mathewhe/aqua_rat huggingface dataset:
Question: If x and y are different integers, both divisible by 11, then which is not necessarily true?
(A) x^2 + y^2 is divisible by 11
(B) x - y is divisible by 11
(C) xy is divisible by 11
(D) x + y is divisible by 11
(E) x + y is divisible by 22
Rationale: Let x = 11k and let y = 11j.
Then x+y = 11(k+j) and k+j could be even or odd.
Thus 11(k+j) is not necessarily divisible by 22.
The answer is E.
Answer: (E) x + y is divisible by 22
Question: In a simultaneous throw of 2 dice what is the probability of getting a total of 2?
(A) 1/4
(B) 1/36
(C) 2/11
(D) 3/13
(E) 1/5
Rationale: n(S) = 6*6 = 36
E = {(1,1)}
Probability = 1/36
Answer is B
Answer: (B) 1/36
Question: How many Three digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is replaced?
(A) 5
(B) 10
(C) 15
(D) 20
(E) 30
Rationale: Since each desired number is divisible by 5, so we must have 5 at the unit place. So, there is 1 way of doing it.
Tens place can be filled by any of the remaining 5 numbers.
So, there are 5 ways of filling the tens place.
The hundreds place can now be filled by any of the remaining 4 digits. So, there are 4 ways of filling it.
Therefore Required number of numbers = 1 x 5 x 4 = 20.
Answer D.
Answer: (D) 20
Question: If a - b = 3 and a2 + b2 = 29, find the value of ab.
(A) 10
(B) 12
(C) 15
(D) 18
(E) 20
Rationale: Explanation:
2ab = (a2 + b2) - (a - b)2
= 29 - 9 = 20
ab = 10.
Answer: A
Answer: (A) 10
Question: The ratio between the present ages of P and Q is 6:7. If Q is 4 years old than P, what will be the ratio of the ages of P and Q after 4 years?
(A) 3:4
(B) 3:5
(C) 4:3
(D) data inadequate
(E) None of these
Rationale: Let P's age and Q's age be 6x and 7x years respectively.
Then, 7x - 6x = 4 => x = 4
Required ratio = (6x + 4) : (7x + 4)
28 : 32 = 7:8
ANSWER:E
Answer: (E) None of these
Question: (X)+4671+6514-7687=19190. Calculate the value of X
(A) 15615
(B) 15692
(C) 15687
(D) 15112
(E) 15690
Rationale: x+4671+6514-7687=19190
=x+4671+6514=19190+7687
=x+11185=26877
=x=26877-11185
=15692
Answer is B
Answer: (B) 15692
Question: If the complement of a certain angle is seven times the measure of that certain angle, then what is the measure of that certain angle?
(A) 45°
(B) 30°
(C) 11.25°
(D) 18°
(E) 15°
Rationale: The complement of angle A is the angle which, when added to angle A, gives 90 degrees. The two acute angles of a right triangle are complements, for example.
The original angle is x, so the complement is 7x, and together, these add up to 90 degrees.
x + 7x = 90
8x = 90
x = 11.25°
Answer = (C)
Answer: (C) 11.25°
Question: A father said to his son, "I was as old as you are at present at the time of your birth." If the father's age is 50 years now, the son's age 10 years back was?
(A) 12yr
(B) 15yr
(C) 14yr
(D) 10yr
(E) 20yr
Rationale: Let the son's present age be x years
Then, 50-x = x
x = 25
Son's age 10 years back = 25-10 = 15years
Answer is B
Answer: (B) 15yr
Question: For how many integers pair (x,y) satisfies the result
(1/x)+((1/y)=1/16
(A) a) 12
(B) b) 6
(C) c) 10
(D) d) 16
(E) e) 19
Rationale: It seems that the accepted answer is wrong, according to WolframAlpha. The answer should be 31, which isn't even listed as a selectable answer.
E
Answer: (E) e) 19
Question: A bag contains 2 yellow, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?
