3.5 + x = 8 ⇔ x = (8 - 3.5) ⇔ x = 4.5
Answer D
Answer: (D) 4.5
Question: A unit square is subdivided into a grid composed of 9 squares each with sidelength 1/3 . A circle
is drawn through the centers of the 4 squares in the outermost corners of the grid. Compute the
area of this circle.
(A) 1π/9
(B) 3π/9
(C) 5π/9
(D) 7π/9
(E) 2π/9
Rationale: The circle's radius lies between the centers of two diagonally adjacent small squares.
Therefore it is equal to the diagonal of one small square, and r =√2/3.The circle's area is thus
2π/9 .
correct answer E
Answer: (E) 2π/9
Question: How many seconds will a train 100 meters long take to cross a bridge 170 meters long if the speed of the train is 36 kmph?
(A) 54 sec
(B) 65 sec
(C) 25 sec
(D) 45 sec
(E) 27 sec
Rationale: D = 100 + 170 = 270
S = 36 * 5/18 = 10 mps
T = 270/10 = 27 sec
Answer:E
Answer: (E) 27 sec
Question: By how much is three-fifth of 360 greater than four-seventh of 210 ?
(A) 96
(B) 100
(C) 110
(D) 120
(E) 130
Rationale: Explanation:
3/5 of 350 - 4/7 of 210 = 216 - 120 = 96.
Answer: A
Answer: (A) 96
Question: Shalu started a business by investing Rs.50,000. After six months , Nitesh joined her with a capital of Rs.80,000. After 3 years , they earned a profit of Rs. 24,500. What was Shalu's share in the profit?
(A) Rs 9423
(B) Rs 10250
(C) Rs 10500
(D) Rs 14000
(E) None of these
Rationale: Shalu : Nitesh =(50000x36):(80000x30) = 3 : 4. Shalu's share = Rs.(24500x3/7) = Rs.10,500.
Answer C
Answer: (C) Rs 10500
Question: I have a three digit number in my mind. In that number, the tens digit is seven more than the ones digit and the hundreds digit is six less than the tens digit.
What is the number?
(A) 281
(B) 239
(C) 254
(D) 276
(E) 277
Rationale: A
281
Answer: (A) 281
Question: A certain box has 8 cards and each card has one of the integers from 1 to 8 inclusive. Each card has a different number. If 2 different cards are selected at random, what is the probability that the sum of the numbers written on the 2 cards is less than the average (arithmetic mean) of all the numbers written on the 8 cards?
(A) 1/8
(B) 1/12
(C) 1/14
(D) 1/18
(E) 1/28
Rationale: The average of the numbers is 4.5
The total number of ways to choose 2 cards from 8 cards is 8C2 = 28.
The ways to choose 2 cards with a sum less than the average are: {1,2},{1,3}
The probability is 2/28 = 1/14
The answer is C.
Answer: (C) 1/14
Question: Stacy has a 66 page history paper due in 6 days. How many pages per day would she have to write to finish on time?
(A) 9
(B) 8
(C) 11
(D) 8.5
(E) 6
Rationale: 66/6=11
Answer : C
Answer: (C) 11
Question: For arranging a picnic, each student contributed an amount equal to the number of students while the teacher contributed an amount equal to twice the number of students. However, if each student would have contributed an amount equal to twice the number of students and the teacher would have contributed an amount equal to the number of students, they would have generated Rs. 1056 more. Find the number of students in the group?
(A) 24
(B) 25
(C) 33
(D) 50
(E) Cannot be determined
Rationale: Explanation:
Let the number of students = x. Thus, we get,
[(2x2 + x) – (x2 + 2x)] = 1056
x2 - x - 1056 = 0
Solving the equation, we get, x = 33 or x = - 32.
