mathewhe/aqua_rat huggingface dataset:
Question: If x is an odd negative integer and y is an even integer, which of the following statements must be true?
I. (3x - 2y) is odd
II. xy^2 is an even negative integer
III. (y^2 ) is an odd negative integer
(A) I only
(B) II only
(C) I
(D) I and III
(E) II and III
Rationale: If x is an odd negative integer and y is an even integer, which of the following statements must be true?
I. (3x - 2y) is odd
3x - is always negative and odd
2y - can be 0, when y=0, or always even integer (positivie or negative)
odd integer +/- even integer = always odd
I statement is always true
II. xy^2 is an even negative integer
y can be 0 => xy^2 = 0 (non-negative even) => II statement is not true
III. (y^2 ) is an odd negative integer
y can be 0 => III statement is not true
basing on above, only I statement will always be true
C
Answer: (C) I
Question: Find large number from below question The difference of two numbers is 1200. On dividing the larger number by the smaller, we get 5 as quotient and the 4 as remainder
(A) 1234
(B) 1345
(C) 1456
(D) 1567
(E) 1499
Rationale: Let the smaller number be x. Then larger number = (x + 1200).
x + 1200 = 5x +4
4x = 1196
x = 299
Large number = 299+1200=1499
E
Answer: (E) 1499
Question: Find 62976 ÷ ? = 123
(A) 412
(B) 502
(C) 512
(D) 522
(E) None
Rationale: Answer
Let 62976/N = 123
Then N = 62976 / 123 = 512.
Option: C
Answer: (C) 512
Question: An investor bought 200 shares of stock in ABCD company in 1990. By 1992, the investment was worth only 2/3 of its original value. By 1995, the 200 shares were worth only 1/3 of their value in 1990. By what percent did the value of the investment drop from 1992 to 1995?
(A) 16 2/3%
(B) 25%
(C) 33 1/3%
(D) 50%
(E) 66 2/3%
Rationale: Let price of each share in 1990 = X.
Total cost in 1990 = 200X
Now Price in 1992 = 2/3 * 200X = 400/3 * X
Now price in 1995 = 1/3 *200X= 200/3X
%Change in 1995 from 1992 = [(400/3* X -200/3X) / (400/3 *X) ] *100 = 50%
Answer D
Answer: (D) 50%
Question: The numerator of a fraction is 1 less than twice the denominator. If the numerator and denominator are both increased by 1, the fraction becomes 4/5. Find the fraction?
(A) A)2/3
(B) B)3/5
(C) C)7/4
(D) D)5/9
(E) of these
Rationale: Let the numerator and denominator of the fraction be 'n' and 'd' respectively.
n = 2d - 1
(n + 1)/(d + 1) = 4/5
5n + 5 = 4d + 4
5(2d-1) + 5 = 4d + 4 => d = 4
n = 2d - 1 => n = 7
Hence the fraction is : 7/4
ANSWER:C
Answer: (C) C)7/4
Question: A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 42, the how old is B?
(A) 16
(B) 9
(C) 8
(D) 11
(E) 10
Rationale: Explanation:
Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years.
(2x + 2) + 2x + x = 42
⇒ 5x = 40
⇒ x = 8.
Hence, B's age = 2x = 16 years.
Answer: A
Answer: (A) 16
Question: The two trains of lengths 400 m, 600 m respectively, running at same directions. The faster train can cross the slower train in 180 sec, the speed of the slower train is 48 km. then find the speed of the faster train?
(A) 87 Kmph
(B) 68 Kmph
(C) 54 Kmph
(D) 15 Kmph
(E) 12 Kmph
Rationale: Length of the two trains = 600m + 400m
Speed of the first train = X
Speed of the second train= 48 Kmph
1000/X - 48 = 180
1000/x - 48 * 5/18 = 180
50 = 9X - 120
X = 68 Kmph
Answer: B
Answer: (B) 68 Kmph
Question: Andrew has a certain number of coins in his pocket. He has three times as many dimes as quarters and five times as many nickels as dimes. A nickel is worth $0.05, 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) 9
(B) 10
(C) 18
(D) 24
(E) 21
Rationale: E.
