mathewhe/aqua_rat huggingface dataset:
Question: If two of the four expressions x+y, x+5y, x-y, and 5x-y are chosen at random, what is the probability T that their product will be of the form of x^2-(by)^2, where b is an integer?
(A) 1/2
(B) 1/3
(C) 1/4
(D) 1/5
(E) T=1/6
Rationale: Only (X+y)(x-y) pair will give the form x^2-(by)^2
The probability of selecting these two pairs are 1/4 * 1/3 = 1/12, assuming x+y is picked first, then x-y, but x-y can be picked first followed by x+y. So the probability T= 1/12 * 2 = 1/6
Ans E
Answer: (E) T=1/6
Question: If x = y+3+4.5x and y = x+17, what is the value of x/y ?
(A) -6/5.
(B) -40/113.
(C) 1/4.
(D) 5/6.
(E) 1.5.
Rationale: (1) x = y + 3 + 4.5x
Substitute y for y = x + 17 (Eq. we are given)
x = x + 17 + 3 + 4.5x
Combine like terms
x = 5.5x + 20 --> -4.5x = 20 --> x = -40/9
(2) y = x + 17
Substitute x for x = -40/9
y = (-40/9) + 17 = 113/9
(3) x/y = ?
Substitute x and y we found above
x/y = (-40/9) / (113/9) = (-40/9) * (9/113) = -40/113
My answer: B
Answer: (B) -40/113.
Question: The greatest number of four digits which is divisible by 15, 24, 40 and 75 is :
(A) 9000
(B) 9400
(C) 9600
(D) 9800
(E) None of these
Rationale: Solution
Greatest number of 4 digits is 9999. L.C.M. of 15, 25, 40 and 75 is 600.
On dividing 9999 by 600, the remainder is 399.
∴ Required number =(9999 - 399) = 9600. Answer C
Answer: (C) 9600
Question: Ashley paid 5 dollars for 1 notebook and 1 pencil. If both prices were integers, how many pencils did Ashley buy if she paid 93 dollars for the pencils and for 15 notebooks?
(A) 6.
(B) 16.
(C) 18
(D) 21
(E) 26
Rationale: 5 = 1P + 1 N
93 = XP + 15N, where X is the number of pencils
Possible prices for 1P & 1N (integers):
N = 1 P = 4 then 15N = 15, 4X = 93 - 15 = 78, X = 19.5 (not an integer)
N = 2 P = 3 then 15N = 30, 3X = 93 - 30 = 63, X = 21 (the answer we were looking for, no need to continue calculations)
N = 3 P = 2
N = 4 P =1
Answer: D
Answer: (D) 21
Question: The number of female students in a college in the previous year was 480. If in the current year the number of male students in the college doubled over that of the previous year but the proportion of male students halved, then what is the number of female students in the college in the current year?
(A) 1680
(B) 1760
(C) 1840
(D) 1920
(E) 2000
Rationale: Let x be the number of male students last year. The number of male students this year is 2x.
Let y be the number of female students this year.
x/480 = 2(2x/y)
y = 1920
The answer is D.
Answer: (D) 1920
Question: There are r red ball, b blue ball and w white ball in a bag. What is the ratio of the number of blue ball to the total no. of ball in terms of r, b and w.?
(A) r / (r + b + w)
(B) r
(C) (r + b + w)
(D) r / (r + b)
(E) (r + b + w)*e
Rationale: The total number of marbles is
r + b + w
The total ratio of blue marbles to the total number of marbles is
r / (r + b + w)
A
Answer: (A) r / (r + b + w)
Question: A, B and C invest in a partnership in the ratio: 7/2,4/3,6/5. After 4 months, A increases his share 50%. If the total profit at the end of one year is Rs.21,600, then what is B's share in the profit?
(A) 1000
(B) 2000
(C) 3000
(D) 4000
(E) 5000
Rationale: Ratio of the initial investment
=7/2:4/3:6/5=105:40:36
Therefore, let the initial investments of A, B and C be 105x,40x and 36x respectively
A increases his share 50% after 4 months. Hence the ratio of their investments
=(105x×4)+(105x×150/100×8) :40x×12:36x×12
=105+(105×3/2×2) :40×3:36×3
=105×4:40×3:36×3
=35×4:40:36
=35:10:9
B's share = total profit × 10/54
=21600×10/54=4000
Answer is D.