Since the number of students are to be positive, number of students = x = 33
ANSWER: C
Answer: (C) 33
Question: A can do a piece of work in 10 days, B in 15 days. They work together for 5 days, the rest of the work is finished by C in two more days. If they get Rs. 3000 as wages for the whole work, what are the daily wages of A, B and C respectively (in Rs):
(A) 200, 250, 300
(B) 300, 200, 250
(C) 200, 300, 400
(D) None of these
(E) Cannot be determined
Rationale: Explanation:
A's 5 days work = 50%
B's 5 days work = 33.33%
C's 2 days work = 16.66% [100- (50+33.33)]
Ratio of contribution of work of A, B and C = 50:33 1/3 :16 2/3
= 3 : 2 : 1
A's total share = Rs. 1500
B's total share = Rs. 1000
C's total share = Rs. 500
A's one day's earning = Rs.300
B's one day's earning = Rs.200
C's one day's earning = Rs.250
Answer: B
Answer: (B) 300, 200, 250
Question: The smallest 3 digit prime number is?
(A) 101
(B) 103
(C) 109
(D) 113
(E) None
Rationale: The smallest 3-digit number is 100, which is divisible by 2.
100 is not a prime number.
101 < 11 and 101 is not divisible by any of the prime numbers 2, 3, 5, 7, 11.
101 is a prime number.
Hence 101 is the smallest 3-digit prime number.
A)
Answer: (A) 101
Question: If 5 gallons of gasoline are added to a tank that is already filled to 3/4 of its capacity, the tank is then filled to 9/10 of its capacity. How many gallons does the tank hold?
(A)  20
(B)  30
(C)  36
(D)  40
(E)  60
Rationale: Let the Capacity of the tank=C
(3/4)C + 5 = (9/10)C
=>(9/10)C - (3/4)C = 5
=>(3/20)C = 5
=>C = (5*20)/3 = 33.33
Number of gallons of gasoline that the tank currently holds = 3/4*C +5 = 24.99+5 = 29.99=30
Answer B
Answer: (B)  30
Question: Right triangle ABC is to be drawn in the xy-plane so that the right angle is at A and AB is parallel to the y-axis. If the x- and y-coordinates of A, B, and C are to be integers that are consistent with the inequalities -5 ≤ x ≤ 2 and 4 ≤ y ≤ 9 , then how many different triangles can be drawn that will meet these conditions?
(A) 54
(B) 1440
(C) 2,160
(D) 2,916
(E) 148,824
Rationale: We have the rectangle with dimensions 9*5 (9 horizontal dots and 5 vertical). AB is parallel to y-axis and AC is parallel to x-axis.
Choose the (x,y) coordinates for vertex A: 9C1*5C1;
Choose the x coordinate for vertex C (as y coordinate is fixed by A): 8C1, (9-1=8 as 1 horizontal dot is already occupied by A);
Choose the y coordinate for vertex B (as x coordinate is fixed by A): 4C1, (5-1=4 as 1 vertical dot is already occupied by A).
9C1*5C*8C1*4C1=1440.
Answer: B.
Answer: (B) 1440
Question: What is the cost price of an article sold by a trader at 10% loss, given that the trader would have made a profit of 9% if he had sold it for $60 more?
(A) $526.31
(B) 527.31
(C) 516.31
(D) 528.31
(E) 524.31
Rationale: Let C.P. be $x
Then 109% of x - 90% of x = 100
19% of x = 100
19/100 *X = 100
19x = 10000
x = 526.31
Answer is A
Answer: (A) $526.31
Question: For all positive integers m and v, the expression m Θ v represents the remainder when m is divided by v. What is the value of (( 90 Θ 33 ) Θ 17 ) - ( 99 Θ (33 Θ 17)) ?
(A) 10
(B) 8
(C) 6
(D) 4
(E) 2
Rationale: (( 90 Θ 33 ) Θ 17 )
The remainder of 90 divided by 33 is 24;
The remainder of 24 divided by 17 is 7;
( 99 Θ (33 Θ 17))
The remainder of 33 divided by 17 is 16;
7 - 3 = 4.