Let number of quarters be q. Therefore , dimes are 3q and nickels are 18q.
Total value = 15q(.05) + 3q(0.1) + .25q =1.3q
Given total value = 10.15
therefore, 1.3q=10.15 or q=8
Number of dimes = 3q or 24
Answer : D
Answer: (D) 24
Question: A train running at the speed of 40 km/hr crosses a pole in 9 seconds. What is the length of the train?
(A) 120 metres
(B) 180 metres
(C) 324 metres
(D) 150 metres
(E) 100 meters
Rationale: Speed=40 x5/18m/sec=100/9	m/sec.
Length of the train = (Speed x Time).
Length of the train =	100/9 x 9m = 100 m.
ANSWER:E
Answer: (E) 100 meters
Question: To reach her destination, Jeanette must drive 90 miles. If she drives 5 miles every 9 minutes, how much time will it take her to reach her destination?
(A) 2 hours and 2 minutes
(B) 2 hours and 42 minutes
(C) 2 hours and 10 minutes
(D) 2 hours and 12 minutes
(E) 2 hours and 15 minutes
Rationale: 9 minute for 5 miles how much for 90? minutes for 1(9/5) mile multiplied by 90 miles.
9*90/5= 162> 2 hours 42 min answer is B
Answer: (B) 2 hours and 42 minutes
Question: For the positive integers x, x + 2, x + 4, x + 7, and x + 37, the mean is how much greater than the median?
(A) 6
(B) 1
(C) 2
(D) 4
(E) 7
Rationale: Mean = (x + x+2 + x+4 + x+7 + x+37)/5
=(5x+50)/5
=x+10
Median = x+4
Thus Mean - Median = x+10 - (x+4)
=6
Answer = A
Answer: (A) 6
Question: The probability that a man will be alive for 10more yrs is 1/4 & the probability that his wife will alive for 10 more yrs is 1/3. The probability that none of them will be alive for 10 more yrs, is
(A) 1/2
(B) 2/3
(C) 3/5
(D) 3/7
(E) 4/9
Rationale: Sol. Required probability = Pg.) x P(B) = (1— D x(1 —I) =: x 1=1/2
Ans.(A)
Answer: (A) 1/2
Question: In how many different ways can the letters of the word ‘PROBE’ be arranged ?
(A) 120
(B) 130
(C) 150
(D) 110
(E) 160
Rationale: A
120
Required number of arrangements = 5! = 120
Answer: (A) 120
Question: Statement : Company X has marketed the product. Go ahead, purchase it if price and quality are your considerations.
Conclusions :
I. The product must be good in quality.
II. The price of product must be reasonable.
(A)  I only
(B)  II only
(C)  I and II only
(D)  I and III only
(E)  II and III only
Rationale: Explanation:
Both conclusions follow as per statement.
Option C
Answer: (C)  I and II only
Question: If Nick gains 10 pounds, he will weigh 50% more than his brother. Currently, their combined weight is 340 pounds. What is Nick's current weight?
(A) 140
(B) 160
(C) 170
(D) 190
(E) 200
Rationale: Given: N+B = 340
N+10 = 1.5B
N+B = 340
Add 10 to both sides
(N+10) + B = 350
2.5B = 350
B = 140
N = 200
Correct answer is E
Answer: (E) 200
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) 233
(B) 877
(C) 100
(D) 286
(E) 181
Rationale: Explanation:
MP = 100
CP = 75
SP = 150
------
75 ---- 75
100 ---- ? => 100%
Answer:C
Answer: (C) 100
Question: A, B and C invest in the ratio of 3 : 4: 5. The percentage of return on their investments are in the ratio of 6 : 5 : 4. Find the total earnings, If B earns Rs. 250 more than A :
(A) 2348
(B) 7250
(C) 2767
(D) 1998
(E) 2771
Rationale: Explanation:
A B C
investment 3x 4x 5x
Rate of return 6y% 5y% 4y%
Return \inline \frac{18xy}{100} \inline \frac{20xy}{100} \inline \frac{20xy}{100}
Total = (18+20+20) = \inline \frac{58xy}{100}
B's earnings - A's earnings = \inline \frac{2xy}{100} = 250
Total earning = \inline \frac{58xy}{100} = 7250
Answer: B) Rs.7250
Answer: (B) 7250
Question: How many liters of pure alcohol must be added to a 100-liter solution that is 20 percent alcohol in order to produce a solution that is 24 percent alcohol?
