mathewhe/aqua_rat huggingface dataset:
Question: If x and y are integers such that |y + 3| ≤ 3 and 2y – 3x + 6 = 0, what is the least possible value E of the product xy?
(A) 	-12
(B) 	-3
(C) 	0
(D) 	2
(E) 	None of the above
Rationale: How to deal with inequalities involving absolute values? First example shows us the so callednumber case
In this case we have |y + 3| ≤ 3 which is generalized |something| ≤ some number. First we solve as if there were no absolute value brackets:
y + 3 ≤ 3
y ≤ 0
So y is 0 or negative
Second scenario - remove the absolute value brackets. Put a negative sign around the other side of the inequality,ANDflip the sign:
y + 3 >= -3
y >= -6
Therefore we have a possible range for y: -6=<y<=0
Ok, so far so good, we're half way through. What about x?
Here's the formula: 2y – 3x + 6 = 0, rewrite it as 2y + 6 = 3x.
You can say that 2y + 6 is a multiple of 3 (=3x). So all values which must be integer must also satisfy this constraint. I'm just saying that, so it's easier to evaluate all the possible numbers (-6, -3, 0). If you plug in y = 0, x will be 2 and xy = 0 as the lowest possible value E.
Hence, Answer Choice C is the one to go.
Answer: (C) 	0
Question: Look at this series 8, 22, 8, 28, 8, ... What number should come next?
(A) 34
(B) 8
(C) 12
(D) 44
(E) 30
Rationale: simple addition series with a random number, 8 - interpolated as every other number. In the series, 6 is added to each number except 8, to arrive at the next number.
ANSWER A
Answer: (A) 34
Question: 2+2+2²+2³ ... +2^11
(A) 2^9
(B) 2^10
(C) 2^16
(D) 2^12
(E) 2^37
Rationale: 2+2=2^2
2^2+2^2=(2^2)*(1+1)=2^3
2^3+2^3=(2^3)*(1+1)=2^4
so you can notice the pattern... in the end you will have 2^11+2^11, which will give you 2^12
Answer D
Answer: (D) 2^12
Question: One fourth of one third of two fifth of a number is 30. What will be40% of that number
(A) A)360
(B) B)150
(C) C)180
(D) D)200
(E) E)220
Rationale: Explanation:
(1/4) * (1/3) * (2/5) * x = 30
then x = 30 * 30 = 900
40% of 900 = 360
Answer: Option A
Answer: (A) A)360
Question: 30 square stone slabs of equal size were needed to cover a floor area of 67.5 sq.m. Find the length of each stone slab?
(A) 150cm
(B) 767cm
(C) 88cm
(D) 666cm
(E) 776cm
Rationale: Area of each slab
=67.5/30m2=2.25m2
Length of each slab √2.25=1.5m=150cm
Answer: (A) 150cm
Question: If a = 105 and a^3= 21 * 25 * 15 * b, what is the value of b?
(A) 35
(B) 42
(C) 45
(D) 147
(E) 54
Rationale: First step will be to break down all the numbers into their prime factors.
105 = 3 * 5 * 7
21 = 7 * 3
25 = 5 * 5
15 = 3 * 5
so, (105)^3 = 3 * 7 * 5 * 5 *3 *5 *b
Therefore (3 * 5 * 7) ^ 3 = 3^2 * 5^3 * 7 *b
Therefore, b = 3^3 * 5^3 * 7 ^3/3 ^2 * 5 ^3 * 7
b = 3*7^2 =3* 49=147
Correct answer D.
Answer: (D) 147
Question: Eight litres are drawn off from a vessel full of water and substituted by pure milk. Again eight litres of the mixture are drawn off and substituted by pure milk. If the vessel now contains water and milk in the ratio 9:40, find the capacity of the vessel.
