mathewhe/aqua_rat huggingface dataset:
Question: Three friends Alice, Bond and Charlie divide $1245 amongs them in such a way that if $10, $20 and $15 are removed from the sums that Alice, Bond and Charlie received respectively, then the share of the sums that they got will be in the ratio of 9 : 10 : 11. How much did Charlie receive?
(A) $460
(B) $471
(C) $455
(D) $425
(E) $465
Rationale: A+B+C = 1245
Given ratio 9:10:11
Let us say the shares of A,B,C deducting 10,20,15 be a,b,c
a+b+c = 1245-45= 1200 = 30K
c share = (1200X11)/30 = 440
C = charlie share = 440+15 = 455
Option C
Answer: (C) $455
Question: The average weight of 29 students is 28 kg. By the admission of a new student, the average weight is reduced to 27.2 kg. The weight of the new student is
(A) 4 kg
(B) 21.6 kg
(C) 22.4 kg
(D) 21 kg
(E) None of these
Rationale: Exp . The total weight of 29 students = 29* 28
The total weight of 30 students = 30* 27.2
Weight of the new student = ( 30*27.2 – 29*28)
= 816 - 812 = 4
Answer:A
Answer: (A) 4 kg
Question: By selling an article at Rs.600, a profit of 25% is made. Find its cost price?
(A) 480
(B) 992
(C) 772
(D) 52
(E) 212
Rationale: SP = 600
CP = (SP)*[100/(100+P)]
= 600 * [100/(100+25)]
= 600 * [100/125] = Rs.480
Answer: A
Answer: (A) 480
Question: 4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it?
(A) 21 days
(B) 40 days
(C) 27 days
(D) 18 days
(E) 17 days
Rationale: Let 1 man's 1 day work = x and 1 woman's 1 day work = y.
Then, 4x + 6y = 1/8 and 3x + 7y = 1/10
Solving these two equations, we get:
x = 11/400 and y = 1/400
1 woman's 1 day work = (1/400 * 10) = 1/40.
Hence, 10 women will complete the work in 40 days.
Answer: B
Answer: (B) 40 days
Question: Set A is {1, 3, 5, 7, 9}
Set B is {14, 16, 18, 20, 22}
For the sets of numbers above, which of the following is true?
I. The mean of Set B is greater than the mean of Set A.
II. The median of Set B is greater than the median of Set A.
III. The standard deviation of Set B is greater than the standard deviation of Set A.
(A) I only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II, and III
Rationale: The mean and median of Set A is 5.
The mean and median of Set B is 18.
Thus statements I and II are both true.
The standard deviation is related to the distance from the mean.
Since the elements of both sets are spaced identically around the mean (+/- 2, +/- 4), the standard deviations of both sets are equal.
The answer is B.
Answer: (B) I and II only
Question: There is a biased dice..wen d dice is thrown. probability of occurrence of odd numbers is thrice that of even numbers. If the dice is thrown twice..find the probability of the products of the numbers appeared being odd.
(A) 8/16
(B) 9/16
(C) 10/16
(D) 11/16
(E) 7/16
Rationale: since, p(odd)=3p(even)
and p(odd)+p(even)=1
hence p(odd)=3/4
now only odd*odd=odd
hence two odd i s p(odd)=3/4*3/4=9/16
ANSWER:B
Answer: (B) 9/16
Question: In order to obtain an income of Rs. 650 from 10% stock at Rs. 96, one must make an investment of :
(A) Rs. 3100
(B) Rs. 6240
(C) Rs. 6500
(D) Rs. 9600
(E) None of these
Rationale: Solution
To obtain Rs. 10, investment = Rs. 96.
To obtain Rs. 650, investment = Rs (96/10x650) =rs.6240
Answer B
Answer: (B) Rs. 6240
Question: If x and y are integers and x divided by y is 15.15, then which of the following integers is a possible value for the remainder when x is divided by y? I. 15 II. 5 III. 3
(A) II,III only
(B) I only
(C) I,III only
(D) II only
(E) III only
Rationale: x=15.15y from which x = 15y + 15y/100 or x = 15y + 3y/20.
