mathewhe/aqua_rat huggingface dataset:
Question: Four of the five parts numbered a, b, c, d and e in the following equation are exactly equal. Which of the parts is not equal to the other four? The number of that part is your answer
(A) 10.36 + 69.802 + 24.938
(B) 2207.1 ÷ 21
(C) 16 2⁄3% of 630.6
(D) 32.84375 × 3.2
(E) 1⁄5 of 1⁄9 of 4729.4
Rationale: The other parts are equal to 105.10.
Answer E
Answer: (E) 1⁄5 of 1⁄9 of 4729.4
Question: An express traveled at an average speed of 100 km/hr, stopping for 4 min after every 75 km. How long did it take to reach its destination 300 km from the starting point ?
(A) 8 hrs 29 min
(B) 6 hrs 28 min
(C) 3 hrs 12 min
(D) 6 hrs 28 min
(E) 1 hrs 28 min
Rationale: Explanation:
Time taken to cover 300 km = 300/100 = 3 hrs.
Number of stoppages = 300/75 - 1 = 3
Total time of stoppages = 4 x 3 = 12 min
Hence, total time taken = 3 hrs 12 min.
Answer: C
Answer: (C) 3 hrs 12 min
Question: 49 × 49 × 49 × 49 = 7?
(A) 4
(B) 7
(C) 8
(D) 16
(E) None of these
Rationale: 49 × 49 × 49 × 49 = 7?
or, 7(2) × 7(2) × 7(2) × 7(2) = 7?
or 7(8) = 7? or, ? = 8
Answer C
Answer: (C) 8
Question: The angle between the minute hand and the hour hand of a clock when the time is 11.30, is
(A) 35°
(B) 65°
(C) 45°
(D) 165°
(E) 95°
Rationale: Angle between hands of a clock
When the minute hand is behind the hour hand, the angle between the two hands at M minutes past H 'o clock
=30(H−M/5)+M/2 degree
When the minute hand is ahead of the hour hand, the angle between the two hands at M minutes past H 'o clock
=30(M/5−H)−M/2 degree
Here H = 11, M = 30 and minute hand is behind the hour hand.
Hence the angle
=30(H−M/5)+M/2
=30(11−30/5)+30/2
=30(11−6)+15
=30×5+15 =165°
Answer is D.
Answer: (D) 165°
Question: Here is a question to keep you busy. Assume that you travel to your friend's place at 20 mph, then how fast you must make the return trip via the same route such that the average speed of your travel becomes 40 mph?
(A) Possible
(B) No Idea
(C) All above 3
(D) Impossible
(E) None of above
Rationale: D
Impossible
Let us first denote everything with variables.
d= distance to your friend's place
T = time taken to get there
t = time required to get back
R = Speed while returning back
d = 20T
T = d/20
d = Rt
t = d/R
We have made equations for T and t and now we can derive an equation for the round trip.
2d = 40(T + t)
2d = 40(d/20 + d/R)
2d = 40d(1/20 + 1/R)
1 = 20(R/20R + 20/20R)
20R = 20(R+20)
R = R + 20
Do you see the paradox here? You literally have to travel back at an infinite speed if you want to make the average speed of your trip 40 mph. The faster return speed will have lesser impact of the average speed but consider that the quicker your return trip is, the faster you will make it.
We are talking about travelling double the distance in the same time that was taken for one way trip. Thus, if you travel at infinite speed, you will be able to attain an average of 40 mph.
Answer: (D) Impossible
Question: Alice’s take-home pay last year was the same each month, and she saved the same fraction of her take-home pay each month. The total amount of money that she had saved at the end of the year was 4 times the amount of that portion of her monthly take-home pay that she did NOT save. If all the money that she saved last year was from her take-home pay, what fraction of her take-home pay did she save each month?