(A) 21 liters
(B) 22 liters
(C) 20 liters
(D) 14 liters
(E) 28 liters
Rationale: Lets start with option:
Vessel capacity be 20litre:
8litre water removed and milk added: W=12litre, M=8litre
8litre mixture removed, (removed proportionately) : W= 12-4.8 = 7.2litre, M= 8-3.2 = 4.8 litre
8litre milk added ; W=7.2 litre, M=12.8 litre
Ratio will be 72/128 = 18/32 = 9/16
As we can see that milk is less so we have to select the ratio even less than 20,
Vessel capcity be 14 litre
8litre water removed and milk added: W=6 litre, M=8 litre
8litre mixture removed, (removed proportionately) : W= 6-3.4 = 2.6 litre, M= 8-4.6 = 3.4 litre
8litre milk added ; W=2.6 litre, M=11.4 litre
Ratio will be 26/114 = 8.66/38 (approx) very close to 9/40
So correct option is D
Answer: (D) 14 liters
Question: A train having a length of 240 m passes a post in 24 seconds. How long will it take to pass a platform having a length of 640 m?
(A) 120 sec
(B) 99 sec
(C) 89 sec
(D) 80 sec
(E) 88 sec
Rationale: Explanation:
v = 240/24 (where v is the speed of the train) = 10 m/s
t = (240+640)/10 = 88 seconds
Answer: Option E
Answer: (E) 88 sec
Question: P, Q and R can do a work in 5 , 7 and 10 days respectively. They completed the work and got Rs.310. What is the share of Q and R respectively?
(A) 100 and 80
(B) 100 and 90
(C) 100 and 110
(D) 70 and 100
(E) 100 and 70
Rationale: The ratio of their working rates = 1/5 : 1/7 : 1/10 = 14 : 10 : 7.
Since, they work together, the share of Q
= 10/31 * 310 = Rs.100
the share of R = 7/31 * 310 = Rs.70
the share of Q and R respectively is Rs. 100 and Rs.70
Answer: E
Answer: (E) 100 and 70
Question: Two trains travelling in the same direction at 40 and 22 kmph completely pass off another in 1 minute. If the length of the first train is 125 m, what is the length of the second train?
(A) 156 m
(B) 189 m
(C) 175 m
(D) 134 m
(E) 972 m
Rationale: RS = 40 – 22 = 18 * 5/18 = 5 mps
T = 60 sec
D = 5 * 60 = 300 m
125
--------
175 m
Answer:C
Answer: (C) 175 m
Question: The probability is 1/2 that a certain coin will turn up heads on any given toss. If the coin is to be tossed three times, what is the probability that on at least one of the tosses the coin will turn up tails?
(A)  1/8
(B)  1/2
(C)  3/4
(D)  7/8
(E)  15/16
Rationale: P(at last 1 tails) = 1 - P(all heads) = 1 - (1/2)^3 = 7/8.
Answer: D.
Answer: (D)  7/8
Question: The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?
(A) 140
(B) 156
(C) 175
(D) 214
(E) None of these
Rationale: Explanation:
Given that the area of the square = 1225 sq.units
=> Side of square = âˆš1225 = 35 units
The radius of the circle = side of the square = 35 units Length of the rectangle = 2/5 * 35 = 14 units
Given that breadth = 10 units
Area of the rectangle = lb = 14 * 10 = 140 sq.units
ANSWER IS A
Answer: (A) 140
Question: Jennifer works 20 days a month at d dollars per day for m months out of the year. Which of the following represents her yearly pay?
(A) m/(20d)
(B) 20d
(C) 10md/6
(D) 20d/m
(E) 20md
Rationale: Total income of Jennifer in a year = d*20*m dollars. = 20dm Answer E
Answer: (E) 20md
Question: In how many ways W can the crew of a ten oared boat be arranged ,when of the ten persons available, 2 of whom can row only on the bow side and 3 of whom can row only on the stroke side?
(A) 1. 10!/(2! * 3!)
(B) 2. 10!/(8! * 7!)
(C) 3. 5!/(3! * 2!)
(D) 4. (5!)^3/(3! * 2!)
(E) 5. 5!/(8! * 7!)
Rationale: Ans is D.
Going by the assumtion that both the Bow side and Stroke side will have 5 person each.
