mathewhe/aqua_rat huggingface dataset:
Question: In a certain game, you pick a card from a standard deck of 52 cards. If the card is a heart, you win. If the card is not a heart, the person replaces the card to the deck, reshuffles, and draws again. The person keeps repeating that process until he picks a heart, and the point is to measure how many draws did it take before the person picked a heart and won. What is the probability that there will be at least four draws involved in a win, i.e. someone picking her first heart on the fourth draw or later?
(A)  1/2
(B)  9/16
(C)  11/16
(D)  13/16
(E)  27/64
Rationale: Probability of picking a heart on any draw = 1/4
Probability of NOT picking a heart on the first draw AND on the second draw And 3rd draw = [1-(1/4)] X [1-(1/4)] X [1-(1/4)]= 3/4 X 3/4 X 3/4 = 27/64
Answer : E
Answer: (E)  27/64
Question: Two employees X and Y are paid a total of Rs. 550 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?
(A) Rs.200
(B) Rs.250
(C) Rs.350
(D) Rs.370
(E) Rs.400
Rationale: Let the amount paid to A per week = x
and the amount paid to B per week = y
Then x + y = 550
But x = 120% of y = 120y/100 = 12y/10
∴12y/10 + y = 550
⇒ y[12/10 + 1] = 550
⇒ 22y/10 = 550
⇒ 22y = 5500
⇒ y = 5500/22 = 500/2 = Rs.250
B)
Answer: (B) Rs.250
Question: A certain bushel of wheat generates one-third the profit of a bushel of corn. If a bushel of corn generates five-fourths the profit of a bushel of truffles, what fraction of the profit from a bushel of wheat is the profit from a bushel of truffles?
(A) 5/12
(B) 4/5
(C) 5/4
(D) 5/3
(E) 12/5
Rationale: Let Corn profit = 3x
Wheat profit = x
Truffle Profit = 4/5 * 3x = 12/5 * x
Wheat Profit / Truffle Profit = x / [12/5 * x] = 5/12
Answer A.
Answer: (A) 5/12
Question: The number 642 is added to a 3-digit number 7x2 to give a 4 digit 13y4 which is exactly divisible by 11.find xy
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Rationale: if a number is divisible by 11,means diff b/w it's digits at odd and even place should be 0 or multiples of 11.
so 13y4 1+y=3+4 y=6 therefore no is 1364
now subtract 642 from 1364=722
therefore x=2
xy=12
ANSWER:A
Answer: (A) 12
Question: If YWVSQ is 27 - 23 - 21 - 19 - 17, Then WKIGF
(A) 13 - 11 - 9 - 7 - 9
(B) 13 - 11 - 9 - 7 - 6
(C) 13 - 11 - 9 - 7 - 7
(D) 13 - 11 - 9 - 7 - 5
(E) 13 - 11 - 9 - 7 - 1
Rationale: WKIGF = 13 - 11 - 9 - 7 - 5
Note: this is a dummy question. Dont answer these questions
Answer:D
Answer: (D) 13 - 11 - 9 - 7 - 5
Question: An bus covers a certain distance at a speed of 140 kmph in 5 hours. To cover the samedistance in 1hr, it must travel at a speed of?
(A) 520 km/hr
(B) 640 km/hr
(C) 656 km/hr
(D) 731 km/hr
(E) 700 km/hr
Rationale: Distance = (140 x 5) = 700 km.
Required speed = 700 km/hr.
E
Answer: (E) 700 km/hr
Question: A not-so-good clockmaker has four clocks on display in the window. Clock #1 loses 17 minutes every hour. Clock #2 gains 15 minutes every hour relative to Clock #1 (i.e., as Clock #1 moves from 12:00 to 1:00, Clock #2 moves from 12:00 to 1:15). Clock #3 loses 20 minutes every hour relative to Clock #2. Finally, Clock #4 gains 20 minutes every hour relative to Clock #3. If the clockmaker resets all four clocks to the correct time at 12 noon, what time will Clock #4 display after 6 actual hours (when it is actually 6:00 pm that same day)?