(A) 1/7
(B) 1/5
(C) 1/4
(D) 1/3
(E) 1/2
Rationale: Suppose the portion of her salary that she saved is X
and the remaining portion is Y
X+Y= total take home salary
given, 12X = 4Y
or 3X = Y
Total take-home salary= X+ 3X= 4X
hence, she saved 1/4-th portion of her take home salary
C
Answer: (C) 1/4
Question: The average of runs of a batsman of seven innings was 38. How many runs must be made in his next innings so as to increase his average of runs by 3?
(A) 72
(B) 54
(C) 70
(D) 62
(E) None of these
Rationale: Explanation :
Average after 8 innings = 41
Required number of runs = ( 41 8) - (38 7) =328 - 266 =62
Answer : D
Answer: (D) 62
Question: A 25 cm wide path is to be made around a circular garden having a diameter of 4 meters. Approximate area of the path is square meters is
(A) 3.34
(B) 45
(C) 44
(D) 33
(E) 77
Rationale: Area of the path = Area of the outer circle - Area of the inner circle = ∏{4/2 + 25/100}2 - ∏[4/2]2
= ∏[2.252 - 22] = ∏(0.25)(4.25) { (a2 - b2 = (a - b)(a + b) }
= (3.14)(1/4)(17/4) = 53.38/16 = 3.34 sq m
Answer: Option A
Answer: (A) 3.34
Question: A train running at the speed of 300 km/hr crosses a pole in 33 seconds. What is the length of the train?
(A) 2750
(B) 2850
(C) 2950
(D) 3050
(E) 3150
Rationale: Speed=(300 x(5/18)m/sec	=(250/3)m/sec.
Length of the train = (Speed x Time).
Length of the train =	((250/3)x 33)m = 2750 m
A
Answer: (A) 2750
Question: Two pipes A and B can fill a tank in 6 and 12 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?
(A) 4
(B) 6
(C) 8
(D) 10
(E) 12
Rationale: Part filled by A in 1 min. = 1/6
Part filled by B in 1 min. = 1/12
part filled by (A + B) in 1 min. = 1/6 + 1/12 = 1/4.
Both the pipes can fill the tank in 4 minutes.
Answer: A
Answer: (A) 4
Question: The sum of two numbers is 40 and their difference is 28. Find their product.
(A) 104
(B) 108
(C) 114
(D) 204
(E) None
Rationale: Sol.
Let the numbers be x and y.
Then, x + y = 40 and
x - y = 28
2x = 68 => x = 34
y = 6
xy = 34 * 6 = 204
Answer : D
Answer: (D) 204
Question: If a no. when divided by 44, gives 432 as quotient and 0 as remainder. What will be the remainder when dividing thesame no. by 31
(A) 3
(B) 6
(C) 5
(D) 8
(E) 9
Rationale: P ÷ 44 = 432
=> P = 432 * 44 = 19008
P / 31 = 19008 / 31 = 613, remainder = 5
C
Answer: (C) 5
Question: An integer n that is greater than 1 is said to be "prime-saturated" if it has no prime factor greater than or equal to n√n. Which of the following integers is prime saturated?
(A) 6
(B) 35
(C) 46
(D) 66
(E) 75
Rationale: According to the definition integer is said to be "prime-saturated" if the square of its largest prime is smaller than the integer itself.
Only E satisfies this: 75=3*5^2 --> the largest prime is 5 --> 5^2=25<75.
Answer: E.
Answer: (E) 75
Question: A family consists of grandparents, parents and three grand children. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family?
(A) 28 4⁄7 years
(B) 31 5⁄7 years
(C) 32 1⁄7 years
(D) 27 1⁄2 years
(E) None of these
Rationale: Required average = (67×2+35×2+6×3/2+2+3)
= (134+70+18/7)=222/7
= 31 5⁄7 years
Answer B
Answer: (B) 31 5⁄7 years
Question: The parameter of a square is double the perimeter of a rectangle. The area of the rectangle is 480 sq cm. Find the area of the square?