Since x and y are integers, 3y/20 must also be an integer. 3 is not divisible by 20, then y must be divisible by 20, and therefore, y/20 is an integer and 3y/20 is an integer which is a multiple of 3. From the given answers, only 15 and 3 are divisible by 3.
Answer C
Answer: (C) I,III only
Question: A man whose bowling average is 12.4, takes 5 wickets for 26 runs and there by decreases his average by 0.4. the number of wickets taken by him before his last match is?
(A) 83
(B) 84
(C) 85
(D) 86
(E) 87
Rationale: 12.4*x+26=(5+x)12
solve equation x=85
so 85 wicket is ans
ANSWER:C
Answer: (C) 85
Question: Let x be a positive integer, what is the remainder when 3^(x+5)+4 is divided by 2?
(A) 4
(B) 3
(C) 2
(D) 1
(E) 0
Rationale: For: (3^(x+5)+4)/2
Let n = x + 5
3^n
3^1 = 3
3^2 = 9
3^3 = 27
3^4 = 81
3^5 = 243, last digit pattern repeats 3, 9, 7, 1, 3, ....
Rule: x^(m+n) = (x^m)(x^n)
(3^(x))(3^5) => Now, (3)(3) + 3 = (9) + 3 => Finally, 12/2 and remainder is 0.
Answer: E
Answer: (E) 0
Question: A sells a Cricket Bat to B at a profit of 20%. B sells it to C at a profit of 25%. If C pays $225 for it, the cost price of the Cricket Bat for A is:
(A) 150
(B) 120
(C) 130
(D) 160
(E) 210
Rationale: A
150
125% of 120% of A = 225
125/100 * 120/100 * A = 225
A = 225 * 2/3 = 150.
Answer: (A) 150
Question: Two varieties of wheat - A and B costing Rs. 9 per kg and Rs. 15 per kg were mixed in the ratio 3 : 7. If 5 kg of the mixture is sold at 25% profit, find the profit made?
(A) 16.5
(B) 15.5
(C) 20.03
(D) 15.65
(E) 17.5
Rationale: Let the quantities of A and B mixed be 3x kg and 7x kg.
Cost of 3x kg of A = 9(3x) = Rs. 27x
Cost of 7x kg of B = 15(7x) = Rs. 105x
Cost of 10x kg of the mixture = 27x + 105x = Rs. 132x
Cost of 5 kg of the mixture = 132x/10x (5) = Rs. 66
Profit made in selling 5 kg of the mixture = 25/100 (cost of 5 kg of the mixture) = 25/100 * 66 = Rs. 16.50
ANSWER A
Answer: (A) 16.5
Question: Using all the letters of the word "TUESDAY", how many different words can be formed?
(A) A)7
(B) B)8!
(C) C)8
(D) D)7!
(E) E)3
Rationale: Explanation:
Total number of letters = 7
Using these letters the number of 7 letters words formed is 8!.
Answer: Option D
Answer: (D) D)7!
Question: A certain experimental mathematics program was tried out in 2 classes in each of 22 elementary schools and involved 31 teachers. Each of the classes had 1 teacher and each of the teachers taught at least 1, but not more than 3, of the classes. If the number of teachers who taught 3 classes is n, then the least and greatest possible values of n, respectively, are
(A) 0 and 13
(B) 0 and 14
(C) 1 and 10
(D) 1 and 6
(E) 2 and 8
Rationale: One may notice that greatest possible values differ in each answer choice in contrast to the least values, which repeat.
To find out the greatest value you should count the total classes (22*2=44), then subtract the total #of teachers since we know from the question that each teacher taught at least one class (44-31=13). Thus we get a number of the available extra-classes for teachers, and all that we need is just to count how many teachers could take 2 more classes, which is 13/2 = 6.5. So the greatest possible value of the # of teachers who had 3 classes is 6.
Only answer D has this option.
Answer: (D) 1 and 6
Question: If the remainder is 15 when the integer n is divided by 28, what is the remainder when 2n is divided by 14?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: n = 28k+15
2n = 2(28k+15) = 4k*14 + 30 = 4k*14 + 2*14 + 2 = 14j + 2
The answer is C.
