mathewhe/aqua_rat huggingface dataset:
Question: A cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 9 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled ?
(A) 4.5 hrs
(B) 5 hrs
(C) 6.5 hrs
(D) 7.2 hrs
(E) 9.2 hrs
Rationale: Net part filled in 1 hour= 1/4 -1/9= 5/36
Therefore the cistern will be filled in 36/5 hours or 7.2 hours.
ANSWER:D
Answer: (D) 7.2 hrs
Question: A lady grows Cauliflower in her garden that is in the shape of a square. Each Cauliflower takes 1 square foot of area in her garden. This year, she has increased her output by 223 Cauliflower when compared to last year. The shape of the area used for growing the Cauliflower has remained a square in both these years. How many Cauliflowers did she produce this year?
(A) 12541
(B) 12542
(C) 12544
(D) 12545
(E) Cannot be determined
Rationale: Explanatory Answer
The shape of the area used for growing Cauliflower has remained a square in both the years.
Let the side of the square area used for growing Cauliflower this year be X ft.
Therefore, the area of the ground used for cultivation this year = X2 sq.ft.
Let the side of the square area used for growing Cauliflower last year be Y ft.
Therefore, the area of the ground used for cultivation last year = Y2 sq.ft.
As the number of Cauliflower grown has increased by 223, the area would have increased by 223 sq ft because each Cauliflower takes 1 sq ft space.
Hence, X2 - Y2 = 223
(X + Y)(X - Y) = 223.
223 is a prime number and hence it will have only two factors. i.e., 223 and 1.
Therefore, 223 can be expressed as product of 2 numbers in only way = 223* 1
i.e., (X + Y)(X - Y) = 223 * 1
So, (X + Y) should be 223 and (X - Y) should be 1.
Solving the two equations we get X = 112 and Y = 111.
Therefore, number of Cauliflower produced this year = X2 = 1122 = 12544.
Alternative Approach : Use answer choices
The area in both the years are squares of two numbers.
That rules out choice A,B and D. as 12541,12542 and 12545 are not the square of any number.
Check Choice C: If this year's produce is 12544, last year's produce would have been 12544 - 223 = 12321
12321 is the square of 111.
So, 12544 is the answer.
Choice C.
Answer: (C) 12544
Question: If f and g are distinct prime numbers less than 10, which of the following cannot be the product of f and g?
(A) 6
(B) 9
(C) 10
(D) 14
(E) 15
Rationale: prime numbers less than 10 are 2, 3, 5, 7
all except 9 is product of any two numbers picked from above set.
Ans: B
Answer: (B) 9
Question: Each cell of a certain kind of bacteria produces two more cells. The life span of each cell is 10 minutes and each cell multiples only once in its life time, when it is exactly one minute old. If a new cell is placed in an empty box at time t = 0, then how many live cells will be there in the box just after t = 20 minutes?
(A) 2048 × 1023
(B) 1024 × 1023
(C) (1024)²
(D) 1023 × 1025
(E) 1023 × 1026
Rationale: see total cells created after
1min be 2^1
2min be 2^2
3 min be 2^3.......
thus after 20 min 2^20 will be created
now after 10 min 1 cell will die (2^0)
after 11 min 2 cells die (2^1)
similarly after 20 min 2^10 cells die
thus total cells remained=(2^20)-(1024)
or (1024)^2-1024
or1024*(1024-1)
i.e, 1024*1023
ANSWER:B
Answer: (B) 1024 × 1023
Question: Two twins sisters Sita and Geeta were standing back to back and suddenly they started running in opposite directions for 6 km each. Then they turned left and ran for another 4.5 km.
What is the distance (in kilometers) between the the two twins when they stop?
(A) 12
(B) 15
(C) 18
(D) 21
(E) 24
Rationale: The distance between them is the hypotenuse of a right angle triangle with sides 9 km and 12 km.
hypotenuse = sqrt(9^2 + 12^2) = 15
The answer is B.