(A) 187
(B) 278
(C) 278
(D) 400
(E) 277
Rationale: Let the side of the square be a cm. Let the length and the breadth of the rectangle be l cm and b cm respectively.
4a = 2(l + b)
2a = l + b
l . b = 480
Answer:D
Answer: (D) 400
Question: If a and b are different positive integers and a + b = a(a + b), then which of the following must be true?
I. a = 1
II. b = 1
III. b > a
(A) I only
(B) II only
(C) III only
(D) I and III
(E) I and II
Rationale: a has to equal a squared, and that only works if a is 1. There are no positive integers less than 1, so I and III are correct.
Answer : D
Answer: (D) I and III
Question: In the x- y plane, there are 4 points (0,0), (0,4), (7,4), and (7,0). If these 4 points makes a rectangle, what is the probability that x+y<4?
(A) 2/3
(B) 3/5
(C) 2/7
(D) 4/9
(E) 7/10
Rationale: The line y=-x+4 intersects the rectangle and these three points of intersection (0,0), (0,4) and (4,0) form a triangle.
The points below the line y=-x+4 satisfy x+y<4.
The area of this triangle is (1/2)(4)(4)=8
The area of the rectangle is 28.
P(x+y<4) = 8/28 = 2/7
The answer is C.
Answer: (C) 2/7
Question: Which of the following must be an integer if the integer x is divisible by both 28 and 21?
(A) x/252
(B) x/84
(C) x/126
(D) x/108
(E) x/81
Rationale: the integer has to be multiple of LCM of 28 and 21, which is 84..
so x/84 will be an integer
ans B
Answer: (B) x/84
Question: If x is a positive number and 1/2 the square root of x is the cube root of x, then x =
(A) 64
(B) 32
(C) 16
(D) 4
(E) 1
Rationale: 1/2 the square root of x is cube root of x.
if x = 64..
then 1/2 the square root of x = 4 and cube of x is 64.
Option A.
Answer: (A) 64
Question: A father said his son , " I was as old as you are at present at the time of your birth. " If the father age is 38 now, the son age 5 years back was :
(A) 14
(B) 36
(C) 28
(D) 29
(E) 11
Rationale: Explanation:
Let the son's present age be x years .Then, (38 - x) = x x= 19.
Son's age 5 years back = (19 - 5) = 14 years
Answer: A) 14
Answer: (A) 14
Question: At what rate percent on simple interest will a sum of money double itself in 30 years?
(A) 3 1/3%
(B) 3 1/6%
(C) 3 1/5%
(D) 3 5/3%
(E) 7 1/3%
Rationale: P = (P*30*R)/100
R = 3 1/3%
Answer: A
Answer: (A) 3 1/3%
Question: Davidson has a corporate proposal. The probability that vice-president Adams will approve the proposal is 0.7. The probability that vice-president Baker will approve the proposal is 0.5. The probability that vice-president Corfu will approve the proposal is 0.4. The approvals of the three VPs are entirely independent of one another.
Suppose the Johnson must get VP Adam’s approval, as well as the approval of at least one of the other VPs, Baker or Corfu, to win funding. What is the probability that Johnson’s proposal is funded?
(A) 0.8
(B) 0.7
(C) 0.6
(D) 0.5
(E) 0.49
Rationale: probability of adams approval = 0.7
baker approval =0.5
corfu approval=0.4
proabability of approval is must adam approval and atleast one approval
= adam approval*baker approval*corfu approval(approval of both remaining)+adam approval*baker approval*corfu not approval(atleast one remaining approval)+
adam approval*baker not approval*coffu approval( atleast one remaining approval
= 0.7*0.5*0.4+0.7*0.5*0.6+0.7*0.5*0.4
=0.14+0.21+0.14
=0.49
E
Answer: (E) 0.49
Question: A certain sum is invested at simple interest at 18% p.a. for two years instead of investing at 12% p.a. for the same time period. Therefore the interest received is more by Rs. 840. Find the sum?