Answer: (C) 2
Question: A man can row downstream at the rate of 24 Kmph and upstream at 7 Kmph. Find the man’s rate in still water and rate of current?
(A) 8.5
(B) 8.0
(C) 9.5
(D) 9.0
(E) 8.25
Rationale: Rate of still water = 1/2 (down stream + upstream)
= 1/2 (24 + 7) = 15.5 Kmph
rate of current = 1/2 (down stream - upstream)
= 1/2 (24 - 7)
= 1/2 (17)
= 8.5 kmph
Answer is A.
Answer: (A) 8.5
Question: If a + b - c = 2d, and if a - b + c = 2e, then a =
(A) 2(d + e)
(B) d + e
(C) (d + e)/2
(D) d-2e
(E) e-d
Rationale: Add both equations:
a + b - c = 2d
a - b + c = 2e
a+b-c+a-b+c=2d+2e
2a=2d+2e
a=(d+e)
Ans:B
Answer: (B) d + e
Question: What could be the range of a set consisting of odd multiples of 9?
(A) 21
(B) 24
(C) 35
(D) 72
(E) 70
Rationale: Range = the difference between the greatest and the smallest numbers in the sequence. Our sequence is odd and is a multiple of 7. Every number in that sequence can be represented like this: 9*(2n+1) where n is any positive integer.
Range = 9*(2m + 1) - 9*(2n + 1) = 9*2*(m-n) = 18 * (m-n).
m, n - any positive integers
The answer must be divisible by 18, which is only 72.
The correct answer is D
Answer: (D) 72
Question: A man purchased 2 blankets @ Rs.100 each, 5 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.150. Find the unknown rate of two blankets?
(A) 278
(B) 277
(C) 278
(D) 450
(E) 550
Rationale: 10 * 150 = 1500
2 * 100 + 5 * 150 = 950
1500 – 1050 = 550
Answer:E
Answer: (E) 550
Question: A sock drawer contains six socks, each one a different solid color. The colors of the socks are orange, yellow, green, blue, indigo, and violet. If the socks are laid next to each other, how many different arrangements of socks could be made?
(A) 24
(B) 240
(C) 1,024
(D) 2,520
(E) 720
Rationale: I see no condition for arrangement.
So 6! ways - IMO option E is correct answer..
Answer: (E) 720
Question: Positive integer y is 50 percent of 50 percent of positive integer x, and y percent of x equals 25. What is the value of x?
(A) 25
(B) 50
(C) 75
(D) 100
(E) 125
Rationale: y = 0.5*0.5*x = x/4
y%*x = 25
(y/100)*x = 25
(x/400)*x = 25
x^2 = 25*400
x = 100
The answer is D.
Answer: (D) 100
Question: For any number A, A* is defined as the greatest positive odd integer less than or equal to y. What is the value of 12.6 + 12.6*?
(A) 12.6
(B) 11
(C) 16.2
(D) 23
(E) 23.6
Rationale: Since A* is defined as the greatest positive odd integer less than or equal to A, then 12.6* = 11 (the greatest positive even integer less than or equal to 12.6 is 11).
Hence, 12.6 + 12.6* = 12.6 + 11 = 23.6
Answer: E.
Answer: (E) 23.6
Question: A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 640 m long?
(A) 22
(B) 89
(C) 88
(D) 278
(E) 291
Rationale: Speed = 240/24 = 10 m/sec.
Required time = (240 + 640)/10 = 88 sec.
Answer: C
Answer: (C) 88
Question: Each book on a certain shelf is labeled by a single category. For every 3 history books, there are 7 fantasy books and for every 5 fantasy books, there are 8 reference books. If the proportion of history to reference books is doubled, while the proportion of fantasy to reference books is maintained, which of the following could be the number of history books if there are fewer than 60 fantasy books on the shelf after the changes?
(A) 6
(B) 21
(C) 24
(D) 30
(E) 36
Rationale: For every 3 history books, there are 7 fantasy books:
Originally H:F = 3:7 = 15:35.