Answer: (D) 4000
Question: Each student at a certain business school is assigned a 5-digit student identification number. The first digit of the identification number cannot be zero, and the last digit of the identification number must be prime. How many different student identification numbers can the school create?
(A) 9,000
(B) 36,000
(C) 2,700
(D) 2,592
(E) 1,944
Rationale: The identification number is of the form _ _ _ _
1. First digit cannot be 0
2. Middle digits can be anything
3. Last digit has to be prime - 2, 3, 5, 7
We can have the following number of possibilities for each space
__ __ __ __
9 10 10 10 4
Total cases = 36000
Option C
Answer: (C) 2,700
Question: A person borrows Rs. 7000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 6 p.a for 2 years. Find his gain in the transaction per year.
(A) 100 rs
(B) 150 rs
(C) 140 rs
(D) 180 rs
(E) 200 rs
Rationale: Gain in 2 years =
[(7000*6*2)/100]-[(7000*4*2)/100]
840-560=280
Gain in 1 year =(280/2)=140 rs
ANSWER:C
Answer: (C) 140 rs
Question: If 13 = 13w/(1-w) ,then (6w)2 =
(A) 1/4
(B) 1/2
(C) 1
(D) 2
(E) 6
Rationale: 13-13w=13w
26w=13
w=1/2
6w=3
6w*2=3*2=6
ANSWER:E
Answer: (E) 6
Question: Over a three-week period, the price of an ounce of gold increased by 25% in the first week, decreased by 20% in the following week, and increased by 30% in the third week. If the price of gold was G dollars per ounce at the beginning of the three weeks, what was the price at the end of the three weeks?
(A) 1.1G
(B) 1.2G
(C) 1.3G
(D) 1.4G
(E) 1.5G
Rationale: After 3 weeks, the price was 1.3*0.8*1.25*G=1.3G
The answer is C.
Answer: (C) 1.3G
Question: 8th Dec 2007 was Saturday, what day of the week was it on 8th Dec, 2006?
(A) Sunday
(B) Tuesday
(C) Friday
(D) Tuesday
(E) Thursday
Rationale: Explanation:
Given that 8th Dec 2007 was Saturday
Number of days from 8th Dec, 2006 to 7th Dec 2007 = 365 days
365 days = 1 odd day
Hence 8th Dec 2006 was = (Saturday - 1 odd day) = Friday
Answer: Option C
Answer: (C) Friday
Question: The captain of a cricket team of 11 members is 27 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?
(A) 21
(B) 22
(C) 23
(D) 24
(E) 25
Rationale: Let the average age of the whole team be x years.
11x - (27 + 30) = 9 (x - 1)
11x - 9x = 48
2x = 48
x = 24.
The average age of the team is 24 years.
The answer is D.
Answer: (D) 24
Question: If the operation x is defined by a x b = (b - a)^2/a^2 for all numbers a and b, and a ≠ 0, then − 1 x (1 x − 1) =
(A) −1
(B) 0
(C) 1
(D) 25
(E) 29
Rationale: On solving the inner bracket we get 4.
then we get equation as -1 x 4 where b=4 and a=-1
Answer D
Answer: (D) 25
Question: A bus leaves the stop 30 minutes before the scheduled time. The driver decreases its speed by 30km/hr. At the next bus stop 180 km away, the bus reached on time. Find the original speed of the bus?
(A) 110 kms/hr
(B) 120 kms/hr
(C) 130 kms/hr
(D) 140 kms/hr
(E) None of above
Rationale: actual time = t180 = x*t180 = (x – 30)*(t +1/2)Solve both equation, we will get x = 120km/hr Answer : B
Answer: (B) 120 kms/hr
Question: The inverse ratio of 3: 2: 1 is?