Answer: (B) 15
Question: In a certain alphabet, 13 letters contain a dot and a straight line. 24 letters contain a straight line but do not contain a dot. If that alphabet has 40 letters, all of which contain either a dot or a straight line or both, how many letters contain a dot but do not contain a straight line?
(A) 3
(B) 8
(C) 14
(D) 20
(E) 28
Rationale: We are told that all of the letters contain either a dot or a straight line or both, which implies that there are no letters without a dot and a line (no line/no dot box = 0).
First we find the total # of letters with lines: 13 +24 = 37;
Next, we find the total # of letters without line: 40 - 37 = 3;
Finally, we find the # of letters that contain a dot but do not contain a straight line:3 - 0 = 3.
A
Answer: (A) 3
Question: 24 is divided into two parts such that 7 times the first part added to 5 times the second part gives 146. The first part is
(A) 11
(B) 13
(C) 16
(D) 17
(E) None
Rationale: Explanation:
Let the first and second parts be a and 24 a, then
7a+5(24−a)=146
⇒7a+120−5a=146
⇒2a=26 or a = 13
Correct Option: B
Answer: (B) 13
Question: If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 6-letter code words to the number of 4-letter code words?
(A) 5 to 4
(B) 30 to 1
(C) 2 to 1
(D) 5 to 1
(E) 6 to 1
Rationale: Number of ways to form 6-letter code: 10!/4! = 10*9*8*7*6*5
Number of ways to form 4-letter code: 10!/6! = 10*9*8*7
Ratio: 30 to 1
Answer : B
Answer: (B) 30 to 1
Question: An amount of Rs. 3000 becomes Rs. 3600 in four years at simple interest. If the rate of interest was 1% more, then what was be the total amount?
(A) 3729
(B) 2799
(C) 3720
(D) 2884
(E) 2881
Rationale: A = P(1 + TR/100)
=> 3600 = 3000[1 + (4 * R)/100] => R = 5%
Now R = 6%
=> A = 3000[1 + (4 * 6)/100] = Rs. 3720.
Answer:C
Answer: (C) 3720
Question: Jaime earned enough money by selling seashells at 22 cents each to buy several used paperback books at 55 cents each. If he spent all of the money he earned selling seashells to buy the books, what is the least number of seashells he could have sold ?
(A) 5
(B) 11
(C) 17
(D) 25
(E) 30
Rationale: Let's TEST Answer A: 5 seashells...
With 5 seashells, Jamie would have 5(22) = 110 cents. This would allow him to buy 2 books for 110 cents total, so this is the correct answer.
A
Answer: (A) 5
Question: Which number is the odd one out ?
9654 4832 5945 7642 7963 8216 3646
(A) 3646
(B) 9654
(C) 5945
(D) 7963
(E) 8216
Rationale: The product of first two digits in a number equals the last two digits, except in 3646. Hence, it is the odd one.
The answer is 3646.
ANSWER:A
Answer: (A) 3646
Question: Mr. Karan borrowed a certain amount at 6% per annum simple interest for 9 years. After 9 years, he returned Rs. 8410/-. Find out the amount that he borrowed.
(A) s. 5266
(B) s. 5269
(C) s. 5461
(D) s. 5218
(E) s. 52192
Rationale: Explanation:
Let us assume Mr. Karan borrowed amount is Rs. A. (the principal)
By formula of simple interest, S.I. = PRT / 100
Where P = The principal, R = Rate of interest as a %, T = Time in years
S.I. = (P * 6 * 9)/100 = 54 P/100
Amount = Principal + S.I.
8410 = P + (54P/100)
8410 = (100P + 54P)/100
8410 = 154P/100
P = (8410 * 100)/154 = Rs. 5461.039
ANSWER: C
Answer: (C) s. 5461
Question: If 15648 books need to be placed in boxes and each box can contain at most 9 books. How many books will be in the last unfilled box?
Options:
8
(A) 12 books
(B) 6 books
(C) 24 books
(D) 18 books
(E) 5 books
Rationale: The number of books that can be placed in boxes of 9 books is the first number that is divisible by 9 that occurs before 15648.