For every 5 fantasy books, there are 8 reference books:
F:R = 5:8 = 35:56
H:F:R = 15:35:56
After the changes, H:F:R = 30:35:56
There are fewer than 60 fantasy books, so there are 35 fantasy books.
The number of history books is 30.
The answer is D.
Answer: (D) 30
Question: Two train each 500 m long, and running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one.
(A) 20 sec
(B) 25 sec
(C) 24 sec
(D) 30 sec
(E) 22 sec
Rationale: speed = (45+30)
=75*5/18==>125/6
req time = 500*6/125 = 24 sec
ANSWER C
Answer: (C) 24 sec
Question: By investing in 1623% stock at 64, one earns Rs. 1900. The investment made is
(A) s. 9600
(B) s. 7500
(C) s. 5640
(D) s. 5760
(E) -7296
Rationale: Explanation :
Market Value = Rs.64
Face Value is not given and hence take it as Rs.100
16 2/3% of the face value = 50/3
ie, to earn 50/3, investment = Rs.64
Hence, to earn Rs.1500, investment needed = 64×3×1500/50=5760
Answer : Option D
Answer: (D) s. 5760
Question: A certain sum of money is divided among A, B and C so that for each Rs. A has, B has 65 paisa and C 40 paisa. If C's share is Rs.32, find the sum of money?
(A) 288
(B) 262
(C) 72
(D) 205
(E) 164
Rationale: A:B:C = 100:65:40
= 20:13:8
8 ---- 32
41 ---- ? => Rs.164
Answer: E
Answer: (E) 164
Question: In what time will a train 200 metres long cross an electric pole, if its speed be 124 km/hr?
(A) 4.8 sec
(B) 5.9sec
(C) 5.0sec
(D) 5.4sec
(E) 5.8sec
Rationale: Solution
Speed	= (124 x 5 /18) m/sec
= 34.44 m / sec
Time taken	= (200 /34.44) sec
= 5.8 sec.
Answer E
Answer: (E) 5.8sec
Question: Simplify (16^3−15^3)(16^2−15^2) =
(A) 22468
(B) 22351
(C) 22216
(D) 22192
(E) 22106
Rationale: (16^3 - 15^3)(16^2 - 15^2) =
= ({number with units digit of 6} - {smaller number with units digit of 5})*({number with units digit of 6} - {smaller number with units digit of 5}) =
= {number with units digit of 1}*{number with units digit of 1} = {number with units digit of 1}.
Answer: B
Answer: (B) 22351
Question: When 52416 is divided by 312, the quotient is 168. what will be the quotient when 52.416 is divided by 0.0168?
(A) 5
(B) 6
(C) 4
(D) 3
(E) 8
Rationale: for the 1st no. there are 2 digits after decimal
for the 2nd no. there are 5 digits after decimal
total no. of decimals = 7
req. no. of digits=(n-1)=(7-1)=6
ANSWER :B
Answer: (B) 6
Question: A family made a down payment of $300
and borrowed the balance on a set of
encyclopedias that cost $750. The
balance with interest was paid in 9
monthly payments of $57 each and a
final payment of $21. The amount of
interest paid was what percent of the
amount borrowed?
(A)  6%
(B)  12%
(C)  14%
(D)  18.66%
(E)  20%
Rationale: interest paid = 57*9+21 - 450 = 84
% off the balance = (84/450) * 100 = 18.66%
Answer is D.
Answer: (D)  18.66%
Question: In how many different number of ways 5 men and 3 women can sit on a shopa which can accommodate persons?
(A) 17
(B) 18
(C) 56
(D) 21
(E) 23
Rationale: 8p2 = 8 x 7 = 56
Answer: C
Answer: (C) 56
Question: A can finish a work in 6 days and B can do same work in half the time taken by A. then working together, what part of same work they can finish in a day?
