mathewhe/aqua_rat huggingface dataset:
Question: David walks to a viewpoint and returns to the starting point by his car and thus takes a total time of 2 hours . He would have gained 1 hour by driving both ways. How long would it have taken for him to walk both ways.
(A) 3 h
(B) 3 h 15 min
(C) 4 h
(D) 5 h
(E) 6 h
Rationale: 1.Walking to to a viewpoint+Driving back=2 hours
2.Driving to a viewpoint+Driving back=2 hours - 1 hour=1 hour,
thereforeone way driving=1 hour/2 = 30 minutes.
3. From 1.one way driving=2 hours-30 minutes=1 hour 30 minutes.
4.Walking to to a viewpoint+Walking back=1 hours 30 minutes+1 hours 30 minutes=3 hours
Answer: A
Answer: (A) 3 h
Question: 8.5 × 6.4 + 4.5 × 11.6 = ? ÷ 4
(A) 426.2
(B) 426.4
(C) 106.6
(D) 422.4
(E) 522.5
Rationale: Explanation:
(54.4+52.2) × 4 = 426.4
Answer: Option B
Answer: (B) 426.4
Question: In the xy-plane, line w passes through point (3,-2) and intersect perpendicularly with line n that passes through points (0,3) and (3,5). What is the equation of line w?
(A) 3x+2y-5=0
(B) 3x+2y+5=0
(C) 2x-3y-12=0
(D) 2x+3y=0
(E) 4x+3y-6=0
Rationale: If two lines intersect perpendicularly, we get -1 when we multiply two slopes together. The slope of a line n is (5-3)/(3-0)=2/3. Hence, the slope of a line w should be -3/2. Since it crosses (3,-2), if we calculate we get 3x+2y=5. Hence, the correct answer is A.
Answer: (A) 3x+2y-5=0
Question: A drawer holds 5 red hats and 5 blue hats. What is the probability of getting exactly three red hats or exactly three blue hats when taking out 4 hats randomly out of the drawer and returning each hat before taking out the next one?
(A) 1/8
(B) 1/4
(C) 1/2
(D) 3/8
(E) 7/12
Rationale: Let's find the probability of getting exactly 3 red hats.
One possible case is red-red-red-blue.
The probability of this is 1/2*1/2*1/2*1/2 = 1/16
There are 4C3 = 4 such cases so we need to multiply this by 4.
P(exactly 3 red hats) = 4*1/16 = 1/4
Clearly the probability of getting exactly 3 blue hats will also be 1/4.
The sum of the probabilities is 1/4+1/4 = 1/2
The answer is C.
Answer: (C) 1/2
Question: Kelvin earns $60 a week from his job. His income increased and now makes $70 a week. What is the percent increase?
(A) 16.66%
(B) 18%
(C) 18.2%
(D) 19.3%
(E) 20%
Rationale: Increase = (10/60)*100 = (1/6)*100 = 16.66%.
A
Answer: (A) 16.66%
Question: A bank offers 3% compound interest calculated on quarter-yearly basis. A customer deposits $ 15000 each in 1st month. At the end of the year, the amount he would have gained by way of interest is?
(A) 200
(B) 150
(C) 455
(D) 300
(E) 600
Rationale: Amount = (15000)* (1 + (3/4*100))^4
Amount = 15000 * (1+ 0.0075)^4 = 15455 ------(for investment in 1st month)
Interest = 15455-15000 = 455..............
Ans -C
Answer: (C) 455
Question: Seven years ago the average age of a family of 2 members was 21 years. A child has been born. due to Which the average age of the family is 23 years today. What is the present age of the child?
(A) 10years
(B) 13years
(C) 15years
(D) 17years
(E) 20years
Rationale: Explanation:
Average of the family of two numbers
7 years ago = 21
= (21+ 7) * 2 = 56 years
Average age of the family of three members at present = 23 years
= 23 * 3 = 69 YEARS
Age of child = 69 - 56 = 13 years
Answer: Option B
Answer: (B) 13years
Question: By selling 100 pencil, a trader gains the cost of 33 Pencil. Find his gain percentage?