(A) 1/2
(B) 10/21
(C) 9/11
(D) 7/11
(E) 6/11
Rationale: Total number of balls = 2 + 3 + 2 = 7
Let S be the sample space.
n(S) = Total number of ways of drawing 2 balls out of 7 = 7C2
Let E = Event of drawing 2 balls , none of them is blue.
n(E) = Number of ways of drawing 2 balls , none of them is blue
= Number of ways of drawing 2 balls from the total 5 (=7-2) balls = 5C2
(âˆµ There are two blue balls in the total 7 balls. Total number of non-blue balls = 7 - 2 = 5)
P(E) = n(E)/n(S)=5C2/7C2=(5Ã—4/2Ã—1)/(7Ã—6/2Ã—1)=5Ã—4/7Ã—6=10/21
Answer :B
Answer: (B) 10/21
Question: The volume of a cube is 1728 cc. Find its surface?
(A) 864
(B) 288
(C) 299
(D) 267
(E) 289
Rationale: a3 = 1728 => a = 12
6a2 = 6 * 12 * 12
= 864
Answer:A
Answer: (A) 864
Question: Deepak can read x pages in 10 minutes. At this rate, how long will it take him to read y pages?
(A) (12/x)*y
(B) (5/x)*y
(C) (10/x)*y
(D) (10x)*y
(E) (13/x)*y
Rationale: x page in 10 mins
i.e. 1 page in 10/x mins
i.e. y pages in (10/x)*y
Answer: option C
Answer: (C) (10/x)*y
Question: The speed of a railway engine is 84 Km per hour when no compartment is attached, and the reduction in speed is directly proportional to the square root of the number of compartments attached. If the speed of the train carried by this engine is 24 Km per hour when 9 compartments are attached, the maximum number of compartments that can be carried by the engine is:
(A) 19
(B) 18
(C) 16
(D) 17
(E) 14
Rationale: the reduction in speed is directly proportional to the square root of the number of compartments attached
Doesreductionmean amount subtracted? or percentage decrease? There are at least two interpretations, and the wording does not provide a clear interpretation between them.
Evidently what the question intends is the subtraction interpretation. What is subtracted from the speed is directly proportional to the square root of the number of compartments attached.
In other words, if S = speed, and N = number of compartments, then
S = 84 - k*sqrt(N)
wherekis a constant of the proportionality. In general, if A is directly proportional to B, we can write A = k*B and solve for k.
If N = 9, then S = 24
24 = 84 - k*sqrt(9) =84 - 3k
k = 20
Now, we need to know: what value of N makes S go to zero?
0 = 84 - 20*sqrt(N)
20*sqrt(N) = 84
sqrt(N) = 4.2
n = 4.2^2 >17
With 18 compartments, the train does not budge. Therefore, it would budge if there were one fewer cars. Thus, 17 is the maximum number of cars the engine can pull and still move.
D
Answer: (D) 17
Question: Two out of ten employees are capable of doing a certain task. Sixty percent of the five employees, including the two who are capable, are assigned to a project involving this task. what percentage of employees assigned to the project are not capable?
(A) 43.33%
(B) 66.66%
(C) 13.33%
(D) 38.33%
(E) 23.33%
Rationale: Given 60% of 10 employees including 2 who are capable of doing task.
60% of 10 employeees
= 60/100 * 10
= 6 employees
===> 2 employees who are capable of doing the task and four employee who is not capable.
percentage of employees assigned who are not capable
= 4/6 * 100
= 66.66%
ANSWER:B
Answer: (B) 66.66%
Question: Eight women of eight different heights are to pose for a photo in two rows of four. Each woman in the second row must stand directly behind a shorter woman in the first row. In addition, all of the women in each row must be arranged in order of increasing height from left to right. Assuming that these restrictions are fully adhered to, in how many different ways can the women pose?