(A)  7/2
(B)  5
(C)  20/3
(D)  100/19
(E)  39/4
Rationale: 20% Alcohol solution means; in the 100 liter solution, 20 liters of solution is alcohol and 80 liters other solvents.
If we addxliters of alcohol to the solution, the solution becomes100+xliters and alcohol, which was 20 liters, becomes 20+x liters.
According to the statement;
20+x = 24% of (100+x)
OR
20+x=(100+x)6/25
500+25x=600+6x
19x=100
x=100/19
Ans:D
Answer: (D)  100/19
Question: Area of four walls of a room is 99 m2. The length and breadth of the room are 7.5 m and 3.5m respectively. The height of the room is:
(A) 2.5m
(B) 3.5m
(C) 1.5m
(D) 4.5m
(E) 5.5m
Rationale: 2(7.5+3.5)×h = 99
2(11)h = 99
22h = 99
h = 99/22 = 9/2 = 4.5 m
Answer is D.
Answer: (D) 4.5m
Question: 3 OUT OF 2500 PARTS OF EARTH IS SULPHUR. WHAT IS THE PERCENTAGE OF SULPHUR IN EARTH
(A) 11/50
(B) 1/8
(C) 1/45
(D) 2/45
(E) NONE OF THESE
Rationale: REQUIRED PERCENTAGE=(3/2500*100)%=1/8%
CORRECT OPTIONS: B
Answer: (B) 1/8
Question: How many multiples of 5 are there between 1 and 100 (both are inclusive)?
(A) 1.2
(B) 20.8
(C) 2.3
(D) 6.7
(E) 8.2
Rationale: the answer is (100-1)/5+1=20.8
Answer is B
Answer: (B) 20.8
Question: A truck covers the distance of 550 meters in 1 minute where as a bus covers a distance of 33kms in 45 minutes.Find the ratio of their speed?
(A) 3:1
(B) 4:3
(C) 5:2
(D) 3:4
(E) 2:2
Rationale: Formula: d=s*t
Ratio of speed=[(550/50)*(18/5)]:[33*(45*60)](1 minute=60 sec)
=(11*3):(11*4)
=33:44
=3:4
Ratio of speed in car and bus is 3:4
Answer: option D
Answer: (D) 3:4
Question: The area of a circular place is 17.56 hectares. Find the cost of fencing it at the rate of Rs. 3/meter approximately.
(A) Rs. 4233
(B) Rs. 4350
(C) Rs. 4457
(D) Rs. 4670
(E) Rs. 4756
Rationale: Area = (17.56 x 10000) m2= 175600 m2.
ΠR2 = 175600 ⇔ (R)2 = (175600 x (7/22)) ⇔ R = 236.37 m.
Circumference = 2ΠR = (2 x (22/7) x 236.37) m =1485.78 m.
Cost of fencing = Rs. (1485.78 x 3) = Rs. 4457.
C
Answer: (C) Rs. 4457
Question: A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of A?
(A) 9179
(B) 3000
(C) 2997
(D) 2678
(E) 2682
Rationale: 60*5:36*6:75*3
100: 72: 75
100/247 * 7410 = 3000
Answer: B
Answer: (B) 3000
Question: As x increases from 111 to 112, which of the following increases? I) x−1/x II) 17−1/x III) (17+x)/x
(A) II only
(B) I,II only
(C) III only
(D) I only
(E) I,III only
Rationale: On Increasing the value of x from 111 to 112
I) x−1/x will increase as 1/x will be very small and x will increase by 1 unit
II) 17−1/x Will Increase as the value of 1/x will decrease thereby increasing the value of 17-(1/x)
III) (17+x)/x = (17/x)+1 will Decrease as 1/x will decrease thereby decreasing the value of (17/x)
Answer: B
Answer: (B) I,II only
Question: If the probability T of rain on any given day in city x is 50% what is the probability it with rain on exactly 3 days in a five day period?
