mathewhe/aqua_rat huggingface dataset:
Question: A certain sum is invested at simple interest at 18% p.a. for two years instead of investing at 12% p.a. for the same time period. Therefore the interest received is more by Rs. 600. Find the sum?
(A) 7000
(B) 7029
(C) 2778
(D) 2800
(E) 5000
Rationale: Let the sum be Rs. x.
(x * 18 * 2)/100 - (x * 12 * 2)/100 = 600 => 36x/100 - 24x/100 =600
=> 12x/100 = 600 => x = 5000.Answer:E
Answer: (E) 5000
Question: A number is divided by 406 leaves remainder 115 , What will be the reminder when it will be divided by 29?
(A) 28
(B) 99
(C) 27
(D) 26
(E) 81
Rationale: Let the number be N.
So N = 406x + 115.
Now divide this number by 29. As 406 is exactly divisible by 29, we have to divide 115 by 29 and find the remainder. So remainder = 28
Answer:A
Answer: (A) 28
Question: The average of 11 results is 42, if the average of first six results is 49 and that of the last six is 52. Find the sixth result?
(A) 121
(B) 156
(C) 144
(D) 125
(E) 123
Rationale: 1 to 11 = 11 * 42= 462
1 to 6 = 6 * 49 = 294
6 to 11 = 6 * 52 = 312
6th = 294 + 312 â€“ 462 = 144
Answer:C
Answer: (C) 144
Question: The length of rectangle is thrice its breadth and its perimeter is 96 m, find the area of the rectangle?
(A) 432
(B) 212
(C) 252
(D) 992
(E) 212
Rationale: 2(3x + x) = 96
l = 36 b = 12
lb = 36 * 12 = 432 Answer:A
Answer: (A) 432
Question: A shopkeeper buys mangoes at the rate of 5 a rupee and sells them at 2 a rupee. Find his net profit or loss percent?
(A) 34 %
(B) 30 %
(C) 50 %
(D) 150 %
(E) 33%
Rationale: The total number of mangoes bought by the shopkeeper be 10.
If he buys 5 a rupee, his CP =2
He selling at 2 a rupee, his SP = 5
Profit = SP - CP = 5 - 2 = 3
Profit Percent = 3/2 * 100 = 150 %
Answer:D
Answer: (D) 150 %
Question: The true discount on a bill due 9 months hence at 16% per annum is Rs. 189. The amount of the bill is :
(A) Rs. 1386
(B) Rs. 1764
(C) Rs. 1575
(D) Rs. 2268
(E) None of these
Rationale: Solution
Let P.W. be Rs. x. Then, S.I on Rs. X at 16% for 9 months = Rs. 189.
∴ xX 16x9/12x1x100 = 189 or x = 1575.
∴ P.W = Rs. 1575.
∴ Sum due =P.W + T.D. = Rs. (1575+189) = Rs. 1764.
Answer B
Answer: (B) Rs. 1764
Question: What will come in place of the x in the following Number series? 2, 7, 10, 22, 18, 37, 26, x
(A) 224
(B) 35
(C) 36
(D) 42
(E) 52
Rationale: There are two series here
2, 10, 18, 26, ... (Increase by 8)
7, 22, 37, ... (Increase by 15)
Hence, next term is 37+15 = 52
E
Answer: (E) 52
Question: What is the smallest of six consecutive odd integers whose average (arithmetic mean) is b + 2?
(A) b -3
(B) b- 6
(C) b- 1
(D) b
(E) b+ 1
Rationale: Since the numbers are consecutive odd integers, mean = median = 3rd integer + 4th integer /2
And 1st integer= 3rd integer- 4
let's say 3rd integer = n and 4th integer = n+2
2n+2/2= b+2
n= b+1
1st integer= b+1-4= b-3
A is the answer
Answer: (A) b -3
Question: 5% of (25% of $1600) is?
(A) $20
(B) $30
(C) $45
(D) $15
(E) $60
Rationale: 5% of (25% of $1600) = 5/100 (25/100 * 1600) = $20
Answer is A
Answer: (A) $20
Question: The volume of a cube is 343 cc. Find its surface.