In order to divide the sum in 9 parts, the amount must be divisible by 9
Divisibility rule of 9: The sum of the digits must be divisible by 9
Sum of digits of 15648 =24 and 18 is divisible by 9.
Hence, we need to remove 6 to this number for it to be divisible by 9
Correct Option:B
Answer: (B) 6 books
Question: The simple interest at x% for x years will be Rs. x on a sum of:
(A) x
(B) x^2
(C) 100x
(D) 100x^2
(E) 50x^2
Rationale: Explanation :
P = ?
R = x%
Simple Interest,SI = x
T = x years
P=100× SI/RT=100 × x / x × x=100/x
Answer : Option C
Answer: (C) 100x
Question: For an integer n greater than 1, n* denotes the product of all the integers from 1 to n inclusive. How many prime numbers are there between 7*+2 and 7*+7, inclusive ?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: Given that n* denotes the product of all the integers from 1 to n, inclusive so, 7* + 2 = 7! + 2 and 7* + 7 = 7! + 7.
Now, notice that we can factor out 2 our of 7! + 2 so it cannot be a prime number, we can factor out 3 our of 7! + 3 so it cannot be a prime number, we can factor out 4 our of 7! + 4 so it cannot be a prime number, ... The same way for all numbers between 7! + 2 and 7! +7, inclusive. Which means that there are no primes in this range.
Answer: A.
Answer: (A) 0
Question: What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 54?
(A) 3672
(B) 920
(C) 7290
(D) 6928
(E) 3729
Rationale: Explanation:
Let the side of the square plot be a ft.
a2 = 289 => a = 17
Length of the fence = Perimeter of the plot = 4a = 68 ft.
Cost of building the fence = 68 * 54 = Rs. 3672.
Answer: Option A
Answer: (A) 3672
Question: If the time is currently 1:30 pm, what time will it be in exactly 646 hours?
(A) 11:30 am
(B) 12:30 pm
(C) 1:30 pm
(D) 2:30 pm
(E) 3:30 pm
Rationale: 646 = 26(24) + 22/24
The time will be 22 hours later than 1:30 pm which is 11:30 am.
The answer is A.
Answer: (A) 11:30 am
Question: A train 250 m long passed a pole in 25 sec. How long will it take to pass a platform 650 m long?
(A) 90 sec
(B) 89 sec
(C) 54 sec
(D) 27 sec
(E) 22 sec
Rationale: Speed = 250/25 = 10 m/sec.
Required time = (250 + 650)/10
= 90 sec.
Answer: A
Answer: (A) 90 sec
Question: A barrel full of beer has 2 taps one midway,,which draw a litre in 6 minutes and the other at the bottom,which draws a litre in 4 minutes. The lower tap is lower normally used after the level of beer in the barrel is lower than midway.The capacity of the barrel is 36 litres. A new assistant opens the lower tap when the barrel is full and draws out some beer. As a result the lower tap has been used 24 minutes before the usual time. For how long was the beer drawn out by the new assistant ?
(A) 15 minutes
(B) 16 minutes
(C) 17 minutes
(D) 18 minutes
(E) None of these
Rationale: Sol. The top tab is operational till 18 litres is drawn out.
∴ Time after which the lower tap is usually open
= 18 × 6 = 108 minutes
∴ Time after which it is open now = 108 – 24 = 84 minutes
∴ Litres drawn = 84/6 = 14 litres
∴ 18 – 14 = 4 litres were drawn by the new assistant.
∴ Time = 4 × 4 = 16 minutes Answer B
Answer: (B) 16 minutes
Question: One side of a rectangle is 3 cm shorter than the other side. If we increase the length of each side by 1 cm, then the area of the rectangle will increase by 16 cm2. Find the lengths of all sides.
