mathewhe/aqua_rat huggingface dataset:
Question: The age of Somu is one-third his father's. 8 years back he was one-fifth of his father's age. What is his persent age ?
(A) 11
(B) 13
(C) 14
(D) 16
(E) 10
Rationale: Explanation :
Let Somu's age be x and that of his father be 3x.
So, x - 8 = 3x - 8/5 = x = 16
Answer : Option D
Answer: (D) 16
Question: Noelle walks from point A to point B at an average speed of 4 kilometers per hour. At what speed, in kilometers per hour, must Noelle walk from point B to point A so that her average speed for the entire trip is 6 kilometers per hour?
(A) 6.75
(B) 7
(C) 8
(D) 12
(E) 14
Rationale: Let's suppose that speed while returning was xkm/h
Since the distance is same, we can apply the formula of avg speed
Avg speed= 2S1S2/S1+S2
6= 2*4*x/4+x
x= 12
D is the answer
Answer: (D) 12
Question: The ratio of the area of a square to that of the square drawn on its diagonal is?
(A) 2:5
(B) 3:4
(C) 3:5
(D) 1:2
(E) 2:3
Rationale: Explanation:
a2:(aâˆš2)2
a2:2a2->1:2
ANSWER IS D
Answer: (D) 1:2
Question: A certain mixture of nuts consists of 5 parts almonds to 2 parts walnuts, by weight. What is the number of pounds of almonds in 150 pounds of the mixture ?
(A)  107
(B)  84
(C)  40
(D)  28
(E)  20
Rationale: Almonds : Walnuts = 5 : 2
Total mixture has 7 parts
In a 150 pound mixture, Almonds are 5/7 (total mixture)
= 5/7 * 150 = 107 pounds
Answer (A)
Answer: (A)  107
Question: What is the least value of x. So that 23x58 is divisible by 3.
(A) 2
(B) 0
(C) 1
(D) 3
(E) 4
Rationale: Explanation:
The sum of the digits of the number is divisible by 3, then the number is divisible by3.
2 + 3 + x + 5 + 8 = 18 + x
Least value of x may be 0
Therefore 18 + 0 = 18 is divisible by 3.
Answer: Option B
Answer: (B) 0
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) 288
(B) 261
(C) 500
(D) 287
(E) 271
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
Question: A student had the following scores in an exam (out of 100):
Social Studies: 80
Science: 79
Art: 89
Music: 62
Spanish: 56
What are his average marks ?
(A) 62.2
(B) 73.2
(C) 74.2
(D) 73.2
(E) 75.2
Rationale: Explanation:
Average = (80 + 79 + 89 + 62 + 56 )/ 5 =73.2.
Answer: D) 73.2
Answer: (D) 73.2
Question: If N = 2^0.15 and N^b = 64, b must equal
(A) 3/80
(B) 3/5
(C) 40
(D) 5/3
(E) 80/3
Rationale: 15/100 = 3/20
N = 2 ^ 3/20
N^b = 2^6
(2^3/20)^b = 2^6
b = 40
Answer: C
Answer: (C) 40
Question: If Greg buys 3 shirts, 4 trousers and 2 ties, the total cost is $90. If Greg buys 7 shirts, 2 trousers and 2 ties, the total cost is $50. How much will it cost him to buy 3 trousers, 5 shirts and 2 ties?
(A) $60
(B) $70
(C) $75
(D) $96
(E) Cannot be determined
Rationale: Solution: 3x+4y+2z=90 7x+2y+2z=50
adding both the equations= 10x+6y+4z=140
5x+3y+2z=70
ans B
Answer: (B) $70
Question: The probability that a computer company will get a computer hardware contract is 3/4 and the probability that it will not get a software contract is 3/5. If the probability of getting at least one contract is 5/6, what is the probability that it will get both the contracts?
(A) 7/30
(B) 11/40
(C) 17/50
(D) 19/60
(E) 33/80
Rationale: Let, A ≡ event of getting hardware contract
B ≡ event of getting software contract
AB ≡ event of getting both hardware and software contract.