(A) 2
(B) 14
(C) 15
(D) 16
(E) 18
Rationale: Shortest (1) and highest (8) women are fixed:
XXX8
1XXX
2 and 7 have two options, so total 4 patterns:
1:
2xx8
1xx7
|2468| |2568|
|1357| |1347|
2.
2x78
1xxx
|2478| |2578| |2678|
|1356| |1346| |1345|
3.
xxx8
12x7
|4568| |3468| |3568|
|1237| |1257| |1247|
4.
xx78
12xx
|3478| |3678| |3578| |5678| |4578| |4678|
|1256| |1245| |1246| |1234| |1236| |1235|
14 options.
Answer: B.
Answer: (B) 14
Question: Can you find the smallest non fractional number such that
If the number gets divided by 7 , we get the remainder of 1;
If the number gets divided by 8 , we get the remainder of 2
If the number gets divided by 9 , we get the remainder of 3;
If the number gets divided by 10 , we get the remainder of 4.
(A) 1500
(B) 3210
(C) 2150
(D) 2518
(E) 2300
Rationale: D.2518
As we know LCM of the numbers 7 8 9 & 10 is 2520.
So if i divide 2520 by any of the four number , it gives remainder as 0.
Now to get reminder as desired, is should be 2 short of 2518. (3-1,4-2,5-3,6-4 )
Ans:option D
Answer: (D) 2518
Question: In a race where 10 cars are running, the chance that car X will win is 1/7, that Y will win is 1/3 and that Z will win is 1/5. Assuming that a dead heat is impossible, find the chance that one of them will win.
(A) 1/140
(B) 1/180
(C) 71/105
(D) 21/113
(E) 57/120
Rationale: Required probability = P(X) + P(Y) + P(Z) (all the events are mutually exclusive).
= 1/7 + 1/3 + 1/5
= 71/105
ANSWER:C
Answer: (C) 71/105
Question: The area of a square field is 4802 m(power)2 the length of its diagonal is:
(A) 98m
(B) 102m
(C) 95m
(D) 105m
(E) 96m
Rationale: Let the diagonal be d metres,
Then 1/2 d(power)2 = 4802
d2 = 9604
d = √9604
d = 98 m
Answer is A.
Answer: (A) 98m
Question: The sum of all the digits of the integers from 18 to 21 inclusive is 24 (1 + 8 + 1 + 9 + 2 + 0 + 2 + 1 = 24). What is the sum Q of all the digits of the integers from 0 to 99 inclusive?
(A) 450
(B) 810
(C) 900
(D) 1000
(E) 1100
Rationale: We want the sum of the digits from 0 to 99, so I approximated:
0-9 ->45-> (9+0)*10/2
40-49 ->85(13+4)*10/2
90-99 ->135(18+9)*10/2
We can see at a glance that theweightgoes up as the numbers go up (meaning the difference between 85 and 45 is 40, while 135-85 is 50, this means that the second part of this sequence carries more weight for our result), so we know that the final answer has to be more than 850 (85*10) but close to it, and that's just Q=900:the answer is C.
Answer: (C) 900
Question: A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same time during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. Find the time required by the first pipe to fill the tank ?
(A) 10 hours
(B) 15 hours
(C) 17 hours
(D) 18 hours
(E) 20 hours
Rationale: Explanation:
Suppose, first pipe alone takes x hours to fill the tank .
Then, second and third pipes will take (x -5) and (x - 9) hours respectively to fill the tank.
As per question, we get
1/x+1/x−5=1/x−9
=>x−5+x/x(x−5)=1/x−9
=>(2x−5)(x−9)=x(x−5)
=>x2−18x+45=0
After solving this euation, we get
(x-15)(x+3) = 0,
As value can not be negative, so x = 15
Option B
Answer: (B) 15 hours
Question: X starts a business with Rs.54000. Y joins in the business after 9 months with Rs.27000. What will be the ratio in which they should share the profit at the end of the year?