(A) 1:2:3
(B) 2:3:1
(C) 3:1:2
(D) 2:3:6
(E) None of these
Rationale: Explanation:
1/3: 1/2: 1/1 = 2:3:6
Answer is D
Answer: (D) 2:3:6
Question: Look at this series: 4, 2, 1, (1/2), (1/4), ... What number should come next?
(A) 1/8
(B) 1/3
(C) 1/4
(D) 1/2
(E) 1/5
Rationale: A
Answer: (A) 1/8
Question: A cricketer has a certain average for 10 innings. In the eleventh inning, he scored 108 runs, there by increasing his average by 3 runs. His new average is:
(A) 60 runs
(B) 65 runs
(C) 70 runs
(D) 75 runs
(E) 78 runs
Rationale: Let average for 10 innings be x. Then,
(10x + 108)/11 = x + 3
= 11x + 33 = 10x + 108
= x = 75.
New average = (x + 3) = 78 runs.
Answer:E
Answer: (E) 78 runs
Question: A car is purchased on hire-purchase. The cash price is $21 000 and the terms are a deposit of 10% of the price, then the balance to be paid off over 60 equal monthly instalments. Interest is charged at 12% p.a. What is the monthly instalment?
(A) $503
(B) $504
(C) $505
(D) $506
(E) $507
Rationale: Explanation:
Cash price = $21 000
Deposit = 10% × $21 000 = $2100
Loan amount = $21000 − $2100
= $18900
I=p*r*t/100
I=11340
Total amount = 18900 + 11340 = $30240
Regular payment = total amount /number of payments
Answer: B
Answer: (B) $504
Question: Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 36 kmph and 72 kmph. After how much time will the trains meet?
(A) 10/3 sec
(B) 20/4 sec
(C) 20/7 sec
(D) 22/7 sec
(E) 60/7 sec
Rationale: They are moving in opposite directions, relative speed is equal to the sum of their speeds.
Relative speed = (36 + 72)*5/18 = 6*5 = 30 mps.
The time required = d/s = 100/30 = 10/3 sec.Answer:A
Answer: (A) 10/3 sec
Question: If 21/22 = 0.95.45, what is the 57th digit to the right of the decimal point of the fraction?
(A) 1
(B) 4
(C) 5
(D) 7
(E) 9
Rationale: we are not concerned what 21/22 means..
we have to look at the decimal..
0.9544 means 0.95454545....
so leaving first digit to the right of decimal, all ODD numbered digits are 4 and all EVEn numbered are 5..
here 57 is odd, so ans is 4
Answer is B
Answer: (B) 4
Question: 16 men can complete a piece of work in 28 days. In how many days can 20 men complete that piece of work?
(A) 55 days
(B) 77 days
(C) 22.4 days
(D) 88 days
(E) 44 days
Rationale: 16 * 28 = 20 * x => x
= 22.4 days
Answer: C
Answer: (C) 22.4 days
Question: John left a job paying $75,000 per year to accept a sales job paying $45,000 per year plus 15 percent commission. If each of his sales is for $750, what is the least number of sales he must make per year if he is not to lose money because of the change?
(A) 40
(B) 200
(C) 266
(D) 267
(E) 600
Rationale: In order not to lose money because of the change John's total commission must beat least$75,000-$45,000=$30,000, so total sales must beat least$30,000/0.15=$200,000. Which means that he must makeat least$200,000/750=800/3=266.6 sales, so 267 sales.
Answer: D.
Answer: (D) 267
Question: The diagonals of a rhombus are 14 cm and 20 cm. Find its area?
(A) 176
(B) 190
(C) 140
(D) 278
(E) 292
Rationale: 1/2 * 14 * 20
= 140
Answer:C
Answer: (C) 140
Question: The probability that a visitor at the mall buys a pack of candy is 30%. If three visitors come to the mall today, what is the probability Q that exactly two visitors will buy a pack of candy?
(A) 0.343
(B) 0.147
(C) 0.189
(D) 0.063
(E) 0.027
Rationale: 3C2 * (3/10)^2 * 7/10
= 3 * 9/100 * 7/10
= 189/1000
= 0.189=Q
Answer - C
Answer: (C) 0.189
Question: A train passes a station platform in 36 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) 150 m
(B) 240 m
(C) 589 m
(D) 600 m
(E) 200m
Rationale: Explanation:
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)/36 = 15 => x = 240 m.