P(A) = 3/4, P(~B) =5/9
=> P(B) = 1- (3/5) = 2/5.
A and B are not mutually exclusive events but independent events. So,
P(at least one of A and B ) = P(A) + P(B) - P(AB).
=> 5/6 = (3/4) + (2/5) - P(AB).
=> P(AB) = 19/60.
Hence, the required probability is 19/60.
The answer is D.
Answer: (D) 19/60
Question: In what time will a train 180 m long cross an electric pole, it its speed be 144 km/hr?
(A) 2.5 sec
(B) 1.9 sec
(C) 8.9 sec
(D) 4.5 sec
(E) 2.9 sec
Rationale: Speed = 144 * 5/18
= 40 m/sec
Time taken = 180/40
= 4.5 sec.
Answer: D
Answer: (D) 4.5 sec
Question: A batsman in his 15th innings makes a score of 85, and thereby increases his average by 3. What is his average after the 15th innings? He had never been ’not out’.
(A) 47
(B) 37
(C) 39
(D) 43
(E) 42
Rationale: Average score before 15th innings
= 85 - 3 × 15= 40
Average score after 15th innings
=> 40 + 3 = 43
ANSWER:D
Answer: (D) 43
Question: John traveled 80% of the way from Yellow-town to Green-fields by train at an average speed of 80 miles per hour. The rest of the way John traveled by car at an average speed of v miles per hour. If the average speed for the entire trip was 55 miles per hour, what is v in miles per hour?
(A) 30
(B) 40
(C) 50
(D) 55
(E) 70
Rationale: HiBunuel
THe question seems incorrect. it should not be 80% at the speed of 80. However if it's 20% at the speed of 80, Answer comes out 55.
The question is correct. Here's the explanation:
Let distance be D. We can find the total timeequate it, which comes as:
0.8D / 80 + 0.2D / v = D / 55 => v = 50 (Option C).
Answer: (C) 50
Question: There are 14 songs in that 5 Rock songs, 6 western songs & 3 Hindi pop songs. How many different albums can be formed using the above repertoire if the albums should contain at least 1 Rock song & 1 western song?
(A) 15624
(B) 20000
(C) 21000
(D) 23000
(E) 24000
Rationale: 15624
A
Answer: (A) 15624
Question: A sum of money deposited at C.I. amounts to Rs.3250 in 2 years and to Rs.3830 in 3 years. Find the rate percent?
(A) 30%
(B) 10%
(C) 20%
(D) 17%
(E) 50%
Rationale: 3250 --- 580
100 --- ? => 17%
Answer: D
Answer: (D) 17%
Question: A train, 130 metres long travels at a speed of 45 km/hr crosses a bridge in 30 seconds. The length of the bridge is
(A) 245 metre
(B) 375 metre
(C) 270 metre
(D) 220 metre
(E) 255 metre
Rationale: speed = 45 km/hr=45 Ã— 5/18 m/s=12.5 m/s
Distance travelled = 12.5 Ã— 30 =375 m
Length of the bridge= 375-130 =245 m
ANSWER: A
Answer: (A) 245 metre
Question: The cash realised on selling a 14% stock is Rs.106.25, brokerage being 1/4% is?
(A) 366
(B) 106
(C) 102
(D) 192
(E) 122
Rationale: Cash realised= Rs. (106.25 - 0.25)
= Rs. 106.
Answer: B
Answer: (B) 106
Question: A grown man eats 1 big burger in two bite. a women in 10 bites. If man takes a bite from the burger and hands it to the women and she takes 2 bites and hand it to the child who takes 3 bites and burger is finished. How many bites the child can finish the burger by herself?
(A) 5 bites
(B) 10 bites
(C) 15 bites
(D) 20 bites
(E) 25 bites
Rationale: 1- (1/2+ 2/10 + 3 /x) =0x = 10 bites. ANSWER = B
Answer: (B) 10 bites
Question: 3 + 3 + 3 + 2 × 3^2 + 2 × 3^3 + 2 × 3^4 + 2 × 3^5 + 2 × 3^6 + 2 × 3^7 =
(A) 3^7
(B) 3^8
(C) 3^14
(D) 3^28
(E) 3^30
Rationale: We have the sum of 9 terms. Now, if all terms were equal to the largest term 2*3^7 we would have: sum=9*(2*3^7)=2*3^9=~3^10, so the actual sum is less than 3^10 and more than 3^7 (option A) as the last term is already more than that. So the answer is clearly B.