(A) 26 1/3%
(B) 51 1/3%
(C) 33 %
(D) 53 1/3%
(E) 34 1/3%
Rationale: C
33 %
Let the CP of each pencil be Rs. 1.
CP of 100 pens = Rs. 100
Profit = Cost of 33 pencil = Rs. 33
Profit% = 33/100 * 100 = 33 %
Answer: (C) 33 %
Question: If a quarter kg of onions costs 40 paise, how many paise will 100 gm cost?
(A) 32 paise
(B) 65 paise
(C) 56 paise
(D) 87 paise
(E) 16 paise
Rationale: Explanation:
Let the required cost be x paise.
Less weight, Less cost (Direct proportion)
250 : 100 : : 40 : x
250 * x = (100 * 40)
x = (100 * 40) / 250
x = 16
ANSWER: E
Answer: (E) 16 paise
Question: A 600 meter long train crosses a signal post in 40 seconds. How long will it take to cross a 3 kilometer long bridge, at the same speed?
(A) 4 min
(B) 5 min
(C) 6 min
(D) 8 min
(E) 10 min
Rationale: S = 600/40 = 15 mps
S = 3600/15 = 240 sec = 4 min
ANSWER A
Answer: (A) 4 min
Question: In a simultaneous throw of a pair of dice, find the probability of getting a total more than 10
(A) 5/13
(B) 2/15
(C) 1/12
(D) 3/17
(E) 6/19
Rationale: Total number of cases = 6*6 = 36
Favourable cases = [(5,6)(6,5),(6,6)] = 3
So Probability = 3/36 = 1/12
Answer is C
Answer: (C) 1/12
Question: The speeds of three motor bikes are in the ratio 24 : 4 : 6. The ratio between the time taken by them to travel the same distance is :
(A) 1 : 4 : 4
(B) 1 : 6 : 3
(C) 1 : 6 : 5
(D) 1 : 6 : 4
(E) 1 : 5 : 4
Rationale: Ratio of time taken :
1/24 :1/4 : 1/6 = 1 : 6 : 4
ANSWER:D
Answer: (D) 1 : 6 : 4
Question: Set Q consists of the following five numbers: Q = {5, 8, 13, 21, 34, 42}. Which of the following sets has the same standard deviation as Set Q?
I. {35, 38, 43, 51, 64}
II. {10, 16, 26, 42, 68}
III. {46, 59, 67, 72, 75}
(A)  I only
(B)  III
(C)  IIII
(D)  IIIII
(E)  I, II,III
Rationale: (1)	Multiplying all the numbers change Standard Deviation
(2)	Adding and subtracting all the numbers with the same number keeps the standard deviation same.
If you observe Set I and III are added versions of Set Q .
Set I: 5 has been added to the Set Q
Set III: Subtract each element from 80 and you would find a number there in the Set Q.
Set II: elements are multiplied by 2 and standard deviation changes.
Hence the answer is E.
Answer: (E)  I, II,III
Question: Jamboree and GMAT Club Contest Starts
QUESTION #10:
How many words (with or without meaning)Q can be formed using all the letters of the word “SELFIE” so that the two E’s are not together?
(A)  660
(B)  600
(C)  500
(D)  300
(E)  240
Rationale: In general, repetitions are taken care of by dividing the permutation by the factorial of the number of objects that are identical. in this case,Q if you think logically, A,B,C,D options are not divisible by 6!. 6 is total number of letters in the word SELFIE. Only option E is divisible by 6!. So correct answer is E that is 240
Answer: (E)  240
Question: The perimeters of two squares are 48 cm and 32 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares?
(A) 76 cm
(B) 35.6 cm
(C) 88 cm
(D) 55 cm
(E) 34 cm
Rationale: We know perimeter of square = 4(side)
So Side of first square = 48/4 = 12 cm
Side of second square = 32/4 = 8 cm
Area of third Square = 12*12 - 8*8
= 80 cm
So side of third square = 8.9 [because area of square = side*side]
Perimeter = 4*Side = 4*8.9 = 35.6 cm
Answer:B
Answer: (B) 35.6 cm
Question: All but one of the following statements are definitely true, identify the false statement, given that V is the brother of W and X. Y is V's son and Z is W's son?