(A) 864
(B) 556
(C) 294
(D) 287
(E) 267
Rationale: a3 = 343 => a = 7
6a2 = 6 * 7 * 7 = 294
Answer:C
Answer: (C) 294
Question: Andrew has a certain number of coins in his pocket. He has three times as many dimes as quarters and six times as many nickels as dimes. A nickel is worth $0.5, a dime is worth $0.10 and a quarter is worth $0.25. If he has a total of $10.15, then which of the following represents the number of dimes in Andrew’s pocket?
(A) 3
(B) 10
(C) 18
(D) 20
(E) 21
Rationale: E.
Let number of quarters be q. Therefore , dimes are 3q and nickels are 18q.
Total value = 18q(.5) + 3q(0.1) + .25q =9.55q
Given total value = 10.15
therefore, 9.55q=10.15 or q=1
Number of dimes = 3q = 3
Answer : A
Answer: (A) 3
Question: Car X began traveling at an average speed of 35 miles per hour. After 72 minutes, car Y began traveling at an average speed of 41 miles per hour. When both cars had traveled the same distance, both cars stopped. How many miles did car X travel from the time car Y began traveling until both cars stopped?
(A) 140
(B) 175
(C) 210
(D) 245
(E) 280
Rationale: In 72 minutes, car X travels 42 miles.
Car Y gains 6 miles each hour, so it takes 7 hours to catch car X.
In 7 hours, car X travels 245 miles.
The answer is D.
Answer: (D) 245
Question: a, b are positive integers. The remainder of a to be divided by 5 is 4 and the remainder of b to be divided by 3 is 1
Which is possible to be the remainder of a*b to be divided by 24
(A) a) 2
(B) b) 4
(C) c) 8
(D) d) 12
(E) e) 20
Rationale: Two ways to do it...
a=5x+4..
b=3y+1.
1) convenient way..
Take x and y as 0, and you will get a*b as 4*1=4
Answer : B
Answer: (B) b) 4
Question: The current of a stream runs at the rate of 4 kmph. A boat goes 12 km and back to the starting point in 2 hours, then find the speed of the boat in still water?
(A) A)17.33
(B) B)2
(C) C)18
(D) D)16
(E) E)13.21
Rationale: S = 4
M = x
DS = x + 4
US = x - 4
12/(x + 4) + 12/(x - 4) = 2
x = 13.21
Answer:E
Answer: (E) E)13.21
Question: The length of a rectangle is twice its breadth. If its length is decreased by 5 cm and breadth is increased by 5 cm, the area of the rectangle is increased by 75 sq. cm. Find the length of the rectangle.
(A) 10 cm
(B) 20cm
(C) 30 cm
(D) 40 cm
(E) 50 cm
Rationale: Let breadth = x. Then, length = 2x. Then,
(2x - 5) (x + 5) - 2x * x = 75 <=> 5x - 25 = 75 <=> x = 20.
:. Length of the rectangle = 20 cm.
Option B
Answer: (B) 20cm
Question: In a company of 200 employees, 120 are females. A total of 100 employees have advanced degrees and the rest have a college degree only. If 40 employees are males with a college degree only, how many employees are females with advanced degrees?
(A) 60
(B) 70
(C) 80
(D) 90
(E) 100
Rationale: The number of males is 200-120=80.
The number of males with advanced degrees is 80-40=40.
The number of females with advanced degrees is 100-40=60.
The answer is A.
Answer: (A) 60
Question: The present ages of three persons are in proportions 4:7:9. Eight years ago, the sum of their ages was 56. Find their present ages?
(A) 16, 28, 35
(B) 16, 28, 36
(C) 16, 28, 39
(D) 16, 28, 34
(E) 16, 28, 31
Rationale: Let their present ages be 4x, 7x and 9x years respectively.