Five(3+2) of them had allready been selected(according to their preference), so from the remaining 5 we have to select 2 for the stroke side or 3 for the bow side.
and the 5 crew of each side can be arranged in 5! ways=W
Hence answer is 5C3 * 5! * 5!= (5!)^3/ 3!2!.D
Answer: (D) 4. (5!)^3/(3! * 2!)
Question: A monkey climbs 30 feet at the beginning of each hour and rests for a while when he slips back 20 feet before he again starts climbing in the beginning of the next hour. If he begins his ascent at 10.00 a.m., at what time will he first touch a flag at 120 feet from the ground?
(A) 4 p.m.
(B) 5 p.m.
(C) 6 p.m.
(D) 8 p.m.
(E) None of these
Rationale: Explanation:
Net ascent of the monkey in 1 hour = (30 - 20) feet = 10 feet.
So, the monkey ascends 90 feet in 9 hours i.e. till 7 p.m.
Clearly, in the next 1 hour i.e. till 8 p.m. the monkey ascends remaining 30 feet to touch the flag.
Answer:D
Answer: (D) 8 p.m.
Question: A swimming pool 9 m wide and 12 m long is 1 m deep on the shallow side and 4 m deep on the deeper side. Its volume is:
(A) 260
(B) 262
(C) 270
(D) 272
(E) None of these
Rationale: Explanation:
Volume will be length * breadth * height, but in this case two heights are given so we will take average,
Volume=(12∗9∗(1+4 /2))m312∗9∗2.5m3=270m3
Option C
Answer: (C) 270
Question: In a school 50% of the students are younger than 10, 1/20 are 10 years old and 1/10 are older than 10 but younger than 12, the remaining 70 students are 12 years or older. How many students are 10 years old?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 10
Rationale: Let us write the fraction for each group of students
Group A: younger than 10: 50% = 50/100 = 1/2
Group B: 10 years old: 1/20
Group C: older that 10 but younger than 12: 1/10
Group D: 12 years or older: 70 students
The fraction for group A, B and C together is given by
1 / 2 + 1 / 20 + 1 / 10 = 10 / 20 + 1 / 20 + 2 / 20 , common denominator
= 13 / 20 , add numerators
The fraction for group D is given by
20 / 20 - 13 / 20 = 7 / 20 and corresponds to 70 students
If X is the total number of students, then
7 / 20 of X = 70
or (7 / 20) × X = 70
Solve for X
X = 70 × (20 / 7) = 200
Students who are 10 years old have a fraction of 1 / 20 of the total X and their number is equal to
(1 / 20) of 200 = 10 students
correct answer is E)10
Answer: (E) 10
Question: What is the smallest prime number?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: Explanation :
smallest prime number is 2.
0 and 1 are neither prime numbers nor composite numbers. Answer : Option C
Answer: (C) 2
Question: If a coin has an equal probability of landing heads up or tails up each time it is flipped , what is the probability that the coin will land heads up exactly twice in 2 consecutive flips ?
(A) 0.125
(B) 0.225
(C) 0.25
(D) 0.5
(E) 0.666
Rationale: Total number of ways in which H or T can appear in 3 tosses of coin is
= 2 * 2 = 4 ways
For 2 H
HH,
Thus probability is
= P(HH)
= 1/4
= .25
Answer : C
Answer: (C) 0.25
Question: What will come in place of the x in the following Number series? 6, 12, 21, 33 , x
(A) 33
(B) 35
(C) 39
(D) 48
(E) 42
Rationale: The pattern is + 6, + 9, + 12, +15 â€¦â€¦â€¦..
So the missing term is = 33 + 15 = 48
Answer : D
Answer: (D) 48
Question: Before being simplified, the instructions for computing income tax in country R were to add 4 percent of one's annual income to the average(arithmetic mean) of 100 units of Country R's currency and 1 percent of one's annual income. Which of the following represents the simplified formula for computing the income tax, in country R's currency, for a person in that country whose annual income is I?