Answer: B
Answer: (B) 240 m
Question: A dealer offers a cash discount of 20%. Further, a customer bargains and receives 20 articles for the price of 15 articles. The dealer still makes a profit of 20%. How much percent Q above the cost price were his articles marked?
(A) 100%
(B) 80%
(C) 75%
(D) 66+2/3%
(E) 50%
Rationale: Good question...2:11 min
Marked Price (M) = Cost Price (C) + Mark up...(EQN. A)
Selling price = 20% Discount over M = 0.8*M
Given that, a customer bargains and receives 20 articles for the price of 15 articles-->*afurther loss of 25%to the dealer--> BUT aNET PROFIT of 20%over cost price (C)
0.75* 0.8 * M =1.2 * C
Hence, M/C = 2/1 Q= 200%
From Eqn. A , (C + Mark up)/C = 200% -->Mark up / C = 100%
Ans. A
Answer: (A) 100%
Question: Three pipes A, B and C can fill a tank from empty to full in 20 minutes, 20 minutes and 30 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P, Q and R respectively. What is the proportion of solution R in the liquid in the tank after 3 minutes?
(A) 1/2
(B) 1/5
(C) 1/3
(D) 1/4
(E) 1/6
Rationale: Part filled by (A + B + C) in 3 minutes = 3(1/20 + 1/20 + 1/30) = 6/15
Part filled by C in 3 minutes = 3/30
Required ratio = 3/30 * 15/6 = 1/4
Answer:D
Answer: (D) 1/4
Question: Working simultaneously and independently at an identical constant rate, 4 machines of a certain type can produce a total of x units of product P in 6 days. How many of these machines, working simultaneously and independently at this constant rate, can produce a total of 3x units of product P in 6 days?
(A) 24
(B) 18
(C) 16
(D) 12
(E) 8
Rationale: 4 machines do x units in 6 days
we have x/6 => rate of the 4 machines
we know that we need to have 4x units in 6 days
therefore, we need to get to 4x/6 rate of the machines.
rate of one machine is x/6*1/4 = x/24.
now, we need to know how many machines need to work simultaneously, to get 3x done in 6 days.
3x/6 work needs to be done by machines that work at x/24 rate.
let's assign a constant Y for the number of machines:
(x/24)*y = 3x/6
y = 3x/6 * 24/x
cancel 6 with 24, and x with x and get -> 12. Answer choice D
Answer: (D) 12
Question: The probability that a number selected at random from the first 50 natural numbers is a composite number is?
(A) 17/65
(B) 17/25
(C) 17/28
(D) 17/65
(E) 17/39
Rationale: The number of exhaustive events = ⁵⁰C₁ = 50.
We have 15 primes from 1 to 50.
Number of favourable cases are 34.
Required probability
= 34/50
= 17/25.
Answer: B
Answer: (B) 17/25
Question: A man's speed with the current is 21 km/hr and the speed of the current is 2.5 km/hr. The man's speed against the current is?
(A) 10
(B) 20
(C) 16
(D) 30
(E) 40
Rationale: Man's speed with the current = 21 km/hr
=> speed of the man + speed of the current = 21 km/hr
speed of the current is 2.5 km/hr
Hence, speed of the man = 21 - 2.5 = 18.5 km/hr
man's speed against the current = speed of the man - speed of the current
= 18.5 - 2.5 = 16 km/hr
Answer is C.
Answer: (C) 16
Question: A man can row upstream at 25 kmph and downstream at 35 kmph, and then find the speed of the man in still water?
(A) 28
(B) 27
(C) 30
(D) 29
(E) 12
Rationale: US = 25
DS = 35
M = (35 + 25)/2 = 30
Answer: C
Answer: (C) 30
Question: After 6 games, team B had an average of 70 points per game. If it got only 47 points in game 7, how many more points does it need to score to get its total above 500?