(A) 10 and 3
(B) 9 and 6
(C) 10 and 7
(D) 3 and 10
(E) 10 and 10
Rationale: Let x be the length of the longer side x>3, then the other side's length is x−3 cm. Then the area is S1 = x(x - 3) cm2. After we increase the lengths of the sides they will become (x+1) and (x−3+1)=(x−2) cm long. Hence the area of the new rectangle will be A2=(x+1)⋅(x−2) cm2, which is 16 cm2 more than the first area. Therefore
A1+16=A2
x(x−3)+16=(x+1)(x−2)
x2−3x+16=x2+x−2x−2
2x=18
x=9. So, the sides of the rectangle are 9 cm and (9−3)=6 cm long.
So answer is B.
Answer: (B) 9 and 6
Question: Jim drove 768 miles of a 1200 miles journey. How many more miles does he need to drive to finish his journey?
(A) 432 miles
(B) 532 miles
(C) 632 miles
(D) 732 miles
(E) 832 miles
Rationale: The number of miles to drive to finish his journey is given by
1200 - 768 = 432 miles
correct answer A
Answer: (A) 432 miles
Question: The value of 2*x+x/4+ x(xx) when x = 4 is:
(A) 57
(B) 63
(C) 75
(D) 73
(E) 45
Rationale: 2*x+x/4+ x(xx)
2*4+4/4+4(4*4)
2*4+4/4+4(16)
2*4+4/4+64
2*4+1+64
8+1+64=73
answer D
Answer: (D) 73
Question: In the sequence S, each term after the first is twice the previous term. If the first term of sequence S is 3, what is the sum of the 14th, 15th, 16th, 17th and 18th terms in sequence S?
(A) 3(2^16)
(B) 9(2^15)
(C) 21(2^14)
(D) 9(2^14)
(E) 63(2^13)
Rationale: The terms in the sequence can be shown as
a(n) = 2* a(n-1)
So, the sequence will look like: 3, 2*3, (2^2) *3,...
And the nth term will be given as 2^(n-1) *3
Therefore, a(14) = (2^13)*3, a(15) = (2^14) *3, a(16) = (2^15) *3, a(17) = (2^16) *3 and a(18) = (2^17) *3
So, a(14) + a(15) + a(16)+ a(17)+ a(18) = (2^13) *3 + (2^14) *3 + (2^15) *3+ (2^16) *3+ (2^17) *3
= 3* (2^13) *(1+2+4+8+16) = 3* (2^13) *31
= 63 * (2^13)
Answer : E
Answer: (E) 63(2^13)
Question: The length of the bridge, which a train 130 m long and traveling at 45 km/hr can cross in 30 sec is?
(A) 165 m
(B) 886 m
(C) 245 m
(D) 286 m
(E) 281 m
Rationale: Speed = 45 * 5/18
= 25/2 m/sec.
Time = 30 sec
Let the length of bridge be x meters.
Then, (130 + x)/30
= 25/2
x = 245 m.
Answer: C
Answer: (C) 245 m
Question: The radius of a cylindrical vessel is 9cm and height is 3cm. Find the whole surface of the cylinder?
(A) 308 sq cm
(B) 220 sq cm
(C) 440 sq cm
(D) 132 sq cm
(E) 678.8 sq cm
Rationale: r = 9 h = 3
2πr(h + r) = 2 * 22/7 * 9(12) = 678.8
ANSWER:E
Answer: (E) 678.8 sq cm
Question: The ratio of red boxes to blue boxes in a certain warehouse is 5 to 25. If the number of the red boxes were doubled and the number of blue boxes were increased by 150 the ratio would be halved. How many total boxes are in the warehouse?
(A) 60
(B) 74
(C) 111
(D) 148
(E) 244
Rationale: Ratio = R/B = 5/25 or R = 5/25 B -----------(1)
2R/B+150 = 5/25*1/2 = 1/10 or we can say that 20R=B+150 -------------(2)
solving (1) and (2) we get
B=50 and R =10
so total boxes is B + R = 50+10=60
Hence A. 60 is the correct answer
Answer: (A) 60
Question: There are 5 locks and 5 keys and each of the 5 keys matches each of the 5 locks. What is the minimum and the maximum trial numbers of attempts R needed to confirm that each of the 5 keys matches each of the 5 locks?