(A) V is Z's uncle
(B) W is Y's uncle
(C) X is Y's uncle
(D) X is Y's brother
(E) Y is Z's nephew
Rationale: Explanation:
All the statements are true except D (X is Y's brother), Y is V's son that makes X his uncle, not brother.
Answer: D)
Answer: (D) X is Y's brother
Question: A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 650 m long?
(A) 22
(B) 89
(C) 277
(D) 278
(E) 291
Rationale: Speed = 240/24 = 10 m/sec.
Required time = (240 + 650)/10 = 89 sec.
Answer: B
Answer: (B) 89
Question: The angle between the minute hand and the hour hand of a clock when the time is 4.20, is:
(A) 10 d
(B) 0 d
(C) 15 d
(D) 5 d
(E) 20 d
Rationale: Angle traced hr 13/3 = (360/12 * 13/3) = 130
traced by min hand 20 min = (360/60*20) = 120
req = (130-120) = 10 d
ANSWER A
Answer: (A) 10 d
Question: An auto assembly plant performs six functions with each frame that arrives: add axles, add wheels to the axles, install the windshield to the frame, install the instrument panel, install the steering wheel, and install the interior seating. Once those six tasks are performed, each car goes to a separate building for finishing touches. If these tasks can be arranged along a linear assembly line in any order, except that the axles must be installed before the wheels can be added, how many E ways can the assembly line be arranged?
(A) 120
(B) 240
(C) 360
(D) 480
(E) 720
Rationale: C) 360
short way: there are 6C! ways to do the six tasks. Half will have wheels before axles and half will have axles before wheels. So we want E=6C!/2 -> 720/2 = 360
Answer: (C) 360
Question: The length of the bridge, which a train 130 metres long and travelling at 45 km / hr can cross in 30 seconds, is
(A) 200 m
(B) 225 m
(C) 245 m
(D) 250 m
(E) None
Rationale: Sol.
Speed = [45x5/18] m/sec = (25/2)m/sec; Time = 30 sec.
Let the length of bridge be x metres.
Then, 130 + x / 30 = 25 / 2
⇔ 2(130 + x) = 750
⇔ x = 245 m.
Answer C
Answer: (C) 245 m
Question: If d > x > y > z on the number line, y is halfway between x and z, and x is halfway between w and z, then (y - x)/(y - d) =
(A) 1/4
(B) 1/3
(C) 1/2
(D) 3/4
(E) 1
Rationale: Let y-z=t ---> since y is halfway between x and z and x>y we have x-y=t. Moreover x-z=(x-y)+(y-z)=2t. Similarly since x is halfway between w and z, we have d-x=2t. So y-x=-t, y-d=-3t. ---> (y - x)/(y - d) = 1/3.
The answer is (B).
Answer: (B) 1/3
Question: If 16% of 40% of a number is 7, then the number is
(A) 200
(B) 225
(C) 109.375
(D) 320
(E) None of these
Rationale: Explanation:
Let 16/100×40/100×a=7
a = 7×100×100/16×40=109.375
Correct Option: C
Answer: (C) 109.375
Question: In how many ways can a group of 3 men and 3 women be made out of a total of 7 men and 4 women?
(A) 163
(B) 167
(C) 130
(D) 174
(E) 180
Rationale: We need to select 3 men from 7 men and 3 women from 4 women. Number of ways to do this= 7C3 × 4C3130C)
Answer: (C) 130
Question: Integers 3n+2 and 8n+6 are divisible by an integer p. If p is not equal to 1, then p equals to?
(A) 2
(B) 3
(C) 5
(D) 7
(E) 11
Rationale: If p divides 3n+2, then p divides 24n+16.
If p divides 8n+6, then p divides 24n+18.
Then p must equal 2.
The answer is A.
Answer: (A) 2
Question: The units digit of (10)^(87) + (93)^(46) is:
(A) 9
(B) 4
(C) 6
(D) 8
(E) 0
Rationale: first part will be zero always
2nd part with power of three
Therefore, the second term has a units digit of 9.
Of course 0 + 9 = 9,
A
Answer: (A) 9
Question: one man can do a piece of work in 10days. one boys join him & he complete the work in 6days . if he gets 50rs for his work then what will be the share of the boy.