(A) 85
(B) 74
(C) 67
(D) 33
(E) 28
Rationale: (6*70) + 47 +x >500
420+47+x > 500
467+x >500
=> x>33
Option D
Answer: (D) 33
Question: 18 balls are numbered 1 to 18. A ball is drawn and then another ball is drawn without replacement. What is the probability that both balls have even numbers?
(A) 2/9
(B) 4/17
(C) 6/29
(D) 8/35
(E) 10/43
Rationale: P(1st ball is even) = 9/18
P(2nd ball is also even) = 8/17
P(both balls are even) = 9/18 * 8/17 = 4/17
The answer is B.
Answer: (B) 4/17
Question: How many different 4 letter combinations can be created from the letters M,N,O, and P?
(A) 4
(B) 16
(C) 32
(D) 96
(E) 256
Rationale: This is a case of number of arrangements possible with repetition.
Thus you have 4 options each for the 1st,2nd,3rd and 4th letter giving you a total of 4*4*4*4 = 256 number of possible combinations.
Answer : E
Answer: (E) 256
Question: If an integer n is to be chosen at random from the integers 1 to 86, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 8?
(A) 1/4
(B) 3/8
(C) 1/2
(D) 55/86
(E) 3/4
Rationale: n(n+1)(n+2) will be divisible by 8 when n is a multiple of 2 or when (n+1) is a multiple of 8.
Thus when n is even, this whole expression will be divisible by 8.
from 1 to 86, there are 43 even integers.
Now when (n+1) is multiple by 8, we have 12 such values for (n+1)
probability that n(n+1)(n+2) will be divisible by 8
= (43 + 12)/96
=55/86
Ans isD
Answer: (D) 55/86
Question: A car gets 20 kilometers per gallon of gasoline. How many gallons of gasoline would the car need to travel 130 kilometers?
(A) 8.5 gallons
(B) 7.5 gallons
(C) 6.5 gallons
(D) 5.5 gallons
(E) 4.5 gallons
Rationale: Each 20 kilometers, 1 gallon is needed. We need to know how many 20 kilometers are there in 130 kilometers?
130 / 20 = 6.5 * 1 gallon = 6.5 gallons correct answer C
Answer: (C) 6.5 gallons
Question: When the positive integer j is divided by 9, the remainder is 5. What is the remainder when 3j is divided by 9?
(A) 0
(B) 1
(C) 3
(D) 4
(E) 6
Rationale: Lets take the number as j
when j is divided by 9 the remainder is 5 hence j can be written as
j=9k +5
Multiplying by 3 will give
3j = 27k + 15
we can also write
3j = 27k + 9 + 6
Now 27k and 9 are divisible by 9 leaving the remainder as 6 hence E is the answer.
Answer: (E) 6
Question: Out of 250 students of a college, 160 play football, 90 play cricket and 50 neither play football nor cricket. How many students play both football and cricket?
(A) 30
(B) 40
(C) 50
(D) 60
(E) 70
Rationale: Explanation :
Solution: n(A) = 160, n(B) = 90, n(A U B) = 250-50 = 200.
Required number => n(A ^ B) = n(A) +n(B) - n(A U B) = 160+90-200 = 250-200 = 50.
Answer : C
Answer: (C) 50
Question: The ratio of the cost price and the selling price is 4:5. The profit percent is:
(A) 67%
(B) 45%
(C) 25%
(D) 70%
(E) 50%
Rationale: C
C.P. = Rs. 4x. Then, S.P. = Rs. 5x
Gain = (5x - 4x) = Rs. x
Gain % = (x * 100)/ 4x = 25%.
Answer: (C) 25%
Question: Frederick invested Rs.14000 in a business which he jointly owns with two other persons (James and Greg). If his share of a profit of Rs.1500 is Rs.600 and Greg's share is Rs.300, what is James' capital?
(A) 15500
(B) 12500
(C) 1270
(D) 12505
(E) 12540
Rationale: 600 + 300 = 900
1400 - 900 = 500
600 ---- 15000
500 ---- ? => 12500
ANSWER:B
Answer: (B) 12500
Question: The probability that A speaks truth is 2/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact?
(A) 17/35
(B) 18/37
(C) 18/39
(D) 18/33
(E) 18/31
Rationale: If both agree stating the same fact, either both of them speak truth of both speak false.