(A) 5:00
(B) 5:34
(C) 5:42
(D) 6:00
(E) 6:24
Rationale: C1 loses 15 minutes every hour. So after 60 minutes have passed, C1 displays that 60-15 = 45 minutes have passed.
C2 gains 15 minutes for every 60 minutes displayed on C1. Thus, the time displayed on C2 is 75/60 = 5/4 the time displayed on C1. So after 60 minutes have passed, C2 displays the passing of (5/4 * 45) minutes.
C3 loses 20 minutes for every 60 minutes displayed on C2. Thus, the time displayed on C3 is 40/60 = 2/3 the time displayed on C2. So after 60 minutes have passed, C3 displays the passing of (2/3 * 5/4 * 45) minutes.
C4 gains 20 minutes for every 60 minutes displayed on C3. Thus, the time displayed on C4 is 80/60 = 4/3 the time displayed on clock 3. So after 60 minutes have passed, C4 displays the passing of 4/3 * 2/3 * 5/4 * 45 = 50 minutes.
C4 loses 10 minutes every hour.
In 6 hours, C4 will lose 6*10 = 60 minutes = 1 hour.
Since the correct time after 6 hours will be 6pm, C4 will show a time of 6-1 = 5:34pm.
The correct answer is B.
Answer: (B) 5:34
Question: A sum fetched a total simple interest of Rs. 4016.25 at the rate of 9 p.c.p.a. in 5 years. What is the sum?
(A) 8000
(B) 8925
(C) 8500
(D) 8700
(E) 8750
Rationale: P = (100*4016.25/9*5) ==>8925
ANSWER B
Answer: (B) 8925
Question: The price of commodity X increases by 40 cents every year, while the price of commodity Y increases by 15 cents every year. In 2001, the price of commodity X was $4.20 and the price of commodity Y was $6.30. In which year will the price of commodity X be 15 cents more than the price of commodity Y?
(A) 2010
(B) 2011
(C) 2012
(D) 2013
(E) 2014
Rationale: The price of commodity X increases 25 cents each year relative to commodity Y.
The price difference is $2.10 and commodity X needs to be 15 cents more than commodity Y.
$2.25 / 25 cents = 9 years
The answer is 2001 + 9 years = 2010.
The answer is A.
Answer: (A) 2010
Question: Kate made a deposit in a savings account that pays 5% compound interest annually two years ago. If her current account balance is $1,323, how much did she deposit in the account?
(A) $1000
(B) $1100
(C) $1200
(D) $1300
(E) $1400
Rationale: We are given the final amount at the end of two years (i.e initial amount invested + interest) = $1323
Interest rate = 5%
No of Cycles = 2
A = P (1 +r)^n
1323 = P (1 + .05)^2
1323 = P (1 + 1/20)^2
1323 = P*(21/20)^2
Solving for P = 1200
Option C
Answer: (C) $1200
Question: The average of temperatures at noontime from Monday to Friday is 60; the lowest one is 40, what is the possible maximum range of the temperatures?
(A) 100
(B) 25
(C) 40
(D) 45
(E) 75
Rationale: Average=60, Sum of temperatures=60*5=300
As the min temperature is 40, max would be 300-4*40=140 --> The range=140(max)-40(min)=100
Answer: A
Answer: (A) 100
Question: Find the cost of fencing around a circular field of diameter 28 m at the rate of Rs.1.50 a meter?