(A) 10
(B) 20
(C) 30
(D) 40
(E) 50
Rationale: 1 day work of Man=1/10, If Boy's 1 day work=1/x, then
(1/10)+(1/x)=1/6, x=15
Ratio of work of Man & Boy=1/10:1/15=3:2
So out of 50 Rs. Boy's share=2*50/(3+2)=20
ANSWER:B
Answer: (B) 20
Question: The perimeter of a triangle is 44 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?
(A) 87 cm2
(B) 28 cm2
(C) 98 cm2
(D) 26 cm2
(E) 55 cm2
Rationale: Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle
= 2.5 * 44/2
= 55 cm2
Answer:E
Answer: (E) 55 cm2
Question: A man can hit a target once in 8 shots. If he fires 4 shots in succession, how many ways that he will hit his target?
(A) 71/23
(B) 81/13
(C) 81/29
(D) 17/29
(E) 91/32
Rationale: The man will hit the target if he hits it once or twice or thrice or all four times in the four shots that he takes.
So, the only possibility when the man will not hit the target is when he fails to hit the target in even one of the four shots that he takes.
The event of not hitting the target even once is the complement of the event of hitting the target at least once.
The probability that he will not hit the target in any given shot = 1 - 1/8= 7/8
Therefore, the probability that he will not hit the target in any of the four shots = 7/8 ^4 = 17/29
D
Answer: (D) 17/29
Question: How many zeroes are there at the end of the number N, if N = 150! + 300! ?
(A) 28
(B) 31
(C) 34
(D) 37
(E) 40
Rationale: The number of zeroes at the end of 150! will be less than the number of zeroes at the end of 300!
Hence it is sufficient to calculate the number of zeroes at the end of 150!
The number of zeroes = [150/5] + [150/25] + [150/125] = 30 + 6 + 1 = 37
The answer is D.
Answer: (D) 37
Question: The average of 10 numbers is calculated as 14. It is discovered later on that while calculating the average, one number namely 36 was wrongly read as 26. The correct average is?
(A) A)16
(B) B)15
(C) C)19
(D) D)22
(E) E)24
Rationale: Explanation:
10 * 14 + 36 – 26 = 150=>150/10 = 15
B)
Answer: (B) B)15
Question: 9 children can complete a piece of work in 360 days; 18 men can complete the same piece of work in 72 days and 12 women can complete it in 162 days. In how many days can 4 men, 12 women and 10 children together complete the piece of work?
(A) 68 days
(B) 81 days
(C) 96 days
(D) 124 days
(E) 126 days
Rationale: Explanation:
1 child’s 1 day’s work = 1/360 ×9 = 1/3240
10 children’s 1 day’s work = 1/324
1 man’s 1 day’s work = 1/72 × 18 = 1/1296
4 men’s 1 day’s work = 1 ×4/1296 = 1/324
12 women’s 1 day’s work = 1/162 given
Then, (4 men + 12 women + 10 children)’s 1 day’s work = 1/324 + 1/162 + 1/324
= 1/324 + 2/324 + 1/324 = 4/324 = 1/81
Therefore, the required No. of days = 81 days.
Answer: Option B
Answer: (B) 81 days
Question: Praveen starts business with Rs.3360 and after 5 months, Hari joins with Praveen as his partner. After a year, the profit is divided in the ratio 2 : 3. What is Hari’s contribution in the capital?
(A) s.7500
(B) s.8640
(C) s.8500
(D) s.9000
(E) s.6000
Rationale: Let Hari’s capital be Rs. x. Then, 3360 * 12/7x = 2/3
=> 14x = 120960
=> x = 8640.
ANSWER:B
Answer: (B) s.8640
Question: The difference between the value of a number increased by 12.5% and the value of the original number decreased by 25% is 30. What is the original number R?
(A) 60
(B) 80
(C) 40
(D) 120
(E) 160
Rationale: (1 + 1/8)x - (1 - 1/4)x = 30
(9/8)x - (3/4)x = 30
x = 80=R
Answer: B
Answer: (B) 80
Question: The banker's discount on Rs.1350 due a certain time hence is Rs.135. Find the true discount and the banker's gain.