Answer: B.
Answer: (B) 3^8
Question: Determine the value of 27/31−54/62
(A) 0
(B) 1
(C) 2
(D) 3
(E) none
Rationale: Solution:
Both fractions should be reduced before performing arithmetic operations. We get 27/31−2.27/2.31=27/31−27/31=0
Answer A
Answer: (A) 0
Question: The average age of a class of 32 students is 16 yrs. if the teacher's age is also included, the average increases by one year. Find the age of the teacher?
(A) 30 Years
(B) 49 Years
(C) 51 Years
(D) 55 Years
(E) 57 Years
Rationale: Total age of students is 32X16 = 512 Years
Total age inclusive of teacher = 33X (16+1) = 561
So, Teacher's age is 561-512 = 49 Yrs
There is a shortcut for these type of problems
Teacher's age is 16+(33X1) = 49 Years
B)
Answer: (B) 49 Years
Question: A can finish a work in 20 days, B in 15 days and C in 12 days. B and C start the work but are forced to leave after 2 days. The remaining work was done by A in :
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Rationale: (B+C)’s one day’s work = 1/15 + 1/12 = 3/20
Work done by B and C in 2 days = 3* 2/20 = 3/10
Remaining work = 1- 3/10 = 7/10
1/20 work is done by A in 1 day.
So, 7/10 work is done by A in 20 * 7/10 = 14 days
ANSWER:E
Answer: (E) 14
Question: On the planet Oz, there are 8 days in a week- sunday to saturday and another day called Oz day.There are 36 hours in a day and each hours has 90 minutes while each minute has 60 seconds.As on the earth, the hour hand covers the dial twice everyday. Find the approximate angle between the hands of a clock on Oz when the time is 12:40am.
(A) > 111 degrees
(B) > 251 degrees
(C) > 71 degrees
(D) > 89 degrees
(E) > 99 degrees
Rationale: As, we have 36 hour in a day. So, the dial has 18 hours(36/2=18) to cover daily twice. Now a dial has 360*. So, in one hour hand moves 360/18=20*.
So, for 12 hour hand moves 12x20=240*.
Now for minutes, hour hand moves 20/90
for 40 minutes it moves 20/90x40=8.88*
So for 12:40 hour hand moves 240+8.88=248.88*.
Now, minute hand moves 90 minutes to complete one hour.
for one minute it moves 360/90=4*
for 40 minutes it moves 4x40=160*
So, the angle between hour hand and minute hand is 248.88-160=88.88
The ans is 89*
ANSWER:D
Answer: (D) > 89 degrees
Question: A number which is divided by 13 and 26 yields same remainder?
(A) 108
(B) 61
(C) 86
(D) 78
(E) 92
Rationale: We can find it with the help of option
108=108/13 and 108/26 not gives the remainder 6 and 3
61=61/13 and 61/26 not gives the remainder 6 and 3
86=86/13 and 86/26 not gives the remainder 6 and 3
78=78/13 and 78/26 gives same remainder 0
Option D
Answer: (D) 78
Question: If x and y are the two digits of the number 653xy. Such that this number is divisible by 80, then x+y is equal to
(A) 3
(B) 2
(C) 4
(D) 1
(E) 0
Rationale: Since 653xy is divisible by 5 as well as 2.
So y =0
Now 653x0 must be divisible by 8
So 3x0 must be 8
This happens when x=2
Hence, x+y=2+0 =2
ANSWER B 2
Answer: (B) 2
Question: All the water in container A which was filled to its brim was poured into two containers B and C. The quantity of water in container B was 62.5% less than the capacity of container A. If 148 liters was now transferred from C to B, then both the containers would have equal quantities of water. What was the initial quantity of water in container A?
(A) 1188 liters.