Then, (4x - 8) + (7x - 8) + (9x - 8) = 56
20x = 80 => x = 4
Their present ages are 16, 28 and 36 years respectively.Answer: B
Answer: (B) 16, 28, 36
Question: Pipes A and B can fill a tank in 4 and 6 hours. Pipe C can empty it in 8 hours. If all pipes are opened together, then the tank will be filled in?
(A) 3/2hr
(B) 24/7 hr
(C) 1hr
(D) 9/7hr
(E) 5/3hr
Rationale: Net part filled in 1 hour = 1/4 + 1/6 - 1/8 = 7/24
The tank will be full in 24/7 hr
Answer is B
Answer: (B) 24/7 hr
Question: A computer program assigns consecutive numbers to the days of the week. Sunday is 1, Monday is 2, ..... and Saturday is 7. Every day, the computer program calculates the value of parameter D according to the following definition: D is the number of the day times the value of D on the previous day. If the computer calculated D to be 20 on Wednesday, what would be the value of D calculated on the following Saturday?
(A) 2800
(B) 3400
(C) 3800
(D) 4200
(E) 4500
Rationale: On Saturday, the value would be 7*6*5*20 = 4200
The answer is D.
Answer: (D) 4200
Question: A hall is 15 meters long and 15 meters wide. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, what is the volume of the hall (in cubic meters)?
(A) 975.5
(B) 1250.5
(C) 1465.5
(D) 1687.5
(E) 1824.5
Rationale: 2HL + 2HW = 2LW
H = LW / (L+W)
Volume = LWH = (LW)^2 / (L+W) = 1687.5
The answer is D.
Answer: (D) 1687.5
Question: A and B complete a work in 6 days. A alone can do it in 10 days. If both together can do the work in how many days?
(A) 3.75
(B) 3.76
(C) 3.79
(D) 3.74
(E) 3.71
Rationale: 1/6 + 1/10 = 8/30 = 4/15
15/4 = 3.75 days
Answer: A
Answer: (A) 3.75
Question: Possible arrangements for the word REVIEW if one E can't be next to the other.
(A) 100
(B) 200
(C) 300
(D) 400
(E) 500
Rationale: 1) All arrangements: 6!/2 = 360 (1/2 in order to exclude double counting as [E1, E2] is the same as [E2,E1])
2) All arrangements with two E together: 5!/2 = 60
3) All arrangements in which one E can't be next to the other: 360 - 60 = 300.
ANSWER:C
Answer: (C) 300
Question: A ball team plays games only against the other five teams in its league and always in the following order: John, Paul, George, Ringo and Pete. If the team’s final game of the season is against Ringo, which of the following could be the number of games in the team’s schedule?
(A) 18
(B) 12
(C) 24
(D) 72
(E) 81
Rationale: IMO 'C' is the answer.
Matches will be in multiples of 5x+4. The answer that satisfies this condition is C
Answer: (C) 24
Question: The radius of the wheel of a bus is 70 cms and the speed of the bus is 66 km/h, then the r.p.m. (revolutions per minutes)of the wheel is
(A) 200
(B) 250
(C) 300
(D) 330
(E) None of these
Rationale: Radius of the wheel of bus = 70 cm. Then,
circumference of wheel = 2πr = 140π = 440 cm
Distance covered by bus in 1 minute
= 66⁄60 × 1000 × 100 cms
Distance covered by one revolution of wheel
= circumference of wheel
= 440 cm
∴ Revolutions per minute = 6600000/60×440 = 250
Answer B
Answer: (B) 250
Question: A grocer has a sale of Rs. 5266, Rs. 5744, Rs. 5864, Rs. 6122 and Rs. 6588 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 5750?
(A) 4016
(B) 4076
(C) 4816
(D) 4916
(E) 5916
Rationale: Total sale for 5 months = Rs. (5266 + 5744 + 5864 + 6122+ 6588) = Rs. 29584.
Required sale = Rs. [ (5750 x 6) - 34500 ]
= Rs. (34500 - 29584)
= Rs. 4916.