Answer: D.
Answer: (D) 4
Question: 2^46655 mod 9 = ?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: By remainder theorem
Remainder={[(2^3)^1551*2^2]/9}
=[{(-1)^1551*4}/9]
=5
ANSWER:B
Answer: (B) 5
Question: A man engaged a servant on the condition that he would pay him Rs.1000 and a uniform after one year service. He served only for 9 months and received uniform and Rs.550, find the price of the uniform?
(A) s.80
(B) s.85
(C) s.90
(D) s.800
(E) s.120
Rationale: 9/12 = 3/4 * 1000 = 750
550
-------------
200
1/4 -------- 200
1 --------- ? => Rs.800
ANSWER:D
Answer: (D) s.800
Question: Find the number of terms in an arithmetic progression with the first term 2 and the last term being 62, given that common difference is 2.
(A) 31
(B) 40
(C) 22
(D) 27
(E) 25
Rationale: The n th term = a +(n-1) *d
62 = 2 +(n- 1) *2,
62 – 2 = (n-1) *2,
n = 60/2 +1 = 31.
ANSWER:A
Answer: (A) 31
Question: A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is?
(A) 17
(B) 27
(C) 15
(D) 19
(E) 16
Rationale: Suppose, first pipe alone takes x hours to fill the tank. Then, second and third pipes will take (x - 5) and (x - 9) hours respectively to fill the tank.
1/x + 1/(x - 5) = 1/(x - 9)
(2x - 5)(x - 9) = x(x - 5)
x2 - 18x + 45 = 0
(x- 15)(x - 3) = 0 => x = 15
Answer: C
Answer: (C) 15
Question: If 8 ∙ 2x = 5(y+8), then when y = -8, x =
(A) -4
(B) -3
(C) 0
(D) 4
(E) 8
Rationale: Solution:
8 ∙ 2x = 5(y+8).
or, 8 ∙ 2x = 5(-8+8).
or, 2x = 50.
or, 2x = 1 [anything to the power 0 is 1 then, 50 = 1].
Taking log on both sides,
log 2x = log 1.
or, x log 2 = 0 [since log 1 = 0].
or, x = 0/log 2 [dividing log 2 on both sides].
Therefore, x = 0.
Answer: C
Answer: (C) 0
Question: To fill an art exhibit, the girls in an art course are assigned to create one piece of artwork each in the following distribution: 1/3 are sculptures, 1/8 are oil paintings, 1/2 are watercolors, and the remaining 10 pieces are mosaics. How many girls are in the art class?
(A) 80
(B) 120
(C) 240
(D) 320
(E) 400
Rationale: Let the total number of girls in the art class = s
Distribution of artwork is as
1/3 are sculptures
1/8 are oil paintings
1/2 are watercolors, and the remaining 10 pieces are mosaics
(1/3)s +(1/8)s +(1/2)s + 10 = s
Since remaining 10 pieces are mosaics , (1/24)s = 10
s = 240
Answer C
Answer: (C) 240
Question: Out of 200 donors, ¼ are men and remaining are women. Each male donor donates Rs.3000 per year and each female donor donates ½ of that amount. What is the total yearly collection through donations?
(A) Rs.1, 50,000
(B) Rs.3, 75,000
(C) Rs.1, 40,300
(D) Rs.2, 25,000
(E) Rs.4, 25,000
Rationale: Number of men donors= 200*1/4 =50
Number of women donors=200-50=150
1 man donor donates = Rs.3000
Therefore, 50 men donor donates = 3000* 50= Rs.1,50,000
1 woman donor donates= 3000*1/2 = Rs.1500
Therefore, 150 women donor donates = 1500* 150= Rs.2,25,000
Hence total amount collected = 1,50,000+ 2,25,000
= Rs.3,75,000
ANSWER:B
Answer: (B) Rs.3, 75,000
Question: The principal that amounts to Rs. 4903 in 3 years at 6 1/4 % per annum C.I. compounded annually, is?