(B) 1194 liters.
(C) 1104 liters.
(D) 1184 liters.
(E) 1189 liters.
Rationale: Explanation:
B has 62.5% or (5/8) of the water in A. Therefore, let the quantity of water in container A(initially) be 8k.
Quantity of water in B = 8k - 5k = 3k.
Quantity of water in container C = 8k - 3k = 5k
Container: A B C
Quantity of water: 8k 3k 5k
It is given that if 148 liters was transferred from container C to container B, then both the containers would have equal quantities of water.
5k - 148 = 3k + 148 => 2k = 296 => k = 148
The initial quantity of water in A = 8k = 8 * 148 = 1184 liters.
Answer: Option D
Answer: (D) 1184 liters.
Question: In how many different number of ways 7 men and 4 women can sit on a shopa which can accommodate persons?
(A) 990
(B) 210
(C) 230
(D) 250
(E) 270
Rationale: 11p3 = 11 Ã— 10 Ã— 9 = 990
A)
Answer: (A) 990
Question: A person borrows 9000 for 9 years at 3% p.a. simple interest. He immediately lends it to another person at 7 % p.a. for 9 years. Find his gain in the transaction per year.
(A) 380
(B) 360
(C) 340
(D) 300
(E) 180
Rationale: Gain in 9 years
= [(9000Ã—9Ã—7/100)âˆ’(9000Ã—9Ã—3/100)]
= (5670 â€“ 2430) = 3240
âˆ´ Gain in 1 year = (3240/9) = 360
Answer B
Answer: (B) 360
Question: Albert is 2 times Mary’s age and 4 times as old as Betty. Mary is 12 years younger than Albert. How old is Betty?
(A) 6
(B) 12
(C) 10
(D) 15
(E) 18
Rationale: A = 2M = M+12
M = 12
A = 24
A = 4B, and so B = 6
The answer is A.
Answer: (A) 6
Question: Ramu bought an old car for Rs. 40000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent?
(A) 17%
(B) 22.4%
(C) 18%
(D) 14%
(E) 16%
Rationale: Total CP = Rs. 40000 + Rs. 13000
= Rs. 53000 and SP
= Rs. 64900
Profit(%) = (64900 - 53000)/53000 * 100
= 22.4%
Answer: B
Answer: (B) 22.4%
Question: The function f(P) represents the number of ways that prime numbers can be uniquely summed to form a certain number P such that P = a + b + c + d… where those summed variables are each prime and a ≤ b ≤ c ≤ d ... For instance f(8) = 3 and the unique ways are 2 + 2 + 2 + 2 and 2 + 3 + 3 and 3 + 5. What is f(12)?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: So we can start with 2 and check whether sum of two primes is primes is even.
1) 2(6 times)
2) 2(3 times) + 3(2 times)
3) 2(2 times) + 3 + 5
4) 2 + 3 + 7
5) 2 + 5 + 5
6) 3(4 times)
7) 5 + 7
Answer: D
Answer: (D) 7
Question: 9log9(7) = ?
(A) 1
(B) 2
(C) 7
(D) 4
(E) 5
Rationale: Exponential and log functions are inverse of each other. Hence
aloga(x) = x , for all x real and positive.
and therefore
9log9(7) = 7
correct answer C
Answer: (C) 7
Question: 350 metres long yard, 26 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between 2consecutive trees
(A) 10
(B) 12
(C) 14
(D) 16
(E) 18
Rationale: 26 trees have 25 gaps between them,
Required distance (350/25) = 14
C
Answer: (C) 14
Question: A retailer sells products that belong to different categories, A to F, in alphabetical order. The number of products sold in each category is distinct and in ascending order. If at-least 2 products are sold in any category and a total of 27 products were sold last week, what is the probability that a product sold last week belonged to Category D?
(A) 2/27
(B) 4/27
(C) 5/27
(D) 8/27
(E) 15/27
Rationale: there are 6 distinct categories..