(A) 12
(B) 15
(C) 18
(D) 21
(E) None
Rationale: Solution
Sum	=B.D x T.D/ B.D - T.D
= B.D x T.D/ B.G
T.D / B. G	=Sum / B.D
= 1350 / 135
= 10 / 1
If B.D is Rs. 11,T.D= Rs.10.
If B.D is Rs.135,
T.D	= Rs.(10 / 11 x 135)
= Rs.123.
And, B.G	= Rs(135 - 123)
= Rs.12.
Answer A
Answer: (A) 12
Question: An athlete runs 360 metres race in 24 seconds. What is his speed?
(A) 23
(B) 64.8
(C) 37
(D) 30
(E) 28
Rationale: Speed=Distance/Time = 360/20 = 18 m/s = 18 * 18/5 = 64.8 km/hr
Answer :B
Answer: (B) 64.8
Question: Excluding stoppages, the speed of a bus is 80 kmph and including stoppages, it is 60 kmph. For how many minutes does the bus stop per hour?
(A) 12 min
(B) 20 min
(C) 25 min
(D) 30 min
(E) 15 min
Rationale: Due to stoppages, it covers 20 km less.
Time taken to cover 20 km = (20/80 x 60) min = 15 min
Answer : E
Answer: (E) 15 min
Question: Find a sum for first 7 prime no's from number series?
(A) 24
(B) 56
(C) 30
(D) 34
(E) 36
Rationale: Required sum = (2 + 3 + 5 + 7 + 11+13+17) = 56
Note: 1 is not a prime number
Option B
Answer: (B) 56
Question: A number when divided by 342 gives a remainder 47. When the same number ift divided by 19, what would be the remainder ?
(A) 8
(B) 5
(C) 9
(D) 6
(E) 16
Rationale: On dividing the given number by 342, let k be the quotient and 47 as remainder.
Then, number – 342k + 47 = (19 x 18k + 19 x 2 + 9) = 19 (18k + 2) + 9.
The given number when divided by 19, gives (18k + 2) as quotient and 9 as remainder
Answer C
Answer: (C) 9
Question: Which of the following must be true =>
A) The Average of N Consecutive integers is an integer for N being Even
B) The Average of N Consecutive integers is an integer for N being Odd
C) The product N(N+1)(N+2) for integer N must be divisible by both 3 and 6
D) 2N+1 is always Odd irrespective of N.
(A) B,C,D
(B) A,C,D
(C) B,C
(D) Only D
(E) All of them
Rationale: A) The Average of N Consecutive integers is an integer for N being Even. False. For consecutive integers when number of integers is even, average= middle two terms/2= O+E/2 (can not be an integer)
B) The Average of N Consecutive integers is an integer for N being Odd. The middle term will be the average, and this term is odd integer.
C) The product N(N+1)(N+2) for integer N must be divisible by both 3 and 6. Either the product will be 0 or will have multiple of both 2 and 3 and 6. True.
D) 2N+1 is always Odd irrespective of N. What if =1/2, then 2N+1= 2
only B and C are true.
ANSWER:C
Answer: (C) B,C
Question: area of square = sum of areas of rect1(41*27) and rect2(41*14). find square side
(A) 93
(B) 40
(C) 41
(D) 42
(E) 58
Rationale: area of square=1107+574
area of square=1681
side of the square=sqrt(1681)=41
ANSWER:C
Answer: (C) 41
Question: If $x is invested at a constant annually compound interest rate of k percent, what is the ratio of the total amount including interest after 5n years to that after 3n years?
(A) (1+k/100)^2n
(B) (1+k)^n
(C) (1+kn/100)
(D) (1+n/100)^k
(E) (1+kn)
Rationale: Amount after 3n years will be = x ( 1 + k/100)^5n
Amount after 3n years will be = x ( 1 + k/100)^3n
So, required ratio will be -
{ x ( 1 + k/100)^5n } / {x ( 1 + k/100)^3n } = (1+k/100)^n
Hence answer will be a. (1+k/100)^2n
A
Answer: (A) (1+k/100)^2n
Question: Last year Elaine spent 10% of her annual earnings on rent. This year she earned 15% more than last year and she spent 30% of her annual earnings on rent. The amount she spent on rent this year is what percent of the amount spent on rent last year?