(A) 7000
(B) 7029
(C) 7290
(D) 7010
(E) 7102
Rationale: Let the sum be Rs. x.
(x * 18 * 2)/100 - (x * 12 * 2)/100
= 840 => 36x/100 - 24x/100 =840
=> 12x/100 = 840 => x
= 7000.
Answer:A
Answer: (A) 7000
Question: Out of three consecutive odd numbers ten times the first number is equal to addition of thrice the third number and adding 8 to thrice the second . What is the first number?
(A) 5/6
(B) 45/32
(C) 14/3
(D) 13/2
(E) 15/8
Rationale: Description :
=> 10x=3(x+2)+8+3(x+4)
=> 10x=6x+26
=> 4x=26
X=26/4=13/2
Answer D
Answer: (D) 13/2
Question: Robert is travelling on his cycle and has calculated to reach point A at 2 P.M. if he travels at 10 kmph, he will reach there at 12 noon if he travels at 15 kmph. At what speed must he travel to reach A at 1 P.M.?
(A) 9 km/hour
(B) 10 km/hour
(C) 11 km/hour
(D) 12 km/hour
(E) 13 km/hour
Rationale: Explanation:
We need to calculate the distance, then we can calculate the time and finally our answer.
Lets solve this,
Let the distance travelled by x km
Time = Distance/Speed
x/10−x/15=2
[because, 2 pm - 12 noon = 2 hours]
3x−2x=60x=60.
Time=Distance/Speed
Time@10km/hr=60/10=6hours
So 2 P.M. - 6 = 8 A.M
Robert starts at 8 A.M.
He have to reach at 1 P.M. i.e, in 5 hours
So, Speed = 60/5 = 12 km/hr
Option D
Answer: (D) 12 km/hour
Question: Rajan borrowed Rs.4000 at 5% p.a compound interest. After 2 years, he repaid Rs.2210 and after 2 more year, the balance with interest. What was the total amount that he paid as interest?
(A) Rs.635.50
(B) Rs.613.50
(C) Rs.675.50
(D) Rs.653.50
(E) Rs.673.50
Rationale: 4000
200 ---- I
200
10 ---- II
---------------
4410
2210
--------
2000
110 ---- III
110
5.50 ---- IV
-----------
2425.50
2210
-----------
4635.50
4000
----------
635.50
ANSWER:A
Answer: (A) Rs.635.50
Question: A number x is multiplied with itself and then added to the product of 4 and x. If the result of these two operations is 5, what is the value of x?
(A) -4
(B) -2
(C) 2
(D) 1 and -5
(E) Cannot be determined.
Rationale: A number x is multiplied with itself --> X^2
added to the product of 4 and x --> X^2+4X
If the result of these two operations is -4 --> X^2+4X=5
i.e X^2+4X-5=0 is the Quadratic equation which needs to be solved.
(X-1)(X+5) = 0
Hence X=1. C=-5
IMO D
Answer: (D) 1 and -5
Question: If v and k are integers whose product is 400, which of the following statements must be true?
(A) n + k > 0
(B) n is not equal to k.
(C) Either n or k is a multiple of 10.
(D) If n is even, then k is odd.
(E) If v is odd, then k is even.
Rationale: If v and k are integers whose product is 400, which of the following statements must be true?
A.n + k > 0n and k should have the same sign, but that means that they can also both be negative
B.n is not equal to k.20 x 20 = 400[i]
C.Either n or k is a multiple of 10. [i]25 x 16 = 400
D.If n is even, then k is odd.k can also be even since even x even will be even
E. If v is odd, then k is even.k must be even since odd x even = even
Answer: (E) If v is odd, then k is even.
Question: In a school with 604 students, the average age of the boys is 12 years and that of the girls is 11 years. If the average age of the school is 11 years 9 months, then the number of girls in the school is
(A) 150
(B) 151
(C) 250
(D) 350
(E) None
Rationale: Sol.