ANSWER:D
Answer: (D) 4916
Question: The simple interest and the true discount on a certain sum for a given time and at a given rate are Rs. 90 and Rs. 80 respectively. The sum is:
(A) 1360
(B) 1450
(C) 720
(D) 1800
(E) None
Rationale: Sol.
Sum = S.I. * T.D. / (S.I)-(T.D.) = 90 * 80 / (90 - 80) = Rs.720.
Answer C
Answer: (C) 720
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: You are not just choosing two from 80. Each of the two people chosen fills a particular slot. The first filling the pilot slot and the second filling the copilot slot is different from the first filling the copilot slot and the second filling the pilot slot.
So the answer is in a sense (80C2) x 2 = 6320=E
Answer: (E)  6320
Question: If B and C are digits and 8BC is a 3-digit number that is divisible by 4, which of the following is a possible product of B and C?
(A) 1
(B) 2
(C) 5
(D) 6
(E) 14
Rationale: Try with the options -
A. If BC = 1 , both B and C must be 1
B. If BC = 2 , either B or C must be 1 or 2 ; In that case sum of the digits will be 8 + 1 + 2 = 11 which is not divisible by 3
C. If BC = 5 , either B or C must be 1 or 5 ; In that case sum of the digits will be 8 + 1 + 5 = 14 which is not divisible by 3
D. If BC = 6 , then we can have the following possibilities
i. Either B or C must be 2 or 3 ; In that case sum of the digits will be 8 + 2 + 3 = 13 which is not divisible by 3
ii. Either B or C must be 1 or 6 ; In that case sum of the digits will be 8 + 1 + 6 = 15 which is divisible by 3
E. If BC = 14 , then either B or C must be 2 or 7 ; In that case sum of the digits will be 8 + 2 + 7 = 17 which is not divisible by 4
Thus answer is (C)
Answer: (C) 5
Question: A sun is divided among X, Y and Z in such a way that for each rupee X gets, Y gets 45 paisa and Z gets 50 paisa. If the share of Y is RS. 45, what is the total amount?
(A) 115
(B) 116
(C) 195
(D) 118
(E) 119
Rationale: x:y:z = 100:45:50
20:9:10
9 --- 45
39 --- ? => 195
ANSWER:C
Answer: (C) 195
Question: If (260)(3,000) = (78)(1,000^c), what is the value of c?
(A) 5
(B) 4
(C) 3
(D) 2
(E) 1
Rationale: (260)(3,000) = (78)(100^c)
=> (260)(3,000)/78 = 100^c
=> 10,000 = 100^c
=> 100^2 = 1,000^c
Since, base is same so powers will be same too.
So, c=2
Answer will be D
Answer: (D) 2
Question: The area of an isosceles trapezoid with sides of length 5 and bases of length 7 and 13 is?
(A) 40
(B) 41
(C) 42
(D) 43
(E) 44
Rationale: Isosceles trapezoid indicates that if we draw perpendicular from two vertex of the smaller side, the longer side with side 13 will be divided into 3 parts= 7, 3 and 3 (Making one square and two right triangles)
For the right triangle, height will be= (5^2-3^2)^1/2= 4
And the area of trapezoid = 1/2 (B1+B2)H= 1/2*20*4= 40
A
Answer: (A) 40
Question: Anil and Suresh are working on a special assignment. Anil needs 6 hours to type 32 pages on a computer and Suresh needs 5 hours to type 40 pages. If both of them work together on two different computers, how much time is needed to type an assignment of 150 pages?
(A) 11 hours 15 mins
(B) 8 hours
(C) 9 hours
(D) 7 hours
(E) 6 hours
Rationale: Pages typed by Anil in 1 hour = 32/6 = 16/3
Pages typed by Suresh in 1 hour = 40/5 = 8
Pages typed by Anil and Suresh in 1 hour = 16/3 + 8 = 40/3
Time taken to type 150 pages when Anil and Suresh work together = 150 × 3 /40 = 45/4
= 11 ¼ hours = 11 hour 15 minutes
Answer is A.