(A) s. 3096
(B) s. 4076
(C) s. 4085
(D) s. 4096
(E) s. 5096
Rationale: Principal = [4913 / (1 + 25/(4 * 100))3]
= 4903 * 16/17 * 16/17 * 16/17 = Rs. 4076.
ANSWER:B
Answer: (B) s. 4076
Question: Two pens and three pencils cost 86. Four pens and a pencil cost 112. What is the difference between the cost of a pen and that of a pencil?
(A) 25
(B) 13
(C) 19
(D) Cannot be determined
(E) None of these
Rationale: Let the cost of a pen and a pencil be ‘x’ and ‘y’ respectively. We have to find (x – y).
From the question,
2x + 3y = 86 ..... (i)
4x + y = 112 ......(ii)
Subtracting (i) from (ii), we get
2x – 2y = 26 or, x – y = 13
Answer B
Answer: (B) 13
Question: Three friends had dinner at a restaurant. When the bill was received, Akshitha paid 2/5 as much as Veena paid and Veena paid 1/2 as much as Lasya paid. What fraction of the bill did Veena pay ?
(A) 3/19
(B) 3/12
(C) 5/17
(D) 3/10
(E) 3/14
Rationale: Let Veena paid x,
so Akshitha paid 2x/5 , and Lasya paid 2x,
So total bill paid is given by
x+(2x/5) +2x = 1, we get
i.e. x = 5/17
Answer: C
Answer: (C) 5/17
Question: In the first week of the Year, Jancy saved $1. In each of the next 51 weeks, she saved $1 more than she had saved in the previous week. What was the total amount that Jancy saved during the 52 weeks?
(A) $1,326
(B) $1,352
(C) $1,378
(D) $2,652
(E) $2,756
Rationale: In the first week of the Year, Jancy saved $1.If you don't recall the formula, there is one method:
1 + 2 + 3 + 4 + 5 ........ + 26 + 27 + ............ + 48 + 50 + 51 + 52
Sum of 1stlast digit = 1 + 52 = 53
Sum of 2nd2nd last digit = 2 + 51 = 53
Sum of 3rd3rd last digit = 3 + 50 = 53
.
.
.
.
This is repeated 26 times
So, 26 * 53 = 1378
Answer = C
Answer: (C) $1,378
Question: If 8 ministers are to be seated at a round table conference, then how many different ways can they be seated?
(A) 24
(B) 60
(C) 5040
(D) 720
(E) 180
Rationale: Simple formula:
There are (n - 1)! ways to arrange n distinct objects in a circle.
so its (8-1)! = 7! = 5040=C
Answer: (C) 5040
Question: Simplify: (4 – 5) – (13 – 18 + 2).
(A) -1
(B) –2
(C) 1
(D) 2
(E) 0
Rationale: Solution:
(4 – 5) – (13 – 18 + 2).
= -1-(13+2-18).
= -1-(15-18).
= -1-(-3).
= -1+3.
= 2.
Answer: (D)
Answer: (D) 2
Question: A batsman makes a score of 87 runs in the 17th inning and thus increases his average by 2. Find his average after 17th inning.
(A) 36
(B) 39
(C) 42
(D) 45
(E) None of the above
Rationale: Let the average after 17th inning = x.
Then, average after 16th inning = (x – 2).
∴ 16(x – 2) + 87 = 17x or x = (87 – 32) = 55.
Answer E
Answer: (E) None of the above
Question: If green means red, red means black, black means blue, blue means orange and orange means green, what is the colour of sky in night ?
(A) Blue
(B) Green
(C) Yellow
(D) Orange
(E) Red
Rationale: Explanation:
The colour of sky in night is 'black' and as given 'red' means 'black'.
so, the colour of sky in night is 'red'.
Answer: E
Answer: (E) Red
Question: Find the smallest number of 6 digits which is exactly divisible by 111
(A) 100011
(B) 111111
(C) 101111
(D) 1011111
(E) 211111
Rationale: Smallest number of 6 digits is 100000.