(A) 50 + I/200
(B) 50 + 3I/100
(C) 50+ I/40
(D) 100+ I/50
(E) 50+ 9I/200
Rationale: Income of a person is I
4 percent of ones annual income = 4I/100
100 units of Country R's currency = 100
1 percent of one's annual income = I/100
Average of 100 units and 1 percent annual income = 50 + I/200
Sum of average and 4 percent = 4I/100 + 50 + I/200
= 50 + 9I/200
So answer is E.
Answer: (E) 50+ 9I/200
Question: A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 350 m long platform?
(A) 33
(B) 66
(C) 88
(D) 47
(E) 88
Rationale: Let the length of the train be x m.
When a train crosses an electric pole, the distance covered is its own length.
So, x = 12 * 36 * 5 /18 m = 120 m.
Time taken to cross the platform = (120 +350)/ 36 * 5/18 = 47 min.
Answer:D
Answer: (D) 47
Question: A rectangular football field is fenced on all four sides. The length of the football field is twice the length of its breadth. The cost of fencing the field was $360. The football management has decided to change the dimensions of field by increasing the breadth by 50% of its original value and reducing the length by 5% of its original value and fence the field again.. What will be the cost of the new fencing?
(A) $360
(B) $180
(C) $425
(D) $408
(E) $415
Rationale: Let's take x to be the breadth. Then the length of the football field is 2x.
The perimeter of the old football field is x + 2x + x + 2x = 6x.
Now, for the new football field:
The new breadth = 1.5 times old breadth = 1.5x
The new length is 0.95 times old length = (.95)2x = 1.9x
So the new perimeter is 1.5x + 1.9x + 1.5x + 1.9x = 6.8x.
for old perimeter rate is $360
For new perimeter = (360 * 6.8)/6
= 408
Ans - D
Answer: (D) $408
Question: Reeya obtained 65, 67, 76, 82 and 85 out of 100 in different subjects, What will be the average
(A) 70
(B) 75
(C) 80
(D) 85
(E) 90
Rationale: Explanation:
(65+67+76+82+85 / 5)=75
Option B
Answer: (B) 75
Question: In a lottery, there are 10 prizes and 35 blanks. A lottery is drawn at random. What is the probability of getting a prize?
(A) 1/10
(B) 2/5
(C) 2/7
(D) 2/9
(E) None
Rationale: Solution
P(getting a prize)	= 10 / (10+35)
‹=› 10 / 45
‹=› 2 / 9.
Answer D
Answer: (D) 2/9
Question: During a trip on an expressway, Don drove a total of x miles. His average speed on a certain 5-mile section of the expressway was 30 miles per hour, and his average speed for the remainder of the trip was 60 miles per hour. His travel time for the x-mile trip was what percent greater than it would have been if he had traveled at a constant rate of 60 miles per hour for the entire trip?
(A) 8.5%
(B) 50%
(C) x/12%
(D) 60/x%
(E) 500/x%
Rationale: total dist = x miles
time take to clear 5 mile section at 30 miles/hr = 5/30 = 1/6 hr
time taken to clear x-5 miles section at 60 miles/hr = x-5/60 hr
Total time = 1/6 + x-5/60 = x+5/60 hr
Total time to clear x miles if he traveled at constant rate of 60 miles/hr = x/60 hr
Extra time = 5/60 = 1/12 hr
Percentage greater = (1/12)/(x/60) * 100% = 500/x %
ANSWER:E
Answer: (E) 500/x%
Question: When positive integer k is divided by 6 the remainder is 3. Which of the following CANNOT be an even integer?
(A) k + 1
(B) k -11
(C) 4k + 2
(D) (k-3)/3 +2
(E) k/3
Rationale: First, because k/6 leaves a remainder of 3, we know k must be odd.
(k=6x+3 = 3(2x+1) = odd*odd = odd)
Knowing k is odd we can examine the answer choices:
a. k + 1 --> odd + 1 --> must be even
b. k -11 --> odd - odd --> must be even
c. 4k + 1 --> 4*odd + 1 = even + 1 --> must be odd
d. (k-3)/3 +2 --> (6x+3-3)/3 + 2 = 2x + 2 --> must be even
e. k/3 --> (6x+3)/3 = 2x+1 = Must be odd
ANSWER:C
Answer: (C) 4k + 2
Question: what is the smallest integer that is multiple of 3,5,9
(A) A)70
(B) B)45
(C) C)200
(D) D)280
(E) E)140
Rationale: It is the lcm of 3, 5 and 9 which is 45.