(A) 5,15
(B) 4,15
(C) 5,10
(D) 4,10
(E) 5,20
Rationale: Assume you have locks 1-5 and keys A-E.
Minimum: assume you are lucky to find the correct key/combo on the first try. So, 1 -> A, 2 -> B, 3 ->C, and 4 -> D, then 5 must match with E. Therefore, you only need to try 4 combos at a minimum.
Maximum: assume that it takes as many guesses as possible. So, with the first key you try A, B, C, and D with no success, therefore E must be the match (so 4 attempts). For key 2 you no longer have E available so you try A, B, and C, with no success, therefore D must be the match (3 attempts). And so on for key 3 (2 attempts) and key 4 (1 attempt). Key 5 matches with the remaining lock for a total of R=4 + 3 + 2 + 1 = 10 attempts.D
Answer: (D) 4,10
Question: A train 100 m in length crosses a telegraph post in 12 seconds. The speed of the train is?
(A) 16 kmph
(B) 30 kmph
(C) 54 kmph
(D) 18 kmph
(E) 19 kmph
Rationale: S = 100/12 * 18/5
= 30 kmph
Answer: B
Answer: (B) 30 kmph
Question: a,b and c are positive integers less than or equal to 9. If a,b and c are assembled into the six-digit number abcabc, which of the following must be a factor of abcabc?
(A) 7
(B) 9
(C) 11
(D) 3
(E) none of these
Rationale: The sum of the digits in place 1,3 and 5 is a+c+b is equal to the sum of the digits in place 2,4 and 6 which is b+a+c. thus the number abcabc is divisible by 11. thus 11 must be a factor of abcabc.
Answer: C
Answer: (C) 11
Question: If p and q are positive integers each greater than 1, and 17(p+1)=20(q+1), what is the least possible value of p+q?
(A) 35
(B) 42
(C) 44
(D) 46
(E) none
Rationale: 17(p+1)=29(q+1) --> (p+1)/(q+1) = 20/17 --> the least positive value of p+1 is 20, so the least value of p is 19 and the least positive value of q+1 is 17, so the least value of q is 16 --> the least value of p+q is 19+16=35.
Answer: A
Answer: (A) 35
Question: JOHN and ANDREW can finish John work 30 days if they work together. They worked together for 20 days and then ANDREW left. JOHN finished the remaining work in another 20 days. In how many days JOHN alone can finish the work?
(A) 40
(B) 50
(C) 55
(D) 58
(E) 60
Rationale: Amount of work done by JOHN and ANDREW in 1 day = 1/30
Amount of work done by JOHN and ANDREW in 20 days = 20 × (1/30) = 20/30 = 2/3
Remaining work – 1 – 2/3 = 1/3
JOHN completes 1/3 work in 20 days
Amount of work JOHN can do in 1 day = (1/3)/20 = 1/60
=> JOHN can complete the work in 60 days
E
Answer: (E) 60
Question: Stacy has a 81 page history paper due in 3 days. How many pages per day would she have to write to finish on time?
(A) 9
(B) 27
(C) 10
(D) 8.5
(E) 6
Rationale: 81/3=27
Answer : B
Answer: (B) 27
Question: The compound interest earned by Sunil on a certain amount at the end of two years at the rate of 8% p.a. was Rs.2828.80. Find the total amount that Sunil got back at the end of two years in the form of principal plus interest earned.
(A) 19828.77
(B) 19828.8
(C) 19828.82
(D) 19888.82
(E) 19828.22
Rationale: Let the sum be Rs.P
P{ [ 1 + 8/100]2 - 1 } = 2828.80
P(8/100)(2 + 8/100) = 2828.80 [a2 - b2 = (a - b) ( a + b)] P = 2828.80 / (0.08)(2.08) = 1360/0.08 = 17000 Principal + Interest = Rs. 19828.80
Answer: B
Answer: (B) 19828.8
Question: The area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.1 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost?