Let the number of grils be x.
Then, number of boys = (600 - x).
Then, (11 3/4 × 604)
⇔ 11x + 12(604 - x) ⇔ x = 7248 - 7097 ⇔ 151.
Answer B
Answer: (B) 151
Question: Farm Tax is levied on the 60% of the cultivated Land. The tax department collected total $ 5000 through the farm Tax from the village of Mr. william. Mr. william paid only $ 480 as farm tax. The percentage of total land of Mr. willam over the total taxable land of the village is :
(A) 15%
(B) 16%
(C) 0.125%
(D) 0.2083%
(E) none
Rationale: This will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village. That leads to (480/5000)x100 =9.6%in percentage terms.
But the question asks ratio between his total land to total cultivated land. Hence the answer is 9.6%x (100/60) = 16%
The correct answer is (B).
Answer: (B) 16%
Question: 60 + 5 * 12 / (180/3) = ?
(A) 22
(B) 77
(C) 29
(D) 61
(E) 21
Rationale: 60 + 5 * 12 / (180/3) = 60 + 5 * 12 / (60)
= 60 + (5 * 12)/60 = 60 + 1 = 61.Answer:D
Answer: (D) 61
Question: The ratio of the volumes of two cubes is 2744 : 3375. What is the ratio of their total surface areas?
(A) 71:76
(B) 71:131
(C) 71:145
(D) 71:167
(E) 71:113
Rationale: Ratio of the sides
= ³√2744: ³√3375 = 14 : 15
Ratio of surface areas
= 142 : 152 = 71:76
Answer:A
Answer: (A) 71:76
Question: Two vessels A and B contain mixtures of spirit and water. A mixture of 3 parts from A and 2 parts from B is found to contain 29% of spirit and a mixture of 1 part from A and 9 parts from B is found to contain 34 per cent of spirit. Find the percentage of spirit in A and B.
(A) 35, 25
(B) 40, 20
(C) 25, 35
(D) 50, 50
(E) none of these
Rationale: Let X% be the percentage of spirit in A and Y% in B
3X/100 + 2Y/100 = 29% of (3 + 2)
3X/100 + 2Y/100 = 1.45
3X + 2Y = 145 ----------(i)
X/100 + 9Y/100 = (34/100) x 10
X + 9Y = 340 ----(ii)
Solving (i) and (ii) we get X = 25 and Y = 35
A contains 25% spirit and B contains 35% of spirit.
ANSWER:A
Answer: (A) 35, 25
Question: Find large no. from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 10 as remainder
(A) 1235
(B) 1456
(C) 1567
(D) 1636
(E) 1635
Rationale: Let the smaller number be x. Then larger number = (x + 1365).
x + 1365 = 6x + 10
5x = 1355
x = 271
Large number = 271+1365 = 1636
D
Answer: (D) 1636
Question: A train 110 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) 7 sec
(B) 6 sec
(C) 4 sec
(D) 2 sec
(E) 1 sec
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 = [110 * 3/55] sec
= 6 sec
Answer: B
Answer: (B) 6 sec
Question: A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Area of the park = (60 x 40) m2 = 2400 m2.
Area of the lawn = 2109 m2.
Area of the crossroads = (2400 - 2109) m2 = 291 m2.
Let the width of the road be x metres. Then,
60x + 40x - x2 = 291
x2 - 100x + 291 = 0
(x - 97)(x - 3) = 0
x = 3.
A
Answer: (A) 3
Question: Last year a certain bond price with a face value of 5000 yielded 5% of its face value in interest. If that interest was approx 6.5 of the bond's selling price approx what was the bond's selling price?
(A) 4063
(B) 3846
(C) 5351
(D) 6000
(E) 6154
Rationale: Interest = 0.05*5000 = 0.065*selling price --> selling price = 0.05*5000/0.065 --> selling price = ~3,846
Answer: B.