Answer: (A) 11 hours 15 mins
Question: Eight persons in an organization including X and Y were to be divided in two groups of 4 members each. The total number of groups containing both X and Y is what fraction of the total number of groups which can be formed?
(A) 1/4
(B) 3/14
(C) 4/14
(D) 1/10
(E) 11/14
Rationale: The fraction is nothing but the probability..
Number to choose 4 out of 8= 8C4..
Number to choose X and Y and 2 from remaining 6=6C2..
prob of X and Y choosen=6C2/8C4= {6!/4!2!}/{8!/4!4!}..
6!4!4!/8!4!2!=3/2*7=3/14
Answer : B
Answer: (B) 3/14
Question: Henry has to secure 70% marks to clear his exam of class 6th.
He got 110 marks and failed by 100 marks.
What is the maximum marks ?
(A) 200
(B) 300
(C) 400
(D) 500
(E) 600
Rationale: B
300
To pass the exam ravish needs 110 + 100 = 210 marks.
=> (210/70) *100 = 300
Answer: (B) 300
Question: In which year was the difference between Jyothi's and Arun's monthly income the second highest?
(A) A76
(B) 66
(C) 27
(D) 28
(E) 11
Rationale: Answer:E
Answer: (E) 11
Question: The price of 3 pants and 6 t-shirts is Rs. 750. With the same money one can buy 1 pant and 12 t-shirts. If one wants to buy 8 t-shirts, how much shall she have to pay ?
(A) 150
(B) 250
(C) 400
(D) 450
(E) 550
Rationale: Let the price of a pant and a t-shirt be Rs. x and Rs. y respectively.
Then, 3x + 6y = 750 .... (i)
and x + 12y = 750 .... (ii)
Divide equation (i) by 3, we get the below equation.
= x + 2y = 250. --- (iii)
Now subtract (iii) from (ii)
x + 12y = 750 (-)
x + 2y = 250
----------------
10y = 500
----------------
y= 50
cost of 8 t-shirts = 8*50 = 400
Answer : C
Answer: (C) 400
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 9?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Answer is 6. In the worst case, you could end up drawing 0,1,2,3,4,5. th draw will result in either of 6,7,8 which would result in the numbers adding to 9.
D
Answer: (D) 6
Question: x and y are positive integers. If xy + 3x is odd, then which of the following must be even?
(A) x
(B) y
(C) 3 + y
(D) xy − x
(E) x^2 − y
Rationale: Given that xy + x is odd, which means x(y+3) is odd.
Product of two nos. will be odd only if both the nos. are odd.
Hence x is odd, y+3 is also odd.
y+3 is odd means y is even. Answer will be C.
Answer: (C) 3 + y
Question: Evaluate : 2.5 + 0.0005
(A) 2000
(B) 3000
(C) 1000
(D) 5000
(E) 4000
Rationale: 25/0.0005 = (25*10000) / (0.0005*10000) = 25000 / 5 = 5000
Answer is D.
Answer: (D) 5000
Question: The least number which when divided by 2, 3, 5 and 6 leaves a remainder 3, but when divided by 9 leaves no remainder, is
(A) 16
(B) 63
(C) 73
(D) 83
(E) None of these
Rationale: Explanation:
L.C.M of 2, 3, 5, 6 = 30
therefore Required Number is of the form 30k+3.
Least value of k for which (30k+3) is divisible by 9 is k = 2
therefore Required Number = (30 x 2+3)=63. Answer: B
Answer: (B) 63
Question: Which of the following expressions CANNOT have a negative value
(A) |a + b| + |a – b|
(B) |a + b| – |a|
(C) |2a + b| – |a + b|
(D) a^2 - b^2 – 2|ab|
(E) |a^3 + b^3| – a – b
Rationale: Whenever you are required to find if the equation is a perfect square or not, try to bring everything in the form of a perfect square as they are always positive.
Of the given options, only option D can be written in from of a perfect square.
|a + b| + |a – b|
This will always be positive.