(A) 299
(B) 132
(C) 269
(D) 267
(E) 262
Rationale: 2 * 22/7 * 14 = 88
88 * 1 1/2
= Rs.132
Answer:B
Answer: (B) 132
Question: If the perimeter of square region Q and the perimeter of rectangular region R are equal and the sides of R are in the ratio 2:3 then the ratio of the area of R to the area of Q
(A) 25:16
(B) 24:25
(C) 5:6
(D) 4:5
(E) 4:9
Rationale: We know Perimeter of a square (Pq) = 4*side
Perimeter of a rectangle (Pr) = 2(length+breath)
Let us assume 40 to be the perimeter of the square (since we know each side of a square is equal and the perimeter is divisible by 4, also take in to account the length and breadth of the rectangle is in the ration 2k:3k = 5k; we can assume such a number)
Therefore,
Pq = Pr = 40
Area of the square = 100 sq. units
We know 2(length+breadth) = 40
i.e. length + breadth = 20 (or 5k = 20 given that l:b (or b:l) = 2:3)
Therefore length = 8, breath = 12
Area of the rectangle = 8*12 = 96 sq. units
Question asked = Area of the rectangle : Area of the square = 96:100 ==> 24:25=B
Answer: (B) 24:25
Question: A salt manufacturing company produced a total of 5000 tonnes of salt in January of a particular year. Starting from February its production increased by 100 tonnes every month over the previous months until the end of the year. Find its average monthly production for that year?
(A) 2288
(B) 2776
(C) 5550
(D) 3389
(E) 2882
Rationale: Total production of salt by the company in that year = 5000 + 5100 + 5200 + .... + 6100 = 66600.
Average monthly production of salt for that year = 66600/12 = 5550.
Answer: C
Answer: (C) 5550
Question: Find the cost of fencing around a circular field of diameter 28 m at the rate of Rs.1.50 a meter?
(A) 288
(B) 132
(C) 882
(D) 292
(E) 261
Rationale: 2 * 22/7 * 14 = 88
88 * 1 1/2 = Rs.132
Answer: B
Answer: (B) 132
Question: The speed of a train is 120 kmph. What is the distance covered by it in 40 minutes?
(A) 50 kmph
(B) 60 kmph
(C) 70 kmph
(D) 80 kmph
(E) 85 kmph
Rationale: 120 * 40/60
=80 kmph
Answer: D
Answer: (D) 80 kmph
Question: A courtyard 25 m long and 16 m broad is to be paved with bricks of dimensions 20 cm by 10 cm. The total number of bricks required is
(A) 15000
(B) 18000
(C) 20000
(D) 25000
(E) None
Rationale: Solution
Number of bricks
= [ Area of courtyard / Area of 1 brick ]
= [2500×1600 / 20×10]
= 20000.
Answer C
Answer: (C) 20000
Question: What is the total number of Y integers between 100 and 200 that are divisible by 3?
(A)  33
(B)  32
(C)  31
(D)  30
(E)  29
Rationale: yes there is a different way of arriving at that answer ....
u can also use airthmetic progression to get the answer
since the first term to be divisble by 3 is 102 ..take that as A .. the starting no
and since 198 is the last digit to be divisible by 3 take that as N ...
since the difference is 3 take that as D
no u have to find what term is 198 take that as nth term
the formula for that is N = A + (n-1) * d
198 = 102 +(n-1) * 3
from this u get n =33
Answer: (A)  33
Question: The sum of three consecutive integers is 102. Find the lowest of the three?
(A) 22
(B) 99
(C) 21
(D) 33
(E) 27
Rationale: Three consecutive numbers can be taken as (P - 1), P, (P + 1).
So, (P - 1) + P + (P + 1) = 102
3P = 102 => P = 34.
The lowest of the three = (P - 1) = 34 - 1 = 33.Answer:D
Answer: (D) 33
Question: In a rectangular metallic piece of paper that covers exactly the area of a cube. The length of the piece of paper is 48 inches and the width is 72 inches. What is the volume of the cube in cubic feet is 1 feet is 12 inches?
(A) a 8
(B) b 24
(C) c 27
(D) d 40
(E) e 51
Rationale: l = 48 /12 = 4 ft
w = 72 / 12 = 6 ft
Area of paper = 24
Area of cube = 4 * side^2
side of cube = 2
V of cube = 8
Answer: (A) a 8
Question: If X is to be chosen at random from the integers between 1 to 7, inclusive, and Y is to be chosen at random from the integers between 7 and 11, inclusive, what is the probability that X + Y will be even?
(A) 3/5
(B) 4/7
(C) 5/7
(D) 18/35
(E) 23/35
Rationale: X+Y will be even if X and Y are both even or both odd.