Answer: (B) 3846
Question: In what time will two trains cross each other completely, which are running on the same parallel lines in opposite directions, each train running with a speed of 90 kmph being 160 m and 140 m in length respectively?
(A) 5.6 sec
(B) 6.2 sec
(C) 6.0 sec
(D) 7.2 sec
(E) 6.8 sec
Rationale: D = 160m + 140m = 300m * 1/1000 = 0.3 kms
RS = 90 + 90 = 180 kmph
T = (0.3/180) * 3600 = 6.0 sec
ANSWER:C
Answer: (C) 6.0 sec
Question: By selling an article at Rs.800, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 25%?
(A) Rs.429
(B) Rs.480
(C) Rs.429
(D) Rs.427
(E) Rs.482
Rationale: SP = 800
Profit = 25%
CP = (SP)*[100/(100+P)]
= 800 * [100/125]
= 640
Loss = 25% = 25% of 640 = Rs.160
SP = CP - Loss = 640 - 160 = Rs.480
Answer:B
Answer: (B) Rs.480
Question: The jogging track in a sports complex is 1000 meters in circumference. Deepak and his wife start from the same point and walk in opposite directions at 20 km/hr and 12 km/hr respectively. They will meet for the first time in?
(A) 32min
(B) 40min
(C) 35min
(D) 25min
(E) 20min
Rationale: Clearly, the two will meet when they are 1000 m apart
To be 20+12 = 32 km apart, they take 1 hour
To be 1000 m apart, they take 32 * 1000/1000 = 32 min.
Answer is A
Answer: (A) 32min
Question: What is 5/8 as a percent
(A) 62.5 %
(B) 63 %
(C) 63.5 %
(D) 64.5 %
(E) 65%
Rationale: 5/8 as a percent =(5 / 8 ) x100
= 0.625 x 100
=62.5%
answer : A i.e. 62.5 %
Answer: (A) 62.5 %
Question: Which one of the following can't be the square of natural number ?
(A) 30976
(B) 75625
(C) 28561
(D) 143642
(E) 235685
Rationale: Answer: Option D
The square of a natural number nerver ends in 2.
143642 is not the square of natural number.
Answer: (D) 143642
Question: If 4x + y = 8 and y − 3x = 7, then what is the value of x + 2y?
(A) 1/7
(B) 3
(C) 15
(D) 52/7
(E) 60/7
Rationale: 4x + y = 8
−3x + y = 7
Adding both the equations --> x + 2y = 15
Answer: C
Answer: (C) 15
Question: At a certain university, 68% of the professors are women, and 70% of the professors are tenured. If 90% of the professors are women, tenured, or both, then what percent of the men are tenured?
(A) 25
(B) 37.5
(C) 55
(D) 62.5
(E) 75
Rationale: total women = 68%
total men = 40%
total tenured = 70% (both men and women)
therefore, women tenured + women professors + men tenured = 90%
men tenured = 22%
but question wants to know the percent of men that are tenured
22%/40% = 55%
C
Answer: (C) 55
Question: The output of a factory was increased by 10% to keep up with rising demand. To handle the holiday rush, this new output was increased by 25%. By approximately what percent would the output now have to be decreased in order to restore the original output?
(A) 20%
(B) 24%
(C) 30%
(D) 27%
(E) 79%
Rationale: The original output increases by 10% and then 25%.
Total % change = a + b + ab/100
Total % change = 10 + 25 + 10*25/100 = 37.5%
Now, you want to change it to 0, so,
0 = 37.5 + x + 37.5x/100
x = -37.5(100)/137.5 = 27% approximately
Answer is D
Answer: (D) 27%
Question: 7^9 - 7^2 is approximation of which of the following?
(A) 7^9
(B) 9^8
(C) 9^9
(D) 9^11
(E) 9^10
Rationale: => Since 9^2 is a small number compared to 7^9, it can be disregarded. Thus, 7^9-7^2=7^9 is derived and the answer is A.