(A) 399
(B) 272
(C) 666
(D) 277
(E) 311
Rationale: Answer: Option C
Explanation:
a2 = 3136 => a = 56
56 * 4 * 3 = 672 â€“ 6 = 666 * 1 = 666 Answer: C
Answer: (C) 666
Question: How many 4-digit positive integers are there, where each digit is positive, and no 3 adjacent digits are same?
(A) 1236
(B) 3528
(C) 4096
(D) 4608
(E) 6561
Rationale: First digit.. 9 posibilities
Second digit, 8 possibilities
third digit, 7 possibilities
Fourth digit, 7 possibilities.
9*8*7*7 = 3528.
B
Answer: (B) 3528
Question: The probability of a team winning a match given Matt is playing the match is 0.70. The probability of the team winning a match given Matt is not playing the match is 0.3. The probability of Matt playing any match is 0.7.
If it is known that the team has won the last match, what is the probability that Matt played the match?
(A) A)0.844
(B) B)0.7
(C) C)0.8571
(D) D)0.7531
(E) E)0.8213
Rationale: Out of 100 matches:
Matt is plays in 70 and not plays in 30.
Out of 70 matches Matt plays in, team wins 0.70*70 = 49.
Out of 30 matches Matt does not play in, team wins 0.3*30 = 9.
So, out of 100 matches 49 + 9 = 58 are won.
It is known that the team has won the last match. Out of 58 matches won, Matt is in 49: 49/58 = 0.844...
Answer: A.
Answer: (A) A)0.844
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) 12
(B) 51
(C) 21
(D) 24
(E) 25
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: The product X of two prime numbers is between 15 and 70. If one of the prime numbers is greater than 2 but less than 6 and the other is greater than 13 but less than 25, then X =
(A) 18
(B) 29
(C) 37
(D) 44
(E) 69
Rationale: Option BC can be ruled out as they themselves are prime numbers
18 = 2*9 = 3*6 >> Ignore
44 = 2 * 22 = 4 * 11 >> Ignore
69= 3*23 >> Answer
Answer = E
Answer: (E) 69
Question: Murali travelled from city A to city B at a speed of 70 kmph and from city B to city C at 30 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 2 : 3?
(A) kmph
(B) kmph
(C) kmph
(D) kmph
(E) kmph
Rationale: Let the distances between city A to B and B to C be 2x km and 3x km respectively.
Total time taken to cover from A to C
= (2x)/70 + (3x)/30
= (6x + 21x)/210 = 27x/210
= x/10 Average speed
= (2x + 3x)/(27x/210) = 38.9 kmph.
Answer: B
Answer: (B) kmph
Question: The average age of a group of 10 persons was decreased by 3 years when one person, whose age was 40 years, was replaced by a new person. Find the age of the new person?
(A) 18
(B) 56
(C) 12
(D) 17
(E) 10
Rationale: Initial average age of the 10 persons be P.
Age of the new person Q.
Sum of the ages of the initial 10 persons = 10P
New average
= (P-3) 10(P-3)
= 10P - 40 + Q
=> Q = 10
Answer:E
Answer: (E) 10
Question: A jet plane is rising vertically with a velocity of 10 m/s. It has reached a certain height when the pilot drops a coin, which takes 4 sec to hit the ground. Assuming that there is no resistance to the motion of the coin, the height of the place and the velocity of the coin on impact with the ground are:
(A) 38.4 m, 28.7 m/s
(B) 38.4 m, 29.2 m/s
(C) 26.5 m, 13.5 m/s
(D) 26.5 m, 28.7 m/s
(E) 26 m
Rationale: The coin will move up with the initial velocity of 10 m/s till it comes to rest. Time taken is given by:
0=10âˆ’9.8t
â‡’t=10/9.8 sec.
Time taken to reach the ground from the highest point:
=4âˆ’10/9.8
=29.2/9.8 sec
Velocity of coin on impact
=0+9.8Ã—(29.2/9.8)
=29.2 m/s
If 'h' is the height from which the coin dropped.