The answer is B.
Answer: (B) B)45
Question: A bag contains 12 white and 18 black balls. 2balls are drawn in succession. What is the probability that first is white and second is black?
(A) 36/141
(B) 36/145
(C) 24/122
(D) 20/133
(E) 21/113
Rationale: The probability that first ball is white:
=12C130C1=12C130C1
=1230=1230
=25=25
Since, the ball is not replaced; hence the number of balls left in bag is 29.
Hence, the probability the second ball is black:
=18C129C1=18C129C1
=1829=1829
Required probability,
=(25)×(1829)=(25)×(1829)
=36/145
B
Answer: (B) 36/145
Question: f(x) is a function such that f(x) + 3f(8 - x) = x for all real numbers x. Find the value of f(2)
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: f(x) + 3f(8 - x) =f(2) + 3f(6) = 2 : x = 2 above
f(6) + 3f(2) = 6 : x = 6 above
f(6) = 6 - 3f(2) : solve equation C for f(6)
f(2) + 3(6 - 3f(2)) = 2 : substitute
f(2) = 2 : solve above equation
correct answer C
Answer: (C) 2
Question: A swimming pool 9 m wide and 12 m long is 1 m deep on the shallow side and 4 m deep on the deeper side. Its volume is?
(A) 870m3
(B) 277m3
(C) 270m3
(D) 220m3
(E) 170m3
Rationale: Volume will be length * breadth * height, but in this case two heights are given so we will take average,
Volume=(12∗9∗(1+42))m312∗9∗2.5m3=270m3
Answer: C
Answer: (C) 270m3
Question: A little old lady lives in a house with only her children and the children each have pets. She has twice as many sons as daughters. Each son has a dog, and each daughter has a cat. If the total number of pets and children living with her are Y, then how many dogs live in the house, in terms of Y
(A) Y/8
(B) Y/2
(C) 2*Y
(D) 3*Y
(E) Y/3
Rationale: Since Y is the total of all children and pets, Y = Boys + Girls + Dogs + Cats
Since each boy has a dog then, Boys = Dogs. Since each Girl has a Cat then, Girls = Cats
Thus Y = 2*Boys + 2*Girls
Since there are twice as many boys as girls, Girls = Boys/2.
Thus Y = 2*Boys + 2*(Boys/2) Which simplifies to Y = 2*Boys + 1*Boy, or Y = 3*Boys
Since Boys = Dogs ... Y=3*Dogs
Which converts to Dogs = Y/3
Answer: E
Answer: (E) Y/3
Question: A bus starts from city X. The number of women in the bus is half of the number of men. In city Y, 20 men leave the bus and ten women enter. Now, number of men and women is equal. In the beginning, how many passengers entered the bus ?
(A) 15
(B) 90
(C) 36
(D) 45
(E) 46
Rationale: Explanation:
Originally, let number of women = x. Then, number of men = 2x.
So, in city Y, we have : (2x - 20) = (x + 10) or x = 30.
Therefore Total number of passengers in the beginning = (x + 2x) = 3x = 90.
Answer: B
Answer: (B) 90
Question: If a no. when divided by 44, gives 432 as quotient and 0 as remainder. What will be the remainder when dividing the same no. by 39
(A) 11
(B) 13
(C) 15
(D) 17
(E) 19
Rationale: P Ã· 44 = 432
=> P = 432 * 44 = 19008
P / 39 = 19008 / 39 = 487, remainder = 15
C
Answer: (C) 15
Question: The average height of 35 boys in a class was calculated as 183cm. It has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm. Find the actual average height of the boys in the class (Round off your answer to two decimal places).?