P(X and Y are both even) = 3/7*2/5 = 6/35
P(X and Y are both odd) = 4/7*3/5 = 12/35
P(X+Y is even) = 6/35 + 12/35 = 18/35
The answer is D.
Answer: (D) 18/35
Question: Set #1 = {O, P, Q,R, E}
Set #2 = {A, U, M, N, T, P}
There are these two sets of letters, and you are going to pick exactly one letter from each set. What is the probability of picking at least one vowel?
(A) 1/2
(B) 1/5
(C) 1/6
(D) 3/5
(E) 1/8
Rationale: At least questions are best solved by taking the opposite scenario and subtracting it from 1. Probability of choosing no vowel from set 1 is 3/5 and set 2 is 4/6. Multiply these to get 2/5. Therefore, probability of picking at least one vowel = 1-2/5= 3/5
ANSWER =D
Answer: (D) 3/5
Question: If john makes a contribution to a charity fund at school, the average contribution size will increase by 50% reaching $75 per person. If there were 1 other contributions made before john's, what is the size of his donation?
(A) $100
(B) $150
(C) $200
(D) $250
(E) $450
Rationale: Cavg = average contribution before John
Cavg*1.5 = 75, therefore the average cont is $50 before John.
If he needs to increase the average contribution by $25, he must put in $25 for each of the 1 people.
so $25.
But, he also has to put in the average for himself (the twoth person), so add $75.
So $100 is your answer.
Answer A
Answer: (A) $100
Question: Anne and Katherine are both saving money
from their summer jobs to buy bicycles. If
Anne had $150 less, she would have exactly 1/3
as much as Katherine. And if Katherine
had twice as much, she would have exactly
3 times as much as Anne. How much
money have they saved together?
(
(A) $300
(B) $400
(C) $450
(D) $625
(E) $750
Rationale: If Anne had $150 less, Katherine would have three times more than Anne. Make this
statement into an equation and simplify:
3(a – 150) = k
3a – 450 = k
And if Katherine had twice as much, she would have three times more than Anne:
2k = 3a
Substitute 3a – 450 for k into the last equation and solve for a
2(3a – 450) = 3a
6a – 900 = 3a
–900 = –3a
300 = a
Now substitute 300 for a into the same equation and solve for k:
2k = 3(300)
2k = 900
k = 450
Thus, together Anne and Katherine have 300 + 450 = 750
correct answer E)$750
Answer: (E) $750
Question: A car covers a distance of 360 km in 10 hrs. What is its speed in mps.
(A) 10 m/s
(B) 25 m/s
(C) 20 m/s
(D) 15 m/s
(E) 16 m/s
Rationale: Explanation:
Distance = Speed x Time
Speed = (360/10) = 36 kmph
Spees in mps = 36 x 5/18 = 2 x 5 = 10 mps.
Answer: Option A
Answer: (A) 10 m/s
Question: Exactly 15% of the reporters for a certain wire service cover local politics in Country X. If 25% of the reporters who cover politics for the wire service do not cover local politics in Country X, what percent of the reporters for the wire service do not cover politics?
(A) 20%
(B) 42%
(C) 44%
(D) 80%
(E) 84%
Rationale: Let's assume there are 100 reporters --> 15 reporters cover local politics.
Now, as 25% of the reporters who cover all politics do not cover local politics then the rest 75% of the reporters who cover politics do cover local politics, so if there are x reporters who cover politics then 75% of them equal to 15 (# of reporters who cover local politics): 0.75x=15--> x=20, hence 20 reporters cover politics and the rest 100-20=80 reporters do not cover politics at all.
Answer: D.
Answer: (D) 80%
Question: Two men start together to walk a certain distance, one at 4 kmph and another at 3 kmph.The former arrives half an hour before the latter. Find the distance.
(A) 6 kilometre
(B) 7 km
(C) 8 km
(D) 9 km
(E) None of these
Rationale: Let the distance be x km. Then,
x/3 - x/4 = 1/2
(4x - 3x)/12 = 1/2
x = 6 km
ANSWER:A
Answer: (A) 6 kilometre
Question: The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ?