Probability = 2/5 * 4/7 + 3/5 * 3/7
= 17/35
Answer:A
Answer: (A) 17/35
Question: The sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131. Their sum is:
(A) 20
(B) 98
(C) 37
(D) 26
(E) 17
Rationale: Explanation:
Let the numbers be a, b and C. Then,
a2 + b2 + c2 = 138 and (ab + bc + ca) = 131
(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)
138 + 2 * 131 = 400
(a + b + c) = âˆš400 = 20
Answer:A
Answer: (A) 20
Question: Pipe A can fill a tank in 2 hours. Due to a leak at the bottom, it takes 4 hours for the pipe A to fill the tank. In what time can the leak alone empty the full tank?
(A) 2
(B) 5
(C) 6
(D) 4
(E) 1
Rationale: Let the leak can empty the full tank in x hours 1/2 - 1/x = 1/4
=> 1/x = 1/2 - 1/4 = 1/4
=> x = 4. Answer:D
Answer: (D) 4
Question: Two cars are traveling towards each other. If car A is traveling at a speed of 50 mph and car B is traveling 15% slower, how much time will it take the cars to meet if the initial distance between the two is 705 miles?
(A) Six hours and 30 minutes.
(B) Seven hours and 30 minutes.
(C) Eight hours and 20 minutes.
(D) Nine hours and 15 minutes.
(E) Ten hours and 20 minutes.
Rationale: Speed of second train= 50*85/100= 42.5
Time= toral distance /total speed
705/ (50+42.5)= 705/92.5= 7.___
B is the answer
Answer: (B) Seven hours and 30 minutes.
Question: If (A+B) = 4, (B+C) = 9 and (C+D) = 3, what is the value of (A+D)?
(A) 16.
(B) 8.
(C) 7
(D) 2.
(E) -2
Rationale: Given A+B = 4 => A = 4 - B --> Eq 1
B+C = 9
C+D = 3 => D = 3 - C --> Eq 2
Then Eqs 1 + 2 => A + D = 4 - B + 3 - C
=> 7 - (B+C)
=> 7 - 9 = -2.
Option E...
Answer: (E) -2
Question: An eccentric casino owner decides that his casino should only use chips in $3 and $7 denominations. Which of the following amount cannot be paid out using these chips?
(A) $27
(B) $24
(C) $23
(D) $25
(E) $21
Rationale: Yes, the number of 3 or/and 7 dollar chips can be zero, however both being zero mean that the casino is paying out $0, which is not realistic.
Each option but D can be represented as the sum of a multiple of 3 and a multiple of 7:
A. $27 = 7*3 + 3*2
B. $23 = 7*2 + 3*3
C. $24 = 7*3 + 3*1
E. $21 = 7*3
Answer: D.
Answer: (D) $25
Question: If 5^27 * 4^14 = 2 * 10^n, what is the value of n?
(A) 11
(B) 21
(C) 22
(D) 23
(E) 27
Rationale: My attempt:
5^(27) * 4^(14) = 2*10^p
5^(27) * 2 ^ (28) = 2 * (2*5)^p
5^(27) * 2 ^ (28) = 2 * 2^(p) * 5^(p)
5^(27) * 2 ^ (28) = 2^(p+1) * 5^(p)
=> (p+1) = 28
=> p = 27
Answer: 27 (E)
Answer: (E) 27
Question: If y is the smallest positive integer such that 31,360 multiplied by y is the square of an integer, then y must be
(A) 21
(B) 10
(C) 61
(D) 72
(E) 14
Rationale: 31360= 8*8*7*7*5*2, so we need one 5 and one 2 to make it a square of a number. so 5*2= 10
Ans: B
Answer: (B) 10
Question: One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 34 minutes, then the slower pipe alone will be able to fill the tank in
(A) 144 mins
(B) 140 mins
(C) 136 mins
(D) 132 minw
(E) None of these
Rationale: Explanation:
Let the slower pipe alone fill the tank in x minutes
then faster will fill in x/3 minutes.