(A) 1 : 2
(B) 2 : 1
(C) 8 : 3
(D) 3 : 5
(E) 8 : 1
Rationale: Explanation :
Ratio in which they should share the profit
= Ratio of the investments multiplied by the time period
= 54000 * 12: 27000 * 3
= 54 * 12: 27 * 3
= 2*4: 1
= 8:1. Answer : Option E
Answer: (E) 8 : 1
Question: A circular rim 28 inches in diameter rotates the same number of inches per second as a circular rim 49 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minute does the larger rim makes in terms of x ?
(A) 48pi/x
(B) 75x
(C) 34.2x
(D) 24x
(E) x/75
Rationale: C = (pi)d
C(small): (pi)*28
C(large): (pi)*49
Lets say the time horizon is 60 seconds, so during that time the smaller rim covers a distance of (pi)*28*60 = (pi)*(1680) inches
(pi)*(1680) = (pi)*(49)(x)
pi*(34.2) = pi*(x)
34.2=x
Answer: C. 34.2x
Answer: (C) 34.2x
Question: If the number of boys in a class are 8 times the number of girls, which value can never be the total number of boys?
(A) A - 16
(B) B - 9
(C) C - 10
(D) D - 11
(E) E - 12
Rationale: Let the number of girls = x and the number of boys = 8x Then, total number of students = x + 8x = 9x i.e., the total number of boys must be a multiple of 8 From the given choices, only 16 is multiple of 8. Answer is A.
Answer: (A) A - 16
Question: Three business people who wish to invest in a new company. Each person is willing to pay one third of the total investment. . After careful calculation, they realize that each of them would pay $ 7800 less if they could find two more equal investors. How much is the total investment in the new business.
(A) a)	$ 58,500
(B) b)	$ 54,000
(C) c)	$ 21,000
(D) d)	$ 5,400
(E) e)	$3,600
Rationale: Initially each invest in x. Hence total investment is 3x.
Total investment is also 5(x-7800).
3x = 5(x-7800)
x= 5*7800/2 = 19500
3x = 58500 and the answer is A.
Answer: (A) a)	$ 58,500
Question: Evaluate combination
16C2
(A) 120
(B) 1000
(C) 10
(D) 1
(E) 0
Rationale: Explanation:
nCn=1
nCr=n!/r!(n-r)!
16C2=16!/2!(16-2)!=120
Option A
Answer: (A) 120
Question: Find the largest number which divides 62,132,237 to leave the same reminder
(A) 30
(B) 32
(C) 35
(D) 45
(E) 55
Rationale: Explanation:
Trick is HCF of (237-132), (132-62), (237-62)
= HCF of (70,105,175) = 35
Option C
Answer: (C) 35
Question: Laura took out a charge account at the General Store and agreed to pay 9% simple annual interest. If she charges $35 on her account in January, how much will she owe a year later, assuming she does not make any additional charges or payments?
(A) $2.10
(B) $37.10
(C) $37.16
(D) $38.10
(E) $38.15
Rationale: Principal that is amount taken by Laura at year beginning = 35$
Rate of interest = 9%
Interest = (9/100)*35 = 3.15$
Total amount that Laura owes a year later = 35+3.15 = 38.15 $
Answer E
Answer: (E) $38.15
Question: A number of 47 marbles is to be divided and contain with boxes. If each box is to contain 3, 4, or 5 marbles, what is the largest possible number of boxes?
(A) 10
(B) 12
(C) 15
(D) 16
(E) 17
Rationale: To maximize # of boxes we should minimize marbles per box: 14*3+1*5=47 --> 14+1=15.
Answer: C.
Answer: (C) 15
Question: In the rectangular coordinate system, points (2, 0) and (– 2, 0) both lie on circle C. What is the maximum possible value of the radius of C ?
(A) 2
(B) 4
(C) 8
(D) 16
(E) None of the above
Rationale: The answer is A
It takes 3 distinct points to define a circle. Only 2 are given here.