(A) 240
(B) 270
(C) 295
(D) 360
(E) 252
Rationale: Let the smaller number be x. Then larger number = (x + 1365).
x + 1365 = 6x + 15
5x = 1350
x = 270
Smaller number = 270.
ANSWER B
Answer: (B) 270
Question: At present, the ratio between the ages of Akbar and Denial is 4:3. After 6 years, Arun’s age will be 26 years. What is the age of Deepak at present?
(A) 5
(B) 10
(C) 15
(D) 20
(E) 25
Rationale: Sol.
Let the present ages of Akbar and Danial be 4x years and 3x years respectively. Then,
4x + 6 =26 ⇔ 4x = 20 ⇔ x = 5.
∴ Deepak’s age = 3x =15 years.
Answer C
Answer: (C) 15
Question: When positive integer m is divided by positive integer x, the reminder is 7 and when positive integer n is divided by positive integer y, the reminder is 11. Which of the following R is a possible value for x + y?
I. 18
II. 19
III. 20
(A) I only
(B) II only
(C) R=III only
(D) II and III only
(E) None
Rationale: TIP FOR SUCH QUESTIONS:Make Algebraic Equation in the beginning to understand how to proceed further. Then Start thinking the possible values of variables asked about
i.e.When positive integer m is divided by positive integer x, the reminder is 7can be understood as
m = ax +7which means thevalue of x must be greater than 7as the remainder 7 is possible only when the Divisor is bigger than the Remainder 7
i.e. Min Value of x = 8
AND
i.e.When positive integer n is divided by positive integer y, the reminder is 11can be understood as
n = by +11which means thevalue of y must be greater than 11as the remainder 11 is possible only when the Divisor is bigger than the Remainder 11
i.e. Min Value of y = 12
i.e. Minimum Value of x+y = 8+12 = 20
Hence III only can be True
Answer: Option
C
Answer: (C) R=III only
Question: In how many different number of ways 6 men and 2 women can sit on a shopa which can accommodate persons?
(A) 1680
(B) 1800
(C) 2000
(D) 2100
(E) 2300
Rationale: 8p4 = 8 Ã— 7 Ã— 6 x 5 = 1680
Answer :A
Answer: (A) 1680
Question: At 6'o clock clock ticks 6 times. The time between first and last ticks was 30sec. How much time it takes at 8'o clock.
(A) 54sec
(B) 48sec
(C) 42sec
(D) 70sec
(E) 60sec
Rationale: At 6'0 clock, clock ticks 6 times.
So, there must be 5 intervals between clock ticks.
Time Between first and last ticks = 30sec
So, 1 interval = 30/5 = 6sec
So 6'o clock 5 *6=30sec
7'o clock 6 *6=36sec
8'o clock 7 *6=42sec
So, 42sec at 8'o clock.
ANSWER:C
Answer: (C) 42sec
Question: On a sum of money, the simple interest for 2 years is Rs. 327, while the compound interest is Rs. 340, the rate of interest being the same in both the cases. The rate of interest is
(A) 15%
(B) 14.25%
(C) 7.95%
(D) 10.5%
(E) 11.5%
Rationale: Explanation:
The difference between compound interest and simple interest on Rs. P for 2 years at R% per annum
= (R Ã— SI)/(2 Ã— 100)
Difference between the compound interest and simple interest = 340 - 327 = 13
(R Ã— SI)/(2 Ã— 100) = 13
(R Ã— 327)/(2 Ã— 100) = 13
R = 7.95%
Answer: Option C
Answer: (C) 7.95%
Question: How is 1/2 % expressed as a decimal fraction?
(A) 0.5
(B) 0.05
(C) 0.005
(D) 0.0005
(E) 5
Rationale: as 1/2=0.5 and its percent value will be 0.5/100= 0.005
ANSWER:C
Answer: (C) 0.005
Question: In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 4 boys when No boy gets more than one prize?