Answer: (A) 7^9
Question: Mr. Kramer, the losing candidate in a two-candidate election, received 942,568 votes, which was exactly 42 percent of all votes cast. Approximately what percent of the remaining votes would he need to have received in order to have won at least 50 percent of all the votes cast?
(A) 10%
(B) 12%
(C) 14%
(D) 17%
(E) 20%
Rationale: Let me try a simpler one.
Lets assume that candidate got 42% votes and total votes is 100.
Candidate won = 42
Remaining = 58
To get 50%, candidate requires 8 votes from 100 which is 8% and 8 votes from 58.
8/58 = .137 = 13.7%
Which is approx 14%. Hence the answer is C.
Answer: (C) 14%
Question: If a real number x is chosen at random in the interval [0,4] and a real number y is chosen at random in the interval [0,6], what is the probability that x < y?
(A) 2/5
(B) 3/5
(C) 2/3
(D) 3/10
(E) 7/10
Rationale: Since x is in [0,4] and y is in [0,6] we can draw a rectangle in the coordinate plane with vertices (0, 0), (4, 0), (0, 6), and (4, 6).
The points above the line y=x satisfy x < y.
The part of the rectangle below y=x has an area of 8.
The whole rectangle has an area of 24.
P(x < y) = (24-8)/24 = 16/24 = 2/3
The answer is C.
Answer: (C) 2/3
Question: Mike, Jim and Bob are all professional fisherman. Mike can catch 30 fish in one hour, Jim can catch twice as much and Bob can catch 50% more than Jim. If the three started to fish together and after 40 minutes Mike and Bob left, how many fish did the three fishermen catch in one hour?
(A) 110
(B) 120
(C) 140
(D) 130
(E) 112
Rationale: All of them catch fishes in relation to number 30....
2/3*30+2*30+2*1.5*30*2/3=140
Answer is C
Answer: (C) 140
Question: A boat can travel with a speed of 22 km/hr in still water. If the speed of the stream is 5 km/hr, find the time taken by the boat to go 135 km downstream
(A) 5 hours
(B) 4 hours
(C) 3 hours
(D) 2 hours
(E) None of these
Rationale: Explanation :
Speed of the boat in still water = 22 km/hr
speed of the stream = 5 km/hr
Speed downstream = (22+5) = 27 km/hr
Distance travelled downstream = 135 km
Time taken = distance/speed = 135/27 = 5 hours. Answer : Option A
Answer: (A) 5 hours
Question: A tradesman by means of his false balance defrauds to the extent of 26%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?
(A) 58.76%
(B) 49.89%
(C) 84.67%
(D) 24.65%
(E) 45%
Rationale: g% = 26 + 26 + (26*26)/100
= 58.76%
Answer: A
Answer: (A) 58.76%
Question: At a conference table, 5 employees gather around a table. One of the employees is the manager and he sits at the head of the table. Two of the employees sit on either side of the table. How many different seating arrangements can be made with these five employees?
(A) 5
(B) 10
(C) 24
(D) 32
(E) 120
Rationale: Head's sit is fixed. Now 4 people is left with 4 seats.
4 people can sit on 4 seats in 4! ways or 24 ways.
Ans is C
Answer: (C) 24
Question: How many positive four-digit integers do not contain any digits other than 1 or 0 and are such that the sum of the first two digits equals the sum of the last two digits?
(A) 3
(B) 4
(C) 8
(D) 10
(E) 12
Rationale: The sum of the first two (last two) digits cannot be 0 because 0000 is not a four-digit integer. If the sum of the first two digits is 1, two variants are possible: 1001 and 1010 (we have to remember that 0 cannot be the first digit). If the sum of the first two digits is 2, one variant is possible: 1111. In all, there are three numbers that satisfy the given conditions: 1001, 1010, and 1111.
Answer: A
Answer: (A) 3