Since each category has to have at least 2 products..
let A have 2 and each thereafter has ONE more than previous..
so A,B,C,D,E, and F will have minimum 2+3+4+5+6+7 = 7*8/2 -1 = 28-1 =27..
therefore ONLY possibility of products in each due to restriction of TOTAL as 27 is 2,3,4,5,6,7 so D will have 5 products..
Probability = 5/27
ANSWER:C
Answer: (C) 5/27
Question: In racing over a given distance d at uniform speed, A can beat B by 30 meters, B can beat C by 8 meters, and A can beat C by 37 meters. What is the distance d in meters?
(A) 160
(B) 180
(C) 200
(D) 220
(E) 240
Rationale: When A is at the finish line, B is 30 meters back, and C is 37 meters back.
When B runs another 30 meters to the finish line, C is 8 meters back.
So B gains 1 meter on C every 30 meters covered.
To gain a final difference of 8 meters, B runs a total of 240 meters.
The answer is E.
Answer: (E) 240
Question: A family with 1 mother, 1 father, and 2 children sit in a car with 2 front seats and 2 back seats. If the mother drives with a child in the front, and the father sits in the back center seat with the other one children on either side of him, how many seating arrangements are possible?
(A)  3
(B)  4
(C)  6
(D)  8
(E)  10
Rationale: Mother has a fixed place and father, so there are 3*2 ways to arrange the children, hence C
Answer: (C)  6
Question: If log 27 = 1.491, then the value of log 9 is:
(A) 0.934
(B) 0.994
(C) 0.954
(D) 0.958
(E) 0.987
Rationale: log 27 = 1.491
log (33 ) = 1.491
3 log 3 = 1.491
log 3 = 0.497
log 9 = log(32 ) = 2 log 3 = (2 x 0.497) = 0.994.
Answer: Option B
Answer: (B) 0.994
Question: A number when divided b the sum of 555 and 445 gives two times their difference as quotient and 30 as the remainder. The number is:
(A) 1220
(B) 1250
(C) 2030
(D) 22030
(E) 1350
Rationale: Required number = (555+445)*2*110+30
= 220000+30
= 220030.
ANSWER:D
Answer: (D) 22030
Question: At the opening of a trading day at a certain stock exchange, the price per share of stock K was $8. If the price per share of stock K was $9 at the closing of the day, what was the percent increase in the price per share of stock K for that day?
(A) 1.4%
(B) 5.9%
(C) 11.1%
(D) 12.5%
(E) 23.6%
Rationale: Opening = 8
Closing = 9
Rise in price = 1
So, percent increase = 18∗10018∗100 =>12.50%
Thus answer will be (D)
Answer: (D) 12.5%
Question: Andrew purchased 6kg of grapes at the rate of 74 per kg and 9 kg of mangoes at the rate of 59 per kg. How much amount did he pay to the shopkeeper?
(A) 1000
(B) 975
(C) 980
(D) 1020
(E) 1080
Rationale: Cost of 6 kg grapes = 74 × 6 = 444.
Cost of 9 kg of mangoes = 59 × 9 = 531.
Total cost he has to pay = 444 + 531 = 975
B
Answer: (B) 975
Question: A beaker contains 180 liters of alcohol. On 1st day, 60 l of alcohol is taken out and replaced by water. 2nd day, 60 l of mixture iss taken out and replaced by water and the process continues day after day. What will be the quantity of alcohol in beaker after 3 days
(A) 53.3
(B) 53.8
(C) 53.7
(D) 53.5
(E) 353.3
Rationale: Use the formula,
Final Alcohol = Initial Alcohol ×(1−ReplacementquantityFinalVolume)n×(1−ReplacementquantityFinalVolume)n
Final Alcohol = 180(1−60180)3180(1−60180)3 = 180×(23)3=53.3
Ans: A
Answer: (A) 53.3
Question: If z is a multiple of 8778, what is the remainder when z^2 is divided by 9?
(A) 0
(B) 2
(C) 4
(D) 6
(E) 8
Rationale: The sum of the digits is 8+7+7+8=30.
Thus 3 is a factor of 8778, so 3 is a factor of z.
Then 3^3 = 9 is a factor of z^2.