(A) 20
(B) 21
(C) 23
(D) 24
(E) 28
Rationale: Sol. In this case, repetitions are not allowed. So, the first prize can be given in 4 ways. The second in 3 ways and the third in 2 ways. But fundamental principle, (4 x 3 x 2) ways = 24 ways
4: Or 4p = — 4:- 4X3X2X1- 24 ways
D
Answer: (D) 24
Question: A box contains six light out of which 3 are defective. If three light are chosen at random, find the probability that all the three light are defective?
(A) 2/25
(B) 3/20
(C) 1/30
(D) 3/35
(E) None of these
Rationale: Out of nine light , five are good and four are defective.
Required probability = 3C3/6C3 = 1/20
B
Answer: (B) 3/20
Question: A shopkeeper loses 15%,if an article is sold for Rs. 102. What should be the selling price of the article to gain 20%?
(A) Rs. 150
(B) Rs. 144
(C) Rs. 138
(D) Rs. 132
(E) None of these
Rationale: Given that SP = Rs. 102 and loss = 15%
CP = [100(SP)]/(100 - l%) = (100 * 102)/85 = 20 * 6 = Rs. 120.
To get 20% profit, New SP = [(100 + p%)CP]/100 = (120 * 120)/100 = Rs. 144
ANSWER:B
Answer: (B) Rs. 144
Question: A train 800 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?
(A) 277 m
(B) 776 m
(C) 500 m
(D) 187 m
(E) 1678 m
Rationale: Speed = 78 * 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (800 + x)/60 = 65/3
x = 500 m.
Answer:C
Answer: (C) 500 m
Question: Mohan ranks twenty-first in a class of sixty-five students. What will be his (Mohan's)rank if the lowest candidate is assigned rank 1?
(A) 44th
(B) 45th
(C) 46th
(D) Data inadequate
(E) None of these
Rationale: 65=21+x-1
ans 45
ANSWER:B
Answer: (B) 45th
Question: Two boys are standing side-by-side. One boy, which is 3 feets tall, casts a shadow that is 4.5
feets long. The other boy is 4 feets tall. Compute, in feets, the length of the shadow that
the taller boy casts.
(A) 8
(B) 10
(C) 6
(D) 4
(E) 12
Rationale: The ratio of shadow to height is constant, so if x is the length of the shadow, then
3/4.5 = 4/x and x = 6 .
correct answer C
Answer: (C) 6
Question: What proximate value should come in place of the question mark (?) in the following question?
6.795 Ã— 1084 + 2568.34 â€“ 1708.34 = ?
(A) 6,000
(B) 12,000
(C) 10,340
(D) 8,204
(E) 9,000
Rationale: ? â‰ˆ 6.8 Ã— 1080 + 2560 â€“ 1700 â‰ˆ 7344 + 860 â‰ˆ 8204
Answer D
Answer: (D) 8,204
Question: How much is 80% of 40 is greater than 4/5 of 25?
(A) 4
(B) 6
(C) 9
(D) 12
(E) 15
Rationale: Explanation:
(80/100) * 40 â€“ (4/5) * 25
32 - 20 = 12
ANSWER IS D
Answer: (D) 12
Question: If the area of circle is 1256 sq cm then its circumference?
(A) 125
(B) 135
(C) 140
(D) 110
(E) 145
Rationale: 22/7 r2 = 1256 => r =20
2 * 22/7 * 20 = 125
Answer: B
Answer: (B) 135
Question: The organizers of a week-long fair have hired exactly nine security guards to patrol the fairgrounds at night for the duration of the event. Exactly four guards are assigned to patrol the grounds every night, with no guard assigned consecutive nights. If the fair begins on a Monday, how many different groups of 4 guards will be available to patrol the fairgrounds on the following Saturday night?
(A) 3
(B) 5
(C) 7
(D) 9
(E) 11
Rationale: For any given day, only the guards patrolling on the previous day won't be available. So, 4 guards who patrolled on Friday won't be available. We are thus left with 5 guards.
To choose 4 out of 5, we will have 5C4 = 5 different groups.
The answer is B.