Correct Option: A
Answer: (A) |a + b| + |a – b|
Question: In 2008, the profits of Company N were 10 percent of revenues. In 2009, the revenues of Company N fell by 20 percent, but profits were 16 percent of revenues. The profits in 2009 were what percent of the profits in 2008?
(A) 80%
(B) 105%
(C) 120%
(D) 124.2%
(E) 128%
Rationale: x = profits
r= revenue
x/r = 0,1
x= 10
r=100
2009:
r=80
x/80 = 0,16 = 16/100
x= 80*16/100
x= 12.8
12.8/10 = 1,28 = 128%, Answer E
Answer: (E) 128%
Question: Two identical circles intersect such that their centers and the points at which they intersect form a square of side 2 cm. What is the area of the region where the two circles intersect?
(A) pi^2 - 2
(B) 2pi - 4
(C) 4 - pi
(D) 4 - pi/2
(E) 2 - pi/4
Rationale: Drawing a diagram, we see that the radius of the circle equals the side of the square.
The area of intersection is: pi*r^2/4 - (r^2-pi*r^2/4) = pi*r^2/2 - r^2 = 2pi - 4
The answer is B.
Answer: (B) 2pi - 4
Question: Probability of Cristiano Ronaldo scoring a penalty is twice than the probability of missing it. In a World cup he takes 5 penalties, What is the probability of scoring 3 penalties among the 5?
a) 5 *2 *((2/3)^3 * (1/3)^2)
b) 1-((2/3)^3 * (1/3)^2)
c) 1-((2/3)^2 * (1/3)^3)
d) None of the above.
(A) 5 *2 *((2/3)^3 * (1/3)^2)
(B) 5 *2 *((2/3)^3 * (1/3)^9)
(C) 5 *2 *((2/3)^3 * (1/3)^7)
(D) 5 *2 *((2/3)^3 * (1/3)^5)
(E) 5 *2 *((2/3)^3 * (1/3)^1)
Rationale: Explanation:
We have to use Binomial distribution to solve this question as Ronaldo scoring penalty and not scoring penalty are Dichotomous in nature.
Success + Failure = 1
2x + x = 1
So x = 1/3
Probability of scoring a penalty = p = 2/3 and Not scoring it = q = 1/3
Probability of scoring exactly 'r' of 'n' trials = P(x=r)=nCr.pr.qn−rP(x=r)=nCr.pr.qn−r
P(x=3)=5C3.(23)3.(13)5−3P(x=3)=5C3.(23)3.(13)5−3
= 10.(23)3.(13)210.(23)3.(13)2
Answer:A
Answer: (A) 5 *2 *((2/3)^3 * (1/3)^2)
Question: The sum of two numbers is 66. How much should be added to the sum for it to be exactly divisible by 9 leaving 0 as the reminder?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 1
Rationale: The sum is 66 .Adding 6 to 66 = 66+6=72.
72 is exactly divisible by 9 leaving 0 as the reminder=8. So the answer is A=6
Answer: (A) 6
Question: A completes a work in 6 days and B complete the same work in 12 days. If both of them work together, then the number of days required to complete the work will be?
(A) 4 days
(B) 11 days
(C) 21 days
(D) 22 days
(E) 24 days
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days
Therefore, here, the required number of days = 6 Ã— 12/ 18 = 4 days.
Option 'A'
Answer: (A) 4 days
Question: In May, the grounds keeper at Spring Lake Golf Club built a circular green with an area of 64π square feet. In August, he doubled the distance from the center of the green to the edge of the green. What is the total area of the renovated green?
(A) 100PI
(B) 144PI
(C) 196PI
(D) 256PI
(E) 78
Rationale: AREA OF CIRCLE 64PI SQ FEET =PI R^2 THEREFORE R =8
NOW GREEN RADI DOUBLED I.E R =16 AREA =256 PI
D
Answer: (D) 256PI
Question: A can do a piece of work in 18 days, B in 27 days, C in 36 days. They start worked together . But only C work till the completion of work. A leaves 4 days and B leaves 6 days before the completion of work. In how many days work be completed?