Then
29.2^2âˆ’10^2=2Ã—9.8Ã—h
â‡’h = 38.4 m
Answer : B
Answer: (B) 38.4 m, 29.2 m/s
Question: A man visits a shopping mall almost every day and he walks up an up-going escalator that connects the ground and the first floor. If he walks up the escalator step by step it takes him 16 steps to reach the first floor. One day he doubles his stride length (walks up climbing two steps at a time) and it takes him 12 steps to reach the first floor.
(A) 15
(B) 16
(C) 47
(D) 48
(E) 49
Rationale: Let d be the distance traveled, which remains same in both the cases. if v is the speed of the man and x is the speed of elevator, in case 1 the number of steps taken is
d/v+x=16
In case 2 it is
d/2v+x=12
because now he is traveling at double the speed; eliminating d, we get x=2v; therefore d=48v; when stationery x=0, we get no. of steps as 48v/v=48.
ANSWER:D
Answer: (D) 48
Question: The product of two numbers is 168 and the sum of these two numbers is 26. What is the largest of these two numbers?
(A) 12
(B) 14
(C) 16
(D) 18
(E) None of these
Rationale: Explanation:
Let the numbers be x and (26 – x) .
Therefore,
x (26 – x) = 168
x2 – 26x + 168 = 0
(x – 14) (x – 12) = 0
x = 14 or x = 12
So, the numbers are 14 and 12.
ANSWER: B
Answer: (B) 14
Question: A can run a kilometer race in 4 1/2 min while B can run same race in 5 min. How many meters start can A give B in a kilometer race, so that the race mat end in a dead heat?
(A) 288
(B) 266
(C) 155
(D) 100
(E) 112
Rationale: A can give B (5 min - 4 1/2 min) = 30 sec start.
The distance covered by B in 5 min = 1000 m.
Distance covered in 30 sec = (1000 * 30)/300 = 100 m.
A can give B 100m start.
Answer:D
Answer: (D) 100
Question: The value of X+3X(5X)(X)when X =2 is:
(A) 132
(B) 120
(C) 122
(D) 108
(E) 123
Rationale: Solution:
X+3X(5X)(X)
Put the value of X= 2 in the above expression we get,
2+ 6(2 x 5)(2)
= 2+ 6(10)(2)
= 2 + 120
=122
Answer :C
Answer: (C) 122
Question: Who is second to the right of H?
(A) 67
(B) 88
(C) 166
(D) 19
(E) 911
Rationale: Answer: Option B
Answer: (B) 88
Question: The banker's discount on Rs.1800 at 8% per annum is equal to the true discount on Rs.1872 for the same time at the same rate. Find the time?
(A) 3 months
(B) 4 months
(C) 5 months
(D) 6 months
(E) 7 months
Rationale: Solution
S.I on Rs.1800 = T.D on Rs.1872.
P.W on Rs.1872 is Rs.1800.
Rs.72 is S.I on Rs. 1800 at 8%.
Time	=(100x72 / 8x1800)
= 1/2 year
= 6 months.
Answer D
Answer: (D) 6 months
Question: If p+5/q is a prime integer, which of the following must be true?
1.q=5p
2.q is a prime integer
3. p+5/q is ODD.
(A) None
(B) 1 only
(C) 2 only
(D) 1 and 2 only
(E) 2 and 3 only.
Rationale: I would pick up numbers and do .
i hope the question is (p+5)/q....
let p = 3 , q = 4
3+5/4 = 2 = Prime
1. q is not equal to 5p
2.q is not a prime number
3. (p+5)/q is not odd.
hence A
Answer: (A) None
Question: A train speeds past a pole in 15 sec and a platform 120 m long in 25 sec, its length is?
(A) 50 m
(B) 180 m
(C) 200 m
(D) 300 m
(E) None of these
Rationale: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 15 => y = x/15
(x + 120)/25 = x/15 => x = 180 m.
ANSWER:B
Answer: (B) 180 m