(A) 178.27 cm
(B) 181.29 cm
(C) 978.29 cm
(D) 178.89 cm
(E) 176.29 cm
Rationale: Calculated average height of 35 boys = 183 cm.
Wrong total height of 35 boys = 183 * 35 cm. This was as a result of an actual height of 106 cm being wrongly written as 166 cm. Correct total height of 35 boys = 183 cm - (166 cm - 106 cm)/35
= 183 cm - 60 /35 cm
= 183 cm - 1.71 cm = 181.29 cm.
Answer: B
Answer: (B) 181.29 cm
Question: If Y < X and XM >YM, what must be true?
(A) M < X.
(B) M < Y.
(C) X < 0.
(D) M > 0.
(E) Y < 0.
Rationale: X>Y, bus as soon as M is multiplied to both sides inequality sign changes.
This is only possible when ve is multiplied on both sides. That means M is ve
D is the answer
Answer: (D) M > 0.
Question: The banker's discount on Rs.1650 due a certain time hence is Rs.165. Find the true discount and the banker's gain.
(A) 12
(B) 15
(C) 18
(D) 21
(E) None
Rationale: Solution
Sum	=B.D x T.D/ B.D - T.D
= B.D x T.D/ B.G
T.D / B. G	=Sum / B.D
= 1650 / 165
= 10 / 1
If B.D is Rs. 11,T.D= Rs.10.
If B.D is Rs.165,
T.D	= Rs.(10 / 11 x 165)
= Rs.150.
And, B.G	= Rs(165 - 150)
= Rs.15.
Answer B
Answer: (B) 15
Question: In a recent survey at a local deli, it was observed that 3 out of 5 customers bought a bagel and 5 out of 7 customers bought a coffee. Some customers bought both. If 7 customers are selected, what are the chances that at least 1 customer bought a coffee and a bagel?
(A) 27/343
(B) 3/7
(C) 27/125
(D) 341/422
(E) 9/125
Rationale: Let us take 7*5=35 as the total number of customers. So 7*3=21 customers bought a bagel and 5*5=25 customers bought a coffee.
chances that at least 1 customer bought a coffee and a bagel = 1 - chances that no customer bought a coffee and a bagel
chances that no customer bought a coffee and a bagel= 24/35*23/34*22/33*21/32*20/31*19/30*18/29=81/422
chances that at least 1 customer bought a coffee and a bagel= 1 - 81/422 = 341/422
Answer D.
Answer: (D) 341/422
Question: A motorcycle importer is planning on increasing the price of a certain model by $1000. At this new price 6 fewer motorcycles will be sold per month, but the total revenues will increase by $26,000 to $594,000. What is the number of motorcycles the manufacturer will sell at this new price?
(A) 64
(B) 65
(C) 67
(D) 68
(E) 70
Rationale: Responding to a pm: To solve this question, I will make an equation in x and then make educated guesses. Here's how:
Assuming x motorcycles were sold every month initially.
(568000/x + 1000)(x-6) = 594000
(568/x + 1)(x-6) = 594
Now 568 = 8*71
Assuming x = 71 (We have all integers so it is obvious that 568/x should be an integer.
We get 9*66 = 594 (matches)
So he will sell 71 - 6 = 65 bikes this month
Answer (B)
Answer: (B) 65
Question: An article is bought for Rs.695 and sold for Rs.900, find the gain percent?
(A) 30 1/3%
(B) 33 1/3%
(C) 23 1/3%
(D) 35 1/3%
(E) 29 69/139%
Rationale: E
29 69/139%
695 ---- 205
100 ---- ? => 29 69/139%
Answer: (E) 29 69/139%
Question: Aish started a business investing Rs. 25,000 in 2010, In 2011, he invested an additional amount of Rs. 10,000 and Roshan joined him with an amount of Rs. 35,000. In 2012, Aish invested another additional amount of Rs. 10,000 and Atul joined them with an amount of Rs. 35,000. What will be Roshan’s share in the profit of Rs. 1,20,000 earned at the end of 3 years from the start of the business in 2010?