Then the remainder when z^2 is divided by 9 is 0.
The answer is A.
Answer: (A) 0
Question: Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. After how much time will the trains meet?
(A) 20/89
(B) 20/9
(C) 20/7
(D) 20/6
(E) 20/1
Rationale: They are moving in opposite directions, relative speed is equal to the sum of their speeds.
Relative speed = (54 + 72)*5/18 = 7*5 = 35 mps.
The time required = d/s = 100/35 = 20/7 sec.
Answer:C
Answer: (C) 20/7
Question: A, B and C work on a task. To complete the task alone, B takes twice the time that A would take to complete the task alone and 1/3rd the time that C would take to complete the task alone. If B actually worked for half the number of days that A worked and 3/2 times the number of days that C worked, what proportion of the total work was completed by B?
(A) 1/3
(B) 2/9
(C) 9/46
(D) 7/19
(E) 1/6
Rationale: The first thing to notice is that A is faster than B and B is faster than C.
Since work is proportional to time, in 1 day lets say if A does 2 works, B does 1 work and C does 2/3rd of a work.
If A works for 2 days, B works for 1 day and C works for only 2/3 of the day.
Therefore total work done = (2*2) + (1*1) + (1/3*1/3) = 46/9
Proportion of work done by B = (1*1) / (46/9) = 9/46
Hence Answer C.
Answer: (C) 9/46
Question: The ratio of sum of squares of first n natural numbers to square of sum of first n natural numbers is 17:325. the value of n is
(A) 15
(B) 25
(C) 35
(D) 30
(E) none of these
Rationale: sum of 1st n natural no.s is n(n+1)/2,
sum of sqaures of 1st n natural no.s is n(n+1)(2n+1)/6,
The ratio of sum of squares of first n natural numbers to square of sum of first n natural numbers=n(n+1)(2n+1)*2*2/(n*n*(n+1)*(n+1))
=2(2n+1)/(3n(n+1))
now by hit and trial for the given options,if we put 25 then this will give 17/325
therefore the answer is 25
ANSWER:B
Answer: (B) 25
Question: A man’s speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr.The man’s speed against the current is :
(A) 8.5 km/hr
(B) 9 km/hr
(C) 10 km/hr
(D) 12.5 km/hr
(E) None of these
Rationale: Solution
Man’s rate in still water =(15-2.5) km/hr = 12.5 km/hr.
Man’s rate against the current = (12.5-2.5)km/hr = 10 km/hr. Answer C
Answer: (C) 10 km/hr
Question: A no. when divided by the sum of 555 and 445 gives 2times their difference as quotient & 50 as remainder. Find the no. is?
(A) 145646
(B) 236578
(C) 645353
(D) 456546
(E) 220050
Rationale: (555 + 445) * 2 * 110 + 50 = 220000 + 50 = 220050
E
Answer: (E) 220050
Question: If the sum and the difference of two numbers are 20 and 8 respectively, then the difference of their square is
(A) 12
(B) 28
(C) 160
(D) 180
(E) None
Rationale: Solution
Let the numbers be x and y.
Then, x + y = 20 and x - y = 8.
Therefore,x2 - y2 = (x + y)(x - y)
‹=› 20 x 8
‹=› 160.
Answer C
Answer: (C) 160
Question: Tanks A and B are each in the shape of a right circular cylinder. The interior of tank A has a height of 10 meters and a circumference of 9 meters, and the interior of tank B has a height of 9 meters and a circumference of 10 meters. The capacity of tank A is what percent of the capacity of tank B?
(A) 75%
(B) 90%
(C) 100%
(D) 120%
(E) 125%
Rationale: The radius of tank A is 9/(2*pi).
The capacity of tank A is 10*pi*81 / (4*pi^2) = 405 / (2*pi)
The radius of tank B is 10 / (2*pi).
The capacity of tank B is 9*pi*100 / (4*pi^2) = 450 / (2*pi)
Tank A / Tank B = 405/450 = 9/10 = 90%
The answer is B.