On dividing 100000 by 111, we get 100 as remainder.
Number to be added = (111 - 100) - 11.
Hence, required number = 100011
ANSWER A 100011
Answer: (A) 100011
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 4452 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 = 4452
so x = 424
Nick Contribution is 0.5 more than Archi so 0.5 x =0.5 * 424 = 212
So B. 212 Nis is the correct answer
Answer: (B) 212 Nis
Question: If c = 9/25, w = 15/32, and m + w + c = 1, which of the following gives the values of m, w, and c in increasing order?
(A) c, m, w
(B) c, w, m
(C) m, w, c
(D) m, c, w
(E) w, m, c
Rationale: Answer D - m, c, w
c ~ 1/3
w ~ 1/2
and m+w+c = 1 hence m ~ 1/6
Hence increasing order would be m -> c -> w
Aswer D
Answer: (D) m, c, w
Question: The average salary of the employees in a office is Rs.120/month.The avg salary of officers is Rs.450 and of non officers is Rs 110. If the no.of officers is 15,then find the No of nonofficers in the office.
(A) 400
(B) 420
(C) 430
(D) 495
(E) 510
Rationale: Let no. of non- officers be x
15 * 450 + x * 110 = (x + 15) 120
x = 495
D
Answer: (D) 495
Question: Valentine day 14 Feb. 2005 was celebrated by Anand and shilpa on Monday. They were very happy. What day of the week would come on 14 Feb. 2013?
(A) monday
(B) tuesday
(C) sunday
(D) wednesday
(E) thursday
Rationale: feb 14 2005 - monday
feb 14 2006 - tuesday
feb 14 2007 - wednesday
feb 14 2008 - thursday
feb 14 2009 - saturday [since 2008 is leap year , 2 days ll go forward]
feb 14 2010 - sunday
feb 14 2011 - monday
feb 14 2012 - tuesday
feb 14 2013 - wednesday
ANSWER:D
Answer: (D) wednesday
Question: Let B represent a set of four distinct prime numbers. If the sum of the numbers in B is even and x is a member of B, then what is the least possible value that x can be?
(A) 1
(B) 2
(C) 3
(D) 5
(E) 7
Rationale: We are told that B is a set of four distinct prime numbers, and the sum of the numbers in B is even. Since the question involves odds, evens and the smallest possible prime, you should immediately think of 2, the smallest prime number and the only even prime number.
If 2 were a member of the set, then we would have one even number and three odd numbers. Since such sum would always be odd, 2 cannot be a member of the set. Thus, all the members of B must be odd to yield an even sum.
Since all the members of the set must be odd prime numbers, the answer is the smallest odd prime number, which is 3.
The correct answer is choice (C).
Note:1 is not a prime number.
Answer: (C) 3
Question: A dealer purchased an article at 3/4 of its list price and sold 50% more than the list price. Find his gain percent?
(A) 108%
(B) 300%
(C) 100%
(D) 180%
(E) 200%
Rationale: MP = 100
CP = 75
SP = 150
------
75 ---- 75
100 ---- ? => 100%
Answer: C
Answer: (C) 100%
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 R 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: 40 percent of the ducks included in a certain side effects study were male. If some of the ducks had side effects during the study and 20 percent of the ducks who had side effects were male, what was the ratio of the side effect rate for the male ducks to the side effect rate for the female ducks?
(A) 1/4
(B) 9/14
(C) 2/3
(D) 3/8
(E) 8/7
Rationale: Say total male = 40
Total female =60
Required ratio =( .2/40)/ (.8/60) = 3/8 D is the answer
Answer: (D) 3/8
Question: What do you get if you add 3 to 989 five times?
(A) 902
(B) 990
(C) 678
(D) 992
(E) 309
Rationale: D
992 , 992 , 992 , 992 , 992
Answer: (D) 992