(A) 1/2
(B) 1/6
(C) 1/7
(D) 1/8
(E) None of these
Rationale: Explanation:
Please note in this question, we need to answer part of work for a day rather than complete work. It was worth mentioning here because many do mistake at this point in hurry to solve the question
So lets solve now,
A's 1 day work = 1/6
B's 1 day work = 1/3 [because B take half the time than A]
(A+B)'s one day work =
(1/6+1/3)=1/2
So in one day 1/2 work will be done
Answer: A
Answer: (A) 1/2
Question: John was 31 years old when he married Betty. They just celebrated their fifth wedding anniversary, and Betty's age is now 7/9 of John's. How old is Betty?
(A) 24
(B) 26
(C) 28
(D) 30
(E) 32
Rationale: Assume Betty's age on marriage = x years.
John's age on marriage = 31
John's age after 5 years = 36 years.
Betty's age after 5 years = x + 5
Given: x + 5 = 7/9 (36) = 28
Therefore Betty's current age = 28
Option C
Answer: (C) 28
Question: There are 400 employees in a room. 99% are managers. How many managers must leave the room to bring down the percentage of managers to 98%?
(A) 50
(B) 100
(C) 150
(D) 200
(E) 250
Rationale: There are 396 managers and 4 others. The 4 others would compose 2% of the total number of people if there were 200 people in the room. Thus 200 managers must leave.
The answer is D.
Answer: (D) 200
Question: From a group of 6boys&4girls a Committee of 4 persons is to be formed. In how many different ways can it be done, so that the committee has at least 2 boys?
(A) 120
(B) 135
(C) 185
(D) 190
(E) 210
Rationale: The committee of 4 persons is to be so formed that it has at least 2 men. The different ways that we can choose to form such a committee are:
(i) 2m. 2w in 6C2 x 4 C1=6X5 - 2X1 X 3X3 2X1 =n an (ii) 3m. 1w in 6C3 x 4C1 =6X5X4 3X2X1 X4 _n - a ''''
(iii) 4m in 6C4 -2x1 = 15 Total no. of different ways in which a committee of 4 persons can be formed so that it has at least 2 men. = 90 + 18 + 15 = 185
C
Answer: (C) 185
Question: The length of the bridge, which a train 125 m long and traveling at 45 km/hr can cross in 30 sec is?
(A) 235
(B) 240
(C) 245
(D) 250
(E) 255
Rationale: Speed = 45 * 5/18 = 25/2 m/sec.
Time = 30 sec
Let the length of bridge be x meters.
Then, (125 + x)/30 = 25/2
x = 250 m.
Answer: Option D
Answer: (D) 250
Question: A and B started business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, C joined them with Rs. 20,000. What will be B's share in the total profit of Rs. 18,000 earned at the end of 18 months from the starting of the business?
(A) A)4966
(B) B)7389
(C) C)7379
(D) D)7453
(E) E)7637
Rationale: A:B:C = (20000 * 18) : (15000 * 18) : (20000 * 12) = 12:9:8
B's share = 18000 * 8/29 = Rs.4966
Answer: A
Answer: (A) A)4966
Question: Anand and Deepak started a business investing Rs. 22,500 and Rs. 35,000 respectively. Out of a total profit of Rs. 13,800, Deepak's share is:
(A) Rs.8480
(B) Rs.8409
(C) Rs.8400
(D) Rs.8423
(E) Rs.8430
Rationale: Ratio of their shares = 22500 : 35000
= 9:14
Deepak's share = 13800 * 14/23
= Rs.8400.
Answer: C
Answer: (C) Rs.8400
Question: Two cars cover the same distance at the speed of 60 and 64 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car.
(A) 120 km
(B) 960 km
(C) 240 km
(D) 630 km
(E) 456 km
Rationale: Explanation:
60(x + 1) = 64x
X = 15
60 * 16 = 960 km
B)
Answer: (B) 960 km
Question: Find the Missing Number 1, 2, 4, 10, 16, 40, 64 (Successive terms are related)
(A) 100
(B) 200
(C) 300
(D) 90
(E) 80
Rationale: Well, the pattern looked REALLY familiar to me, like it's a binary progression.
And it is...but with a twist.