(A) 8/125
(B) 2/25
(C) 5/16
(D) 8/25
(E) 3/4
Rationale: 5C3 (1/2)^3(1/2)^2
= (5 * 4 * 3!)/2!3! * 1/32
T= 5/16
Answer - C
Answer: (C) 5/16
Question: a father said to his son ,i was as old as your are at the present at the time of your birth. if the father's age is 38 years now. the son's age five years back was:
(A) 14
(B) 19
(C) 33
(D) 38
(E) 12
Rationale: son's age x years, then (38-x) = x
2x=38, x=19, therefore = son's age 5 years back (19-5)=14 years
correct answer(A)
Answer: (A) 14
Question: On his drive to work, Leo listens to one of three radio stations A, B or C. He first turns to A. If A is playing a song he likes, he listens to it; if not, he turns it to B. If B is playing a song he likes, he listens to it; if not, he turns it to C. If C is playing a song he likes, he listens to it; if not, he turns off the radio. For each station, the probability is 0.15 that at any given moment the station is playing a song Leo likes. On his drive to work, what is the probability that Leo will hear a song he likes?
(A) 0.027
(B) 0.386
(C) 0.417
(D) 0.657
(E) 0.9
Rationale: Probability he hears a song is like:
Tune to A and likes what he is hearing = 0.15
Tune to A, don't find he like what they are airing, then tune to B and likes what he finds there = 0.85 * 0.15 = 0.1275
Tune to A, finds crap there, Tune to B, hears a similar crap, Tune to C and finally falls in love with the program = 0.85^2 * 0.15 = 0.1084
Total = 0.386
Ans B
Answer: (B) 0.386
Question: Three students appear at an examination of Mathematics. The probability of their success are 2/3, 1/4, 1/5 respectively. Find the probability of success of at least two.
(A) 17/60
(B) 2/50
(C) 3/40
(D) 13/50
(E) 14/60
Rationale: The probability of success of at least two students will involve the following possibilities.
The first two students are successful, the last two students are successful, the first and third students are successful and all the three students are successful.
Therefore, the required probability = 2/3 x 1/4 x 4/5 + 1/4 x 1/5 x 1/3 + 2/3 x 1/5 x 3/4 + 2/3 x 1/4 x 1/5 = 17/60
ANSWER:A
Answer: (A) 17/60
Question: A train crosses a platform of 130 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?
(A) 150
(B) 230
(C) 77
(D) 62
(E) 52
Rationale: Length of the train be â€˜Xâ€™
X + 130/15 = X + 250/20
4X + 520 = 3X + 750
X = 230m
Answer: B
Answer: (B) 230
Question: The ratio of the length and the breadth of a rectangle is 4 : 3 and the area of the rectangle is 6912 sq cm. Find the ratio of the breadth and the area of the rectangle?
(A) 1:96
(B) 2:96
(C) 1:86
(D) 1:94
(E) 2:96
Rationale: Let the length and the breadth of the rectangle be 4x cm and 3x respectively.
(4x)(3x) = 6912
12x2 = 6912
x2 = 576 = 4 * 144 = 22 * 122 (x > 0)
=> x = 2 * 12 = 24
Ratio of the breadth and the areas = 3x : 12x2 = 1 : 4x = 1: 96.
Answer:A
Answer: (A) 1:96
Question: Two persons starting from the same place walk at a rate of 4kmph and 5.5kmph respectively. What time will they take to be 9km apart, if they walk in the same direction?
(A) 6 hrs
(B) 22 hrs
(C) 25 hrs
(D) 12 hrs
(E) 14 hrs
Rationale: The relative speed of the boys = 5.5kmph â€“ 4kmph
= 1.5 kmph
Distance between them is 9 km
Time= 9km / 1.5 kmph = 6 hrs
Answer : A.
Answer: (A) 6 hrs
Question: If 4a^4 − 41a^2 + 100 = 0, then what is the sum of the two greatest possible values of a ?