(A)  252.5
(B)  364.5
(C)  367.5
(D)  375
(E)  345
Rationale: For this it is easiest to use simple numbers. Let's assume that Elaine's annual earnings last year were $100.
She would've spent $10 of this on rent.
This year she earned 15% more, or $115.
She would've spent 30% of this on rent, or $34.5
Do $34.5/$10
This will give you 345%
E is the correct answer.
Answer: (E)  345
Question: x, y, a, and b are positive integers. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 14. Which of the following is NOT a possible value for y + b?
(A) 24
(B) 21
(C) 20
(D) 17
(E) 15
Rationale: Important note: remainder is ALWAYS less than divisor, thus y>6 and b>14 --> y+b>20.
Answer: C.
Answer: (C) 20
Question: Machine A can make 350 widgets in 1 hour, and machine B can make 250 widgets in 1 hour. If both machines work together, how much time will it take them to make a total of 2000 widgets?
(A) 3 hour and 20 minutes
(B) 3 hour and 24 minutes
(C) 3 hour and 30 minutes
(D) 3 hour and 36 minutes
(E) 3 hour and 40 minutes
Rationale: (350+250)t=2000
600t=2000
t=10/3
t=3 hour and 20 minutes
Answer: A
Answer: (A) 3 hour and 20 minutes
Question: A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is :
(A) 700
(B) 690
(C) 650
(D) 698
(E) 728
Rationale: Explanation :
Simple Interest (SI) for 1 year = 854-815 = 39
Simple Interest (SI) for 3 years = 39 × 3 = 117
Principal = 815 - 117 = Rs.698
Answer : Option D
Answer: (D) 698
Question: A cycle is bought for Rs.900 and sold for Rs.1080, find the gain percent?
(A) 32
(B) 20
(C) 287
(D) 277
(E) 291
Rationale: 900 ---- 180
100 ---- ? => 20
Answer: B
Answer: (B) 20
Question: Find the value of 1/(3+1/(3+1/(3-1/3)))?
(A) 13/89
(B) 15/87
(C) 27/89
(D) 27/87
(E) 89/27
Rationale: 1/[3 + (1/(3+1/(3 - 1/3)))]
=> 1/[3 + 1/(3 + 1/(8/3))]
=> 1/[3 + 1/(3 + 3/8)]
=> 1/[3 + 8/27]
=> 1/(89/27)
=> 27/89
C)
Answer: (C) 27/89
Question: If the average (arithmetic mean) of 5 positive temperatures is p degrees Fahrenheit, then the sum of the 3 greatest of these temperatures, in degrees Fahrenheit, could be:
(A) 6p
(B) 4p
(C) 5p/3
(D) 3p/2
(E) 3p/5
Rationale: The sum of three greatest should be more than sum of two lowest.
The total sum is; 5p
A. 6p; 6p is more than 5p. Not possible.
B. 4p; 5p-4p=p(Possible)
C. 5p/3; 10p/3; 10p/3 > 5p/3. Not possible
D. 3p/2; 7p/2; 7p/2 > 3p/2. Not possible
E. 3p/5; 22p/5; 22p/5 > 3p/5. Not possible.
Ans:B
Answer: (B) 4p
Question: Each participant in a certain study was assigned a sequence of 3 different letters from the set {A, B, C, D, E, F, G, H}. If no sequence was assigned to more than one participant and if 36 of the possible sequences were not assigned, what was the number of participants in the study? (Note, for example, that the sequence A, B, C is different from the sequence C, B, A.)
(A) 20
(B) 92
(C) 300
(D) 372
(E) 476
Rationale: # of letters = 8, # of ways to choose 3 letters out of 8 when order matters is P38=8!/(8−3)!=336 which means that there can be 336 different sequences. As 36 sequences were not assigned then 336-36=300 sequences were assigned, so there are 300 participants.
ANSWER:C
Answer: (C) 300
Question: A piece of equipment cost a certain factory Rs 600,000. If it depreciates in value, 15% the first year, 13.5 % the next year, 12% the third year, and so on, what will be its value at the end of 10 years, all percentages applying to the original cost?