The two points essentially identify a single chord of the circle C. Since no other information is provided, however, the radius of the circle can essentially be anything. All this information tell us is that the radius isgreater 2
Answer: (A) 2
Question: In an office, totally there are 6400 employees and 65% of the total employees are males. 25% of the males in the office are at-least 50 years old. Find the number of males aged below 50 years?
(A) 3127
(B) 3128
(C) 3120
(D) 3122
(E) 3124
Rationale: Number of male employees = 6400 * 65/100 = 4160
Required number of male employees who are less than 50 years old = 4160 * (100 - 25)%
= 4160 * 75/100 = 3120.
Answer: C
Answer: (C) 3120
Question: If a and b are nonzero integers such that 2a+1 = 5b+1, then each of the following must be true EXCEPT
(A) 0 < b/a < 1
(B) ab is positive.
(C) On the number line, b lies between 0 and a.
(D) The ratio of a to b is equivalent to 10/4.
(E) a – b is positive.
Rationale: This question can be solved by TESTing VALUES. Based on its wording, you would likely need to do 2 TESTs to get to the correct answer though.
We're told that A and B are NONZERO INTEGERS and that 2a+1 = 5b+1 or 2A = 5b. We're told that each of the answer is always true EXCEPT for one of them...
Before we get to the actual work, it's important to note a few details:
1) We are NOT told that A and B are positive - we're just told that they're NONZERO - that's interesting - it means that we have to consider the possibility that they're both NEGATIVE...
2) 4 of the answers will always be true, while one of them will EITHER be sometimes true OR never true. We'll have to keep working until we find 1 answer that is not true (for whatever reason) - that will be the solution to this question.
Since 2A = 5B, I'm going to run 2 pairs of TESTs at the same time...
A = 5
B = 2
AND
A = -5
B = -2
Answer A: 0 < B/A < 1
2/5 and -2/-5 both = 2/5. Answer A appears true.
Answer B: AB is positive
(2)(5) and (-2)(-5) both = +10. Answer B appears true.
Answer C: B is between 0 and A on the number line
0....2....5
-5....-2....0
Answer C appears true.
Answer D: A/B = 10/4
5/2 = -5/-2
10/4 = 5/2
Answer D appears true.
Answer E: A - B is positive
5 - 2 = 3
-5 - (-2) = -3 *****This is NOT always true.
Final Answer:
E
Answer: (E) a – b is positive.
Question: A corporation seven times its annual bonus to 5 of its employees. What percent of the employees’ new bonus is the increase?
(A) 1.35%
(B) 85.71%
(C) 3.12%
(D) 4.78%
(E) 3.69%
Rationale: Let the annual bonus be X.
A corporation triples its annual bonus.
So new bonus = 7X.
Increase = 7X-X =6X
The increase is what percent of the employees’ new bonus
= (6X/7X)*100
= 85.71%
Hence B.
Answer: (B) 85.71%
Question: A boatman can row 3 km against the stream in 20 minutes and return in 18 minutes. Find the rate of current ?
(A) 1/3 kmph
(B) 2/3 kmph
(C) 1/4 kmph
(D) 1/2 kmph
(E) 1/6 kmph
Rationale: Explanation:
Speed in upstream = Distance / Time = 3 x 60/20 = 9 km/hr.
Speed in downstream = 3 x 60/18 = 10 km/hr
Rate of current = (10-9)/2 = 1/2 km/hr.
ANSWER IS D
Answer: (D) 1/2 kmph
Question: 1/2, 1/4, 1/8, 1/16, 1/32,1/64, 1/128 ....
In the sequence above each term after after the first one-half the previous term. If x is the tenth term of the sequence, then x satisfies which of the following inequalities?
(A) 0.1 < x < 1
(B) 0.01 < x < 0.1
(C) 0.001 < x < 0.01
(D) 0.0001 < x < 0.001
(E) 0.000001 < x < 0.00001
Rationale: In the Sequence notice that the sequence is just the 1/(2^n) ...
so for 1st term=1/2^1=1/2
2nd term=1/(2^2)1/4, 3rd term=1/(2^3)=1/8 and so on...