(A) Rs.40000
(B) Rs.50000
(C) Rs.60000
(D) Rs.70000
(E) None of these
Rationale: Explanation :
Aish : Roshan : Atul
= (25000 x 12 + 35000 x 12 + 45000 x 12) : (35000 x 24) : (35000 x 12)
= 1260000 : 840000 : 420000 = 3 : 2 : 1
Roshan's share = Rs. 120000 x 2/6
= Rs. 40000.
Answer : A
Answer: (A) Rs.40000
Question: Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.
(A) 4
(B) 7
(C) 9
(D) 13
(E) 12
Rationale: Explanation:
Required number = H.C.F. of (91 - 43), (183 - 91) and (183 - 43)
= H.C.F. of 48, 92 and 140 = 4.
ANSWER IS A
Answer: (A) 4
Question: A,B worker are doing a job. Worker A takes 8 hours to do a job. B takes 10 hours to do a job. How long should it take both A and B, working together to do same job.
(A) 4 4/9
(B) 3 3/9
(C) 3 2/9
(D) 5 2/9
(E) 6 4/9
Rationale: In this type of questions, first we need to calculate 1 hours work, then their collective work as,
A's 1 hour work is 1/8
B's 1 hour work is 1/10
(A+B)'s 1 hour work = 1/8 + 1/10
= 9/40
So both will finish the work in 40/9 hours
= 4 4/9
ANSWER A
Answer: (A) 4 4/9
Question: A shopkeeper sold an article at $100 with 40% profit. Then find its cost price?
(A) $120
(B) $100
(C) $91
(D) $71
(E) $69
Rationale: cost price = selling price *100/(100+profit)
C.P. = 100*100/140 = $71(approximately)
Answer is D
Answer: (D) $71
Question: An investment of d dollars at k percent simple annual interest yields $200 over a 2 year period. In terms of d, what dollar amount invested at the same rate will yield $2,400 over a 3 year period?
(A) (2d)/3
(B) (3d)/4
(C) (4d)/3
(D) (3d)/2
(E) 8d
Rationale: 200 dollars in 2 years means 100 dollars in 1 year.
To get 2400 dollars' it will take 24 years.
To get 2400 in 3 years, we need 24/3 =8 times money. Answer is E.
Answer: (E) 8d
Question: In a match, awards are given to each of 11 members of the team and a trophy to the team. In all winning team gets 2.75kg weight awards. If the weight of match wining trophy is 1.275kg, what the weight of each player giving weight of trophy ?
(A) 134.09 gms
(B) 144.09 gms
(C) 154.09 gms
(D) 164.09 gms
(E) 174.09 gms
Rationale: Total weight of all the awards for winning team is 2.75kg = 2750gms
trophy weight is 1.275 kg=1275gms
now rest weight = 2750-1275= 1475gms
rest weight divided in 11 players is = 1475/11 = 134.09 gms
ANSWER:A
Answer: (A) 134.09 gms
Question: 10^25 - 760 is divisible by all of the following except:
(A) A.12
(B) B.8
(C) C.5
(D) D.4
(E) E.7
Rationale: The last three digits ( 1000 - 760 ) 240
240 is divisible by 12,4,8,5
240 is not evenly divisible by 7 so the answer is E) 7
Answer: (E) E.7
Question: If N = 16 × 10^(-p) and −4 < p < 4, how many different integer values of p will make N a perfect square?
(A) 0
(B) 2
(C) 3
(D) 5
(E) 7
Rationale: I think the answer should be C.
Thoose are P-Values that satisfy given restriction: -2, 0, 2 (note, a fraction can be also a perfect square) --> 16*100, 16*1, 16/100
Answer: (C) 3
Question: Two same glasses are respectively 1/4th 1/5th full of milk. They are then filled with water and the contents mixed in a tumbler. The ratio of milk and water in the tumbler is?
(A) 9:38
(B) 9:31
(C) 9:390
(D) 9:36
(E) 9:33
Rationale: 1/4 : 3/4 = (1:3)5 = 5:15
1/5 : 4/5 = (1:4)4 = 4:16
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9:31
Answer: B
Answer: (B) 9:31