Part filled by slower pipe in 1 minute = 1/x
Part filled by faster pipe in 1 minute = 3/x
Part filled by both in 1 minute =
1/x+3/x=1/34
=>4/x=1/34
x=34∗4=136mins
Option C
Answer: (C) 136 mins
Question: The average height of 35 boys in a class was calculated as 181cm. It has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm. Find the actual average height of the boys in the class (Round off your answer to two decimal places).?
(A) 178.27 cm
(B) 179.29 cm
(C) 978.29 cm
(D) 178.89 cm
(E) 176.29 cm
Rationale: Calculated average height of 35 boys = 181 cm.
Wrong total height of 35 boys = 181 * 35 cm. This was as a result of an actual height of 106 cm being wrongly written as 166 cm. Correct total height of 35 boys = 181 cm - (166 cm - 106 cm)/35
= 181 cm - 60 /35 cm
= 181 cm - 1.71 cm = 179.29 cm.
Answer: B
Answer: (B) 179.29 cm
Question: At 6'o clock clock ticks 6 times. The time between first and
last ticks was 30sec. How much time it takes at 7'o clock.
(A) 36sec
(B) 62sec
(C) 66sec
(D) 64sec
(E) 76sec
Rationale: At 6'0 clock, clock ticks 6 times.
So, there must be 5 intervals between clock ticks.
Time Between first and last ticks = 30sec
So, 1 interval = 30/5 = 6sec
So 6'o clock 5 *6=30sec
7'o clock 6 *6=36sec
So, 36sec at 7'o clock.
ANSWER:A
Answer: (A) 36sec
Question: The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %?
(A) 8
(B) 18
(C) 15
(D) 20
(E) 25
Rationale: 1500 ---- 270
100 ---- ? => 18%
ANSWER B
Answer: (B) 18
Question: If x -5 > -3 and x - 3 < 4, the value of x must be between which of the following pairs of numbers?
(A)  -3 and 10
(B)  -3 and 4
(C)  2 and 7
(D)  3 and 4
(E)  3 and 10
Rationale: Let’s isolate x in each inequality.
x - 5 >-3
x > 2
Next we simplify x – 3 < 4.
x – 3 < 4
x < 7
We know that x is greater than 2 and less than 7.
The answer is C.
Answer: (C)  2 and 7
Question: In X game of billiards, X can give Y 20 points in 45 and he can give Z 30 points in 45. How many points can Y give Z in X game of 100?
(A) 30
(B) 20
(C) 25
(D) 40
(E) 50
Rationale: X scores 45 while Y score 40 and Z scores 30.
The number of points that Z scores when Y scores 100 = (100 * 30)/25 = 60.
In X game of 100 points, Y gives (100 - 60) = 40 points to C.
D
Answer: (D) 40
Question: A tap can fill a tank in 10 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?
(A) 5hr 45min
(B) 6hr 30min
(C) 4hr
(D) 3hr 25min
(E) 2hr 10min
Rationale: Time taken by one tap to fill the half tank = 5 hr
part filled by the 4 taps in 1hour = 4*1/6 = 2/3
Remaining part = 1-1/2 = 1/2
2/3:1/2::1:x
x = 3/4hr = 45min
Total time taken = 5hr 45min
Answer is A
Answer: (A) 5hr 45min
Question: How many different number-plates for cars can be made if each number-plate contains four of the digits 0 to 9 followed by a letter A to Z, assuming that repetition of digits is allowed?
(A) 2.6 * 10^4
(B) 2.6 * 10^5
(C) 26 * 10^5
(D) 26 * 10^4
(E) 30 * 10^4
Rationale: With repetition, we have simply:
(number of digits from 0000 to 9999)times×26 = 10 * 10 * 10 * 10 * 26
= 10^4 * 26
= 2.6 * 10^5
Ans- B
Answer: (B) 2.6 * 10^5
Question: If 216 is divided into four parts proportional to 5, 7, 4, 8 then the smallest part is :
(A) 36
(B) 14
(C) 20
(D) 18
(E) 22
Rationale: Given ratio = 5 : 7 : 4 : 8 , sum of ratio = 24
:. The smallest part = (216 *4/24) = 36
ANSWER:A
Answer: (A) 36