(A) 4
(B) 9/2
(C) 7
(D) 41/4
(E) 25
Rationale: just forget about the value of a^4 for the moment and let a^2= X. (its better to work with power of 2 than 4)
now we have equation as 4x^2 -41x +100 =0, factoring them gives us 4X^2 -16x -25x +100 =0. which can be solved as (4x-25)(x-4) , so x= 4 and 25/4.
so a^2 = 4 and 25/4
so a= +2 and minus 2 and +5/2 and minus 5/2
The two greatest values are +2 and +5/2. so their sum 2+5/2 =9/2 = B
Answer: (B) 9/2
Question: Only a single rail track exists between stations A and B on a railway line. One hour after the north bound super fast train N leaves station A for station B, a south-bound passenger train S reaches
station A from station B. The speed of the super fast train is twice that of a normal express train E, while the speed of a passenger train S is half that of E. On a particular day, N leaves for B from A, 20 min behind the normal schedule. In order to maintain the schedule, both N and S increased their speeds. If the super fast train doubles its speed, what should be the ratio (approximately) of the speeds of passenger train to that of the super fast train so that the passenger train S reaches exactly at the scheduled time at A on that day?
(A) 1 : 3
(B) 1 : 4
(C) 1 : 5
(D) 1 : 6
(E) None of these
Rationale: Explanation :
If speed of N = 4, speed of S = 1.
=> Average speed = (2 X 4 x 1) / ( 4 + 1) = 1.6.
Because time available is 2/3, speed = 3/2.
Now Average speed = 2.4
Now speed of N = 8.
Speed of S = y.
=> (2 x 8 x y) / (8+y) = 2.4
=> y = 1.3
The required ratio is 1.3 : 8 i.e 1 : 6.
Answer : D
Answer: (D) 1 : 6
Question: In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 52, the dividend is:
(A) 5324
(B) 5334
(C) 6812
(D) 7356
(E) 7400
Rationale: Divisor = (5 * 52) = 260
= 10 * Quotient = Divisor
=> Quotient = 260/10 = 26
Dividend = (Divisor * Quotient) + Remainder
Dividend = (260 * 26) + 52 = 6812
C
Answer: (C) 6812
Question: P, Q, R subscribe Rs. 50,000 for a business. P subscribes Rs. 4000 more than Q and Q Rs. 5000 more than R. Out of a total profit of Rs. 25,000, what will be P's share?
(A) 10,509
(B) 10,502
(C) 10,500
(D) 10,501
(E) 10,506
Rationale: Explanation:
Let amount subscribed for R be x.
Therefore, Q = x + 5000 and P = x + 5000 + 4000 = x + 9000
So, x + x + 5000 + x + 9000 = 50000
3x = 36000
x = 12000
P : Q : R = 21000 : 17000 : 12000 = 21 : 17 : 12
ANSWER: Rs. 10,500
P’s share = 25000 X (21/50) = Rs. 10,500
ANSWER:C
Answer: (C) 10,500
Question: Sravan and Bhavan began business with Rs.16000 and Rs.20000 after 8 months, Sravan advances Rs.4000 more and Bhavan withdraws Rs.4000. At the end of two years, their profits amounted to Rs.5535 find the share of Sravan.
(A) 2850
(B) 2870
(C) 3000
(D) 2800
(E) 2825
Rationale: (16*8 + 20*16):(20*8 + 16*16)
14:13
14/27 * 5535 = 2870. Answer: B
Answer: (B) 2870
Question: In a class, the average age of 30 boys is 13 years and the average of 20 girls is 12 years. what is the average age of the whole class?
(A) 10.6
(B) 11.6
(C) 12.6
(D) 13.6
(E) 14.6
Rationale: Explanation:
Total age of 50 students
(30X 13+20 X 12) = 630
Average = 630/50 = 12.6 Years
Answer C
Answer: (C) 12.6
Question: A certain school supplies store arranges pencils on display such that each of the six different colors of pencils, yellow, orange, green, red, blue, and purple are consecutive in a repeating pattern. If seven consecutively displayed pencils are purchased, what is the probability that two of the pencils
are purple?