2^0 = 1
2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 16
2^5 = 32
2^6 = 64
You'll note that all the numbers up there match your sequence...except for 2^3 = 8 (10 in your sequence) and 2^5 = 32 (40 in your sequence).
BUT, if you convert 8 to base 8, you get 10.
And if you convert 32 to base 8, you get 40.
Which indicates that every other number starting with the first one is expressed in base 10 and every other number starting with the second number is expressed in base 8.
If this is true, then you next number would be:
2^7 = 128
That is the base 10 number. Since this number should be expressed in base 8 (following the pattern), it should be 200. ANSWER:A
Answer: (A) 100
Question: Ms.Jane invested in Fund D and Fund B. The total amount she invested, in both funds combined, was $100,000. In one year, Fund D paid 23% and Fund B paid 17%. The interest earned in Fund B was exactly $200 greater than the interest earned in Fund D. How much did Ms. Morris invest in Fund D?
(A)  $32,000
(B)  $36,000
(C)  $40,000
(D)  $42,000
(E)  $45,000
Rationale: 0.17B-0.23D = 200 | * 100
17B-23D=20,000
D+B=100,000
B=100,000 - D
17(100,000 - D) - 23D = 20,000
1,700,000 - 17D - 23D = 20,000
1,680,000 = 40D
divide by 40
first two digits: 42...so answer is D.
Answer: (D)  $42,000
Question: The present ages of three persons are in proportions 4:7:9. Eight years ago, the sum of their ages was 56. Find their present ages.
(A) 20, 35, 45
(B) 16, 28, 36
(C) 8, 20, 28
(D) None of these
(E) 30,25,12
Rationale: Answer: Option B
:
Let their present ages be 4x, 7x and 9x years respectively.
Then, (4x - 8) + (7x - 8) + (9x - 8) = 56
20x = 80 => x = 4
Their present ages are 16, 28 and 36 years respectively.
Answer: (B) 16, 28, 36
Question: At what rate of CI per year will a sum of Rs. 1200 become Rs. 1348.32 in 2 years?
(A) 5%
(B) 6%
(C) 8%
(D) 9%
(E) 11%
Rationale: Let the rate be R% p.a.
Then, 1200 x 1 + R 2 = 1348.32
100
1 + R 2 = 134832 = 11236
100 120000 10000
1 + R 2 = 106 2
100 100
1 + R = 106
100 100
R = 6%
B
Answer: (B) 6%
Question: The area of sector of a circle whose radius is 12 metro and whose angle at the center is 42° is?
(A) 52.5
(B) 52.9
(C) 52.8
(D) 52.1
(E) 52.2
Rationale: 42/360 * 22/7 * 12 * 12 = 52.8 m2
Answer: C
Answer: (C) 52.8
Question: If x is an integer, which of the following is a possible value of D=(x^2 +2x – 7)/9?
(A) -2.4
(B) 0.268
(C) 1.166 repeating
(D) 4.555 repeating
(E) 8.125
Rationale: x is an integer, which of the following is a possible value of D=(x^2 +2x – 7)/9?
Used process of elimination
A. -2.4
when this is multiplied by 9, x is not an integer
B. 0.268
when this is multiplied by 9, x is not an integer
C. 1.166 repeating
when this is multiplied by 9, x is not an integer
D. 4.555 repeating
E. 8.125
when this is multiplied by 9, x is not an integer
Answer choice D seems to fit
Answer: (D) 4.555 repeating
Question: The probability that event B occurs is 0.6, and the probability that events A and B both occur is 0.25. If the probability that either event A or event B occurs is 0.4, what is the probability that event A will occur?
(A) 0.05
(B) 0.15
(C) 0.45
(D) 0.5
(E) 0.55
Rationale: P(A or B) = P (A) + P(B) - p(a n b)
0.4= 0.6 + P(A) - 0.25
P(A) = 0.05
Ans : A
Answer: (A) 0.05
Question: Evaluate: 983 x 207 - 983 x 107
(A) 93700
(B) 97300
(C) 93800
(D) 98300
(E) None of them
Rationale: 983 x 207 - 983 x 107
= 983 x (207 - 107)
= 983 x 100 = 98300.