(A) 12
(B) 15
(C) 14
(D) 13
(E) 11
Rationale: Explanation:
Let the work be completed in x days
(x-4)days of A + (x-6)days of B + x days of C = 1
=>x-4/18 + x-6/27 + x/36 = 1
=> 13 x-48 /108 =1
x=12
Total time = 12 days
ANSWER IS A
Answer: (A) 12
Question: A goods train runs at the speed of 72 km/hr and crosses a 280 m long platform in 26 sec. What is the length of the goods train?
(A) 278
(B) 166
(C) 151
(D) 240
(E) 109
Rationale: Speed = 72 * 5/18 = 20 m/sec.
Time = 26 sec.
Let the length of the train be x meters.
Then, (x + 280)/26 = 20
x = 240 m.
Answer:D
Answer: (D) 240
Question: If x and y are different prime numbers, each greater than 4, which of the following must be true?
I. x+y is an even integer
II. xy is an odd integer
III. (x/y) is not an integer
(A) III only
(B) I,II and III
(C) I only
(D) II only
(E) I,II only
Rationale: This question tests your knowledge about the effect of addition and multiplication on odd and even numbers:
Even + Even = Even
Odd + Even = Odd
Odd + Odd = Even
Even * Even = Even
Odd * Even = Even
Odd * Odd = Odd
Given: x and y are different prime numbers, both greater than 4
Statement I: x+y is an even integer
Since x and y are prime numbers greater than 4, they will be odd
Therefore sum will be even.
Correct
Statement II: xy is an odd integer
Since x and y are prime numbers greater than 4, they will be odd
Therefore multiplication will be odd.
Correct
Statement III: (x/y) is not an integer
Since x and y are prime integers, therefore they will not have any common factor apart from 1
Hence (x/y) will not be an integer
Correct
Hence all three statements I, II and III are correct
Answer : B
Answer: (B) I,II and III
Question: The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?
(A) 4 years
(B) 8years
(C) 10 years
(D) 12 years
(E) None of these
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.
Age of the youngest child = x = 4 years.
ANSWER:A
Answer: (A) 4 years
Question: A certain sum of money at simple interest amounted Rs.645 in 12 years at 5% per annum, find the sum?
(A) 403
(B) 410
(C) 500
(D) 340
(E) 455
Rationale: 645 = P [1 + (12*5)/100]
P = 403
Answer: A
Answer: (A) 403
Question: The ages of two persons differ by 16 years. 6 years ago, the elder one was 3 times as old as the younger one. What are their present ages of the elder person
(A) 22
(B) 66
(C) 77
(D) 30
(E) 88
Rationale: Let's take the present age of the elder person = x
and the present age of the younger person = x – 16
(x – 6) = 3 (x-16-6)
=> x – 6 = 3x – 66
=> 2x = 60
=> x = 60/2 = 30
Answer: D
Answer: (D) 30
Question: There are 11 women and 8 men in a certain club. If the club is to select a committee of 2 women and 2 men, how many different such committees are possible?
(A) 120
(B) 720
(C) 1,540
(D) 1,520
(E) 1,980
Rationale: Answer is E. Can somebody tell me what answer I may have found if I had added the 11C2 and 8C2 (55+28=83)?
I'm guessing that would've been the number of 2-member committees which had men and women separately. Is that right?
C
Answer: (C) 1,540
Question: a and b are positive integers less than or equal to 9. If a and b are assembled into the six-digit number abab, which of the following must be a factor of abab?
(A) 3
(B) 4
(C) 5
(D) 6
(E) none of the above
Rationale: 4848 when divided by 3 gives the result 1212
CONCEPT: Rule of Divisibility of 4 isIf sum of the digits of the Number is divisible by 4 then the number will be divisible by 2
SUm of the digits of No. 4848 is 27 which is divisible by 4 hence the Number 4848 will be divisible by 4
B
Answer: (B) 4