(A) 1/6
(B) 1/36
(C) 1/20
(D) 2/3
(E) 2/5
Rationale: After yellow, orange, green, red, blue, and purple, the next pencil can be of any given six colours, therefore we have total six possibilites, out of which we need purple i.e. 1 therefore prob is 1/6.
Answer: (A) 1/6
Question: From the beginning to the end of 2007, the price of a stock rose 20 percent. In 2008, it dropped 25 percent. In 2009, it rose 20 percent. What percent of the stock’s 2007 starting price was the price of the stock at the end of 2009?
(A) 80
(B) 90
(C) 95
(D) 100
(E) 108
Rationale: Assume a value at the beginning of 2007. As this is a % question, assume P=100.
At the end of 2007 it becmae = 1.2*100=120
At the end of 2008 it decreased by 25% = 120*.75 = 90
At the end of 2009 it increased by 20% = 90*1.2 = 108
Thus ratio = 108/100 = 1.08 (in % terms = 108%). Thus E is the correct answer.
Answer: (E) 108
Question: At the wholesale store you can buy an 8-pack of hot dogs for $1.55, a 20-pack for $3.05, and a 250-pack for $20.95. What is the greatest number of hot dogs you can buy at this store with $300?
(A)  3,108
(B)  3,100
(C)  3,108
(D)  3,540
(E)  3,256
Rationale: To maximize number of hot dogs with 300$
Total number of hot dogs bought in 250-pack = 20.95*14 =293.30$
Amount remaining = 300 - 293.30 = 6.7$
Total number of hot dogs bought in 20-pack = 3.05*2 =6.10$
Amount remaining = 6.70 - 6.10= 0.6$
This amount is too less to buy any 8- pack .
Greatest number of hot dogs one can buy with 300 $ = 250*14+20*2 = 3,540
Answer D
Answer: (D)  3,540
Question: if A and B both work for 6 hrs,B and C work for 7.5 hrs,C and A work for 10 hrs .
i dont remember but ......its arrange in increasing order by their work
(A) cab
(B) cba
(C) abc
(D) bac
(E) none of these
Rationale: A and B both can finish the work in 6 days means
1/A+1/B=1/6 ................(i)
B and C both can finish the work in 7.5 days means
1/B+1/C=1/7.5 ...................(ii)
C and A both can finish the work in 10 days means
1/A+1/B=1/10 ........................(iii)
Adding (i),(ii) and (iii), we get
2(1/A+1/B+1/C)=2/5 ......................(iv)
from (i) we have 1/A+1/B=1/6 put in (iv) ,we wiil get
1/6+1/C=1/5
C=30
Similarly, we will get A=15 and B=10
so in increasing order it will be BAC
ANSWER:D
Answer: (D) bac
Question: A and B invests Rs.10000 each, A investing for 8 months and B investing for all the 12 months in the year. If the total profit at the end of the year is Rs.25000, find their shares?
(A) Rs.1300
(B) Rs.1599
(C) Rs.7290
(D) Rs.15000
(E) Rs.72821
Rationale: The ratio of their profits A:B = 8:12 = 2:3
Share of A in the total profit = 2/5 * 25000 = Rs.10000 Share of A in the total profit = 3/5 * 25000 = Rs.15000
Answer:D
Answer: (D) Rs.15000
Question: If x is a positive integer with fewer than 3 digits, what is the probability Q that x*(x + 1) is a multiple of either 4 or 5?
(A) 4/99
(B) 2/25
(C) 8/99
(D) 49/100
(E) 86/99
Rationale: Interesting question! Also one that we should be able to answer very quickly be keeping an eye on our best friends, the answer choices.
We know that x belongs to the set {1, 2, 3, ... , 99}. We want to know the probability Q that x(x+1) is a multiple of either 4 or 5.
When will this happen? If either x OR (x+1) is a multiple of 4 or 5.
Since 4*5 is 20, let's look at the first 20 numbers to get a rough idea of how often this happens.