Answer is D.
Answer: (D) 98300
Question: At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.15000?
(A) 6620
(B) 4965
(C) 2776
(D) 2997
(E) 2718
Rationale: A = 15000(11/10)^3
= 19965
= 15000
----------
4965
Answer:B
Answer: (B) 4965
Question: What is the smallest number which is a perfect square and is divisible by 16, 20 and 24?
(A) 2400
(B) 3600
(C) 7200
(D) 1600
(E) 1500
Rationale: Explanation:
3600. The number is perfect square of 60.
It is divisible by 36 24 and 20. Only two numbers 3600 and 7200 fit these conditions.
It is clear that 3600 is the smaller number.
ANSWER B
Answer: (B) 3600
Question: A train running at the speed of 60 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) 140 metres
Rationale: Speed of the train=60kmph or300/18m/s
Let the length of the train=L
Now the equation is;
L*18/300=9sec
Now solving L=150m
ANSWER:D
Answer: (D) 150 metres
Question: 9 men and 12 boys finish a job in 12 days, 12 men and 12 boys finish it in 10 days. 10 men and 10 boys shall finish it in how many days?
(A) 11 days
(B) 12 days
(C) 17 days
(D) 16 days
(E) 18 days
Rationale: B
12 days
9M + 12B ----- 12 days
12M + 12B ------- 10 days
10M + 10B -------?
108M + 144B = 120M +120B
24B = 12M => 1M = 2B
18B + 12B = 30B ---- 12 days
20B + 10B = 30B -----? => 12 days
Answer: (B) 12 days
Question: A train 220 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
(A) 4
(B) 6
(C) 5
(D) 12
(E) 8
Rationale: Speed of train relative to man = (60 + 6) km/hr = 66 km/hr
[66 * 5/18] m/sec = [55/3] m/sec.
Time taken to pass the man = [220 * 3/55] sec = 12 sec
ANSWER:D
Answer: (D) 12
Question: The original price of a car was $18,000. Because the car owner thought he could get more money for the car, he set a new price by increasing the original price of the car by 10%. After a week, the car had not sold, so the owner discounted the new price by 10%, and the car was finally sold. What price was the car sold for?
(A) $17,740
(B) $17,760
(C) $17,780
(D) $17,800
(E) $17,820
Rationale: The car was sold for (0.9)(1.1)($18,000)=$17,820.
The answer is E.
Answer: (E) $17,820
Question: Difference between the length &breadth of a rectangle is 30 m. If its perimeter is 300 m, then its area is?? We have: (l - b) = 30 and 2(l + b) = 300 or (l + b) = 150?
(A) 3:5
(B) 2:3
(C) 3:6
(D) 3:4
(E) 3:2
Rationale: Solving the two equations, we get: l = 90 and b = 60.
The ratio of length and breath is 90:60 =3:2
E
Answer: (E) 3:2
Question: The average of two numbers is XY. If one number is X, then the other number is
(A) Y
(B) Y⁄2
(C) 2XY – X
(D) X(Y – 1)
(E) None of these
Rationale: Let the other number is N.
Then , X+N/2 = XY ⇒ N = 2XY - X
Answer C
Answer: (C) 2XY – X
Question: A person incurs a loss of 5% be selling a watch for Rs. 1140. At what price should the watch be sold to earn 5% profit.
(A) Rs.1200
(B) Rs.1230
(C) Rs.1260
(D) Rs.1290
(E) Rs.1270
Rationale: Explanation:
Let the new S.P. be x, then.
(100 - loss%):(1st S.P.) = (100 + gain%):(2nd S.P.)
=>(951/140=105/x)=>x=1260
ANSWER IS C
Answer: (C) Rs.1260
Question: A train running at the speed of 60 km/hr crosses a pole in 4 seconds. Find the length of the train.
(A) 66.67
(B) 882
(C) 772
(D) 252
(E) 121
Rationale: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 4 = 66.67 meter.Answer: A
Answer: (A) 66.67