(A) Rs2,00,000
(B) Rs1,05,000
(C) Rs4,05,000
(D) Rs 6,50,000
(E) None
Rationale: Explanatory Answer
Let the cost of an equipment is Rs. 100.
Now the percentages of depreciation at the end of 1st, 2nd, 3rd years are 15, 13.5, 12, which are in A.P., with a = 15 and d = - 1.5.
Hence, percentage of depreciation in the tenth year = a + (10-1) d = 15 + 9 (-1.5) = 1.5
Also total value depreciated in 10 years = 15 + 13.5 + 12 + ... + 1.5 = 82.5
Hence, the value of equipment at the end of 10 years=100 - 82.5 = 17.5.
The total cost being Rs. 6,00,000/100 * 17.5 = Rs. 1,05,000.
Answer B
Answer: (B) Rs1,05,000
Question: A persons salary iis decreased by steps of 20%, 15% and 10%. What will be the percentage decrease, if the salary is decreased in a single shot?
(A) 34.8%
(B) 36.8%
(C) 38.8%
(D) 39.8%
(E) 32.8%
Rationale: Let x is his initial salary.
After 1st decrease, x1 = x- (x*20/100) = x - x/5 = 4x/5
After 2nd decrease, x2 = 4x/5 - ((4x/5)*15/100) = 4x/5 - 3x/25 = 17x/25
After 3rd decrease, x3 = 17x/25 -((17x/25)*10/100) = 17x/25 - 17x/250 = 153x/250
So if its decreased in single shot, x - y(decreased) = 153x/250
=> y = x - 153x/250 => y = 97x/250 => y = 0.388x => y = 38.8%
ANSWER:C
Answer: (C) 38.8%
Question: Aman started a business investing Rs. 70,000. Rakhi joined him after six months with an amount of Rs. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business ?
(A) 2:3:9
(B) 24:25:36
(C) 7:6:10
(D) 12 : 15 : 16
(E) None of these
Rationale: Explanation:
Aman : Rakhi : Sagar =(70000Ã—36)=(70000Ã—36) :(105000Ã—30):(105000Ã—30) :(140000Ã—24):(140000Ã—24)
=12:15:16=12:15:16.
ANSWER IS D
Answer: (D) 12 : 15 : 16
Question: 35 binders can bind 1400 books in 21 days. How many binders will be required to bind 1600 books in 20 days?
(A) 87
(B) 18
(C) 42
(D) 16
(E) 10
Rationale: Binders Books Days
35 1400 21
x 1600 20
x/35 = (1600/1400) * (21/20) => x = 42
Answer:C
Answer: (C) 42
Question: Which of the following numbers has the greatest number of distinct prime factors?
(A) 165
(B) 192
(C) 228
(D) 330
(E) 332
Rationale: 165=3*5*11
192=2^6 *3
228=2^2 *3*19
330=2*3*5*11
332=2^2 * 83
330 has 4 distinct prime factors
Answer D
Answer: (D) 330
Question: Find the area of a rhombus whose side is 25 cm and one of the diagonals is 30 cm?
(A) 766 sq.cm
(B) 165 sq.cm
(C) 186 sq.cm
(D) 168 sq.cm
(E) 600 sq.cm
Rationale: Consider the rhombus ABCD. Let the diagonals intersect at E. Since diagonals bisect at right angles in a rhombus.
BE2 + AE2 = AB2
252 = 152 + AE2 AE = √(625 - 225) = √400 = 20,
AC = 20 + 20 = 40 cm.
Area of a rhombus = 1/2 * d1d2
= 1/2 * 40 * 30 = 600 sq.cm.
Answer:E:
Answer: (E) 600 sq.cm
Question: An bus covers a certain distance at a speed of 300 kmph in 5 hours. To cover the samedistance in 1hr, it must travel at a speed of?
(A) 1520 km/hr
(B) 1640 km/hr
(C) 1656 km/hr
(D) 1500 km/hr
(E) 1520 km/hr
Rationale: Distance = (300 x 5) = 1500 km.
Required speed = 1500 km/hr.
D
Answer: (D) 1500 km/hr