Out of the numbers from 1 to 20:
4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 16, 17, 20
So, 14 out of the first 20 numbers match our criteria. Since:
probability = (# of desired outcomes)/(total # of possibilities), we guesstimate the answer to be 14/20. Since (E) is the only answer greater than 1/2, we go with (E).
Answer: (E) 86/99
Question: A can do piece of work in 15 days and B in 20 days they finished the work with the assistance of c in 5 days and got Rs.45 as their wages find the share for each in wages?
(A) 11,12,13
(B) 15,11,13
(C) 15,11.25,18.75
(D) 11,15.25,18.75
(E) None of these
Rationale: Explanation:
A’s 1 day work =1/3
B’s 1 day work =1/4
C’s 1 day work =1-1/4-1/3 =5/12
A’s share =45 *1/3 = 15
B’s share= 45*1/4 = 11.25
C’s share =45*5/12 = 18.75
Answer: Option C
Answer: (C) 15,11.25,18.75
Question: The rate of spin of a certain gyroscope doubled every 10 seconds from the moment a particular stopwatch started. If after a minute and a half the gyroscope reached a speed of 6400 meters per second, what was the speed, in meters per second, when the stopwatch was started?
(A) 25/2
(B) 25/4
(C) 25/8
(D) 25/16
(E) 25/32
Rationale: Let x be the original speed when the stopwatch was started.
In 90 seconds, the speed doubled 9 times.
2^9 * x = 6400
x = (2^8 * 25) / 2^9 = 25/2
The answer is A.
Answer: (A) 25/2
Question: If v and t are integers and v^2 – t^2 is an odd integer, which of the following must be an even integer?
I. v + t + 2
II. v^2 + 2vt + t^2
III. v^2 + t^2
(A) None
(B) I only
(C) II only
(D) III only
(E) I, II, and III
Rationale: v^2–t^2 is an odd integer means that either v is even and t is odd or v is odd and t is even.
Check all options:
I. v + t + 2 --> even+odd+even=odd or odd+even+even=odd. Discard;
II. v^2 + 2vt + t^2 --> even+even+odd=odd or odd+even+even=odd. Discard;
III. v^2 + t^2 --> even+odd=odd or odd+even=odd. Discard.
Answer: A.
Answer: (A) None
Question: If Jesse flips a coin seven times in a row, what is the probability that the result will be heads at all the times?
(A) 1/128
(B) 29/128
(C) 35/128
(D) 1/16
(E) 1/4
Rationale: In a flip of a coin seven times in a row, heads at all times means,
Heads = at least 7 heads
Atleast 7 heads in 7 flip.
The total outcome of flip is = 2^7 = 128
For any Coins problem write the ask in the shown format.
HHHHHHH
Once you have written in the above mentioned format the answer is pretty straight.
HHHHHHH = [7!]/[7!] = 1
Sum = 1 =
Answer = 1/128
Answer - A
Answer: (A) 1/128
Question: A girl was asked to multiply a certain number by 43. She multiplied it by 34 and got his answer less than the correct one by 1251. Find the number to be multiplied.
(A) 130
(B) 132
(C) 134
(D) 136
(E) 139
Rationale: Let the required number be x. Then,
43x – 34x = 1251 or 9x = 1251 or x = 139.
Required number = 139.
ANSWER:E
Answer: (E) 139
Question: The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?
(A) 7%
(B) 4%
(C) 5%
(D) 2%
(E) 1%
Rationale: 65*(90/100)*((100-x)/100)
= 56.16
x = 4%
Answer: B
Answer: (B) 4%
Question: How many words can be formed from the letters of the word "SIGNATURE" so that vowels always come together.
(A) 17280
(B) 4320
(C) 720
(D) 80
(E) None of thsee
Rationale: Explanation:
word SIGNATURE contains total 9 letters.
There are four vowels in this word, I, A, U and E
Make it as, SGNTR(IAUE), consider all vowels as 1 letter for now
So total letter are 6.
6 letters can be arranged in 6! ways = 720 ways
Vowels can be arranged in themselves in 4! ways = 24 ways
Required number of ways = 720*24 = 17280
Option A
Answer: (A) 17280