Answer: (B) 90%
Question: Two pipes A and B can fill a cistern in 20 and 30 minutes respectively, and a third pipe C can empty it in 40 minutes. How long will it take to fill the cistern if all the three are opened at the same time?
(A) 19 1/7 min
(B) 15 1/7 min
(C) 17 1/7 min
(D) 7 1/7 min
(E) 9 1/7 min
Rationale: Explanation:
1/20 + 1/30 - 1/40 = 7/120
120/7 = 17 1/7
Answer: Option C
Answer: (C) 17 1/7 min
Question: Which of the following number will completely divide (49^15)-1?
(A) 8
(B) 6
(C) 22
(D) 12
(E) 14
Rationale: x^n - 1 will be divisible by x+1 only when n is even.
49^15 - 1 = (7^2)^15 - 1 = 7^30 - 1 which is divisible by 7+1 i.e. 8
Answer is A
Answer: (A) 8
Question: A’s speed is 16/15 times that of B. If A and B run a race, what part of the length of the race should A give B as a head start, so that the race ends in a dead heat?
(A) 1/8
(B) 1/16
(C) 1/15
(D) 1/32
(E) 1/31
Rationale: Let x be the fraction of the distance that B runs.
Let v be the speed at which B runs.
The time should be the same for both runners.
Time = D / (16v/15) = xD/v
(15/16)*D/v = x*D/v
x = 15/16
B should have a head start of 1/16 of the full distance.
The answer is B.
Answer: (B) 1/16
Question: Two brothers Ram and Ravi appeared for an exam. The probability of selection of Ram is 4/7 and that of Ravi is 1/5. Find the probability that both of them are selected.
(A) 4/35
(B) 2/3
(C) 7/35
(D) 5/7
(E) 7/5
Rationale: Let A be the event that Ram is selected and B is the event that Ravi is selected.
P(A) = 4/7
P(B) = 1/5
Let C be the event that both are selected.
P(C) = P(A) x P(B) as A and B are independent events:
= 4/7 x 1/5 = 4/35
ANSWER:A
Answer: (A) 4/35
Question: Express 45 mps in kmph?
(A) 170
(B) 160
(C) 162
(D) 130
(E) 122
Rationale: 45 * 18/5 = 162 kmph
Answer:C
Answer: (C) 162
Question: In how many ways, a committee of 5 members can be selected from
6 men and 5 ladies, consisting of 3 men and 2 ladies?
(A) 100
(B) 200
(C) 300
(D) 400
(E) 500
Rationale: (3 men out 6) and (2 ladies out of 5) are to be chosen.
Required number of ways = (6c3x5c2) = [6x5x4/3x2x1] x [5x4/2x1] = 200.
Answer B.
Answer: (B) 200
Question: The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 5 per square feet if there is one DOOR of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each?
(A) 4687
(B) 3899
(C) 7815
(D) 4530
(E) 3573
Rationale: Area of the four walls = 2h(l + b)
Since there are DOORS and windows, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft.
Total cost = 906 * 5 = Rs. 4530
Answer: Option D
Answer: (D) 4530
Question: In the xy-coordinate system, line k passes through points (-9m, 0) and (0, 3m). Which of the following is a possible equation of line k?
(A) y = -3x + 3m
(B) y = 1/3*x - 9m
(C) y = 3x + 3m
(D) y = 1/3*x + 3m
(E) y = -1/3*x - 9m
Rationale: The slope of the line is 3m/9m=1/3.
The y-intercept is 3m.
the equation of the line is: y = 1/3*x +3m
The answer is D.
Answer: (D) y = 1/3*x + 3m
Question: Six years ago, the ratio of ages of Kunal and Sagar was 6:5. Four years hence, the ratio of their ages will be 11:10. What is Sagar's age at present?
(A) 16
(B) 17
(C) 8
(D) 12
(E) 10
Rationale: Let the ages of Kunal and Sagar 6 years ago be 6x and 5x years respectively.
Then, [(6x + 6) + 4] / [(5x + 6) + 4] = 11/10
10(6x + 10) = 11(5x + 10) => x = 2
Sagar's present age = (5x + 6) = 16 years.Answer: A
Answer: (A) 16