Thus the 10th term will be 1/(2^10)=1/1024
Roughly, 1/1024 can be 1/1000=0.001 but since denominator is a bit more than 1000 therefore the actual value will be a bit less than 0.001.
thus the ans will lie btw. 0.000001 and 0.0001.(E)
Answer: (E) 0.000001 < x < 0.00001
Question: The population of a town is 10000. It increases annually at the rate of 15% p.a. What will be its population after 2 years?
(A) 13300
(B) 13350
(C) 13225
(D) 13500
(E) 13600
Rationale: Formula :
( After =100 denominator
Ago = 100 numerator)
10000 Ã— 115/100 Ã— 115/100 = 13225
C
Answer: (C) 13225
Question: Ifaequals the sum of the even integers from 2 to 100, inclusive, andbequals the sum of the odd integers from 1 to 99, inclusive, what is the value of a - b ?
(A) 1
(B) 50
(C) 19
(D) 20
(E) 21
Rationale: This is a solution from Beatthegmat:
even numbers:
(100-2)/2 + 1 = 50 even integers.
(100+2)/2 = 51 is the average of the even set.
sum = avg*(#of elements) = 51*50 = 2550 = a
odd numbers:
(99-1)/2 + 1 = 50 odd integers.
(99+1)/2 = 50 is the average of the odd set.
sum = avg*(#of elements) = 50*50 = 2500 = b
a-b = 2550 - 2500 = 50. (B)
Answer: (B) 50
Question: maximun number of identical pieces(of same size) of a cake by making only 3 cuts?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 5
Rationale: since cake is a 3D object, it will have length,breadth, height...
first cut across length now we will get2 pieces
then cut across breadth we will get 4 parts in total now...
now cut across height, finally we will get 8 parts...
ANSWER:C
Answer: (C) 8
Question: The apartment on King-Williams street is an asset that its value is tramping about. From the year 1973 to 1983 it's value decreased by 16% and from 1983 to 1993 it's value increased by 16%. What is the value of the asset in 1993 if in 1973 it was worth $30,000?
(A) $38,796.
(B) $29,232.
(C) $38,976.
(D) $39,679.
(E) $36,796.
Rationale: 30,000 *1.16*.84= Unit and tens digit of the expression is 6 and 7 respectively.
Only option B fulfills the condition and hence is the answer
Answer: (B) $29,232.
Question: The ratio of two numbers is 4 : 5 and their H.C.F. is 4. Their L.C.M. is
(A) 48
(B) 22
(C) 56
(D) 80
(E) 67
Rationale: Explanation:
Let the numbers be 4x and 5x. Then, their H.C.F. = x. So, x = 4.
So, the numbers 16 and 20.
L.C.M. of 16 and 20 = 80.
Option D
Answer: (D) 80
Question: If Ajay drives at 4/5th of his usual speed to his office, he is 6 minutes late. What is his usual time to reach his office?
(A) 36
(B) 24
(C) 30
(D) 18
(E) 19
Rationale: Explanation:
Let t be his usual time to reach his office and v be his usual speed.
v = d/t ……….(d is the distance Ajay travels while going to his office)
vt = d
At v1 = 4v/5 ; t1 = t + 6
4v/5 = d/(t + 6)
4v/5* (t + 6) = d
4v/5* (t + 6) = vt
On solving we get,
t = 24 minutes
ANSWER B
Answer: (B) 24
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train?
(A) 150 meter
(B) 299 meter
(C) 666 meter
(D) 155 meter
(E) 144 meter
Rationale: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 9
= 150 meter
Answer: A
Answer: (A) 150 meter
Question: In a 500 m race, the ratio of the speeds of two contestants A and B is 3 : 4. A has a start of 155 m. Then, A wins by:
(A) 60 m
(B) 20m
(C) 40 m
(D) 20m
(E) 23m
Rationale: To reach the winning post A will have to cover a distance of (500 - 155)m, i.e., 345 m.