Answer: (B) 5
Question: 10+45
(A) 8
(B) 55
(C) 87
(D) 90
(E) 2
Rationale: B
Answer: (B) 55
Question: A student is ranked 16th from right and 6th from left. How many students are there in totality ?
(A) 18
(B) 19
(C) 20
(D) 21
(E) 22
Rationale: From right 16 , From left 6
Total = 16+6-1 = 21
ANSWER:D
Answer: (D) 21
Question: The number of ways in which six boys and six girls can be seated in a row for a photograph so that no two girls sit together is -.
(A) (6!)2
(B) 6! * ⁷P₆
(C) 2(6!)
(D) 6! * 7
(E) None of these
Rationale: We can initially arrange the six boys in 6! ways.
Having done this, now three are seven places and six girls to be arranged. This can be done in ⁷P₆ ways.
Hence required number of ways = 6! * ⁷P₆
ANSWER:B
Answer: (B) 6! * ⁷P₆
Question: In a village of 100 households, 85 have at least one DVD player, 90 have at least one cell phone, and 55 have at least one MP3 player. If x and y are respectively the greatest and lowest possible number of households that have all three of these devices, x – y is:
(A) 65
(B) 55
(C) 45
(D) 35
(E) 25
Rationale: Am I missing something here??? it seems straightforward......
The obvious maximum that have all 3 is 55, because you are limited by the SMALLEST number.
The minimum is simply the sum of the max of each people who DONT have the product, so:
100-90 = 10 don't have Cell
100-85 = 15 don't have DVD
and 100-55 = 45 don't have MP3
SO a total of 10+15+45 = 70 combined who might NOT have SOME combination of the 3 products. So subtract that from 100, to give you the minimum of the people who COULD have all 3 and you get 100-70 = 30.
55-30 = 25
E
Answer: (E) 25
Question: A room of 8m 44cm long and 3m 50cm broad is to be paved with square tiles. Find the least number of square tiles required to cover the floor.
(A) 73850
(B) 73805
(C) 844
(D) 350
(E) 2
Rationale: Explanation:
area of the room = 844 * 350 sq cm
size of largest square tile = H.C.F of 844cm and 350cm= 2cm
area of 1 tile = 2*2 sq cm
no. of tiles required = (844*350) / (2* 2) = 73850
Answer: A) 73850
Answer: (A) 73850
Question: 2^8×39+31=?
(A) 34545
(B) 65657
(C) 65567
(D) 45677
(E) 56782
Rationale: 256*39+31
65567
C
Answer: (C) 65567
Question: When x is divided by y, the quotient is p with remainder r. Which of the following is y in terms of r, x, and p? (Assume both y and p are nonzero.)
(A) x – r – p
(B) (x+r)/p
(C) x/p−r
(D) (x−r)/p
(E) xr –p
Rationale: Given that when x is divided y, the quotient is p and remainder is r. This implies x-r is divisible by y and yp=(x-r) or y = (x-r)/p.
Answer D.
Answer: (D) (x−r)/p
Question: In one hour, a boat goes 11 km along the steram and 5 km against the stream. The speed of the boat in still waer (in km/hr) is:
(A) 2
(B) 4
(C) 8
(D) 12
(E) 15
Rationale: Sol.
Speed in still water = 1/2 (11+5) kmph = 8 kmph.
Answer C
Answer: (C) 8
Question: A and B enter into a partnership with respective capitals of Rs. 20,000 and Rs. 40,000. At the end of the year, the total profit is Rs. 30,000. If A receives Rs. 15,000 as both his salary and profit, then what is his salary?
(A) Rs. 2000
(B) Rs. 4000
(C) Rs. 5000
(D) Rs. 3000
(E) None of these
Rationale: Explanation:
A's capital : B 's capital
20000 : 40000 = 1 : 2
Since, the time period is fixed, the profit is distributed in the ratio of capital 1 : 2
Profit of A = (1/3) * 30,000 = Rs. 10,000
Salary of A = Rs. (15000 – 10000) = Rs. 5000
ANSWER: C
Answer: (C) Rs. 5000