While A covers 3 m, B covers 4 m.
While A covers 345 m, B covers 4 x 345/3	m	= 460 m.
Thus, when A reaches the winning post, B covers 460 m and therefore remains 40 m behind.
A wins by 40 m.
Answer:	C
Answer: (C) 40 m
Question: A city council will select 2 of 9 available firefighters and 1 of 5 available police officers to serve on an advisory panel. How many different groups of 3 could serve on the panel?
(A) 36
(B) 72
(C) 144
(D) 180
(E) 432
Rationale: OA D
9C2 * 5C1
using the combination formula to choose 2 from 9 and 1 from 5
D
Answer: (D) 180
Question: A train passes a station platform in 35 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
(A) 228
(B) 240
(C) 225
(D) 166
(E) 1811
Rationale: Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 20 = 300 m.
Let the length of the platform be x m . Then,
(x + 300)/35 = 15 => x = 225 m.
Answer: C
Answer: (C) 225
Question: Sam purchased 20 dozens of toys at the rate of Rs. 375 per dozen. He sold each one of them at the rate of Rs. 33. What was his percentage profit?
(A) 5.9%
(B) 5.6%
(C) 5.6%
(D) 9.6%
(E) 1.6%
Rationale: C.P. of 1 toy = 375/12 = Rs. 31.25
S.P of 1 toy = Rs. 33
Profit = 1.75/31.25 * 100 = 28/5 = 5.6%
Answer: C
Answer: (C) 5.6%
Question: City A and City B are 140 miles apart. Train C departs City A, heading towards City B, at 4:00 and travels at 40 miles per hour. Train D departs City B, heading towards City A, at 4:35 and travels at 20 miles per hour. The trains travel on parallel tracks. At what time do the two trains meet?
(A) 5:00
(B) 5:30
(C) 6:00
(D) 6:35
(E) 7:00
Rationale: Train C has traveled 20 mi in the half hour before Train D has started its journey.
140-20=120
40+20 =60 mph
120 mi/ 60 mph = 2 hrs
4:35pm + 2 hrs = 6:35pm
Answer:
D. 6:35
Answer: (D) 6:35
Question: If a: b :: 3 : 7, then what is (5a+2b): (a-2b)?
(A) 57:11
(B) -57:11
(C) 11 : 10
(D) -29 : 11
(E) -1 : 10
Rationale: a/b= 3/7
Dividing numerator & denominator of ' (5a+6b)/(a-2b) 'by b,
[5(a/b)+2]/[(a/b)-2]= [5*(3/7)+2]/[(3/7)-2]= -29/11
ANSWER:D
Answer: (D) -29 : 11
Question: Two full tanks one shaped like the cylinder and the other like a cone contain liquid fuel the cylindrical tank held 500 lts more then the conical tank After 200 lts of fuel is pumped out from each tank the cylindrical tank now contains twice the amount of fuel in the canonical tank How many lts of fuel did the cylindrical tank have when it was full?
(A) 1200
(B) 279
(C) 2879
(D) 27976
(E) 27711
Rationale: Let the cylindrical tank capacity x + 500 then the conical tank capacity = x
After 200 lts pumped out, then remaining fuel with the tanks = x +300, x - 200
Given that first term is doubt the second.
x+300x−200=21x+300x−200=21
Solving we get x = 700
Cylindrical tank capacity = 1200 lts
Answer:A
Answer: (A) 1200
Question: By selling 12 pens for a rupee a woman loses 20%. How many for a rupee should he sell in order to gain 20%?
(A) 12
(B) 14
(C) 45
(D) 8
(E) 65
Rationale: D
80% --- 12
120% --- ?
80/120 * 12 = 8
Answer: (D) 8