mathewhe/aqua_rat huggingface dataset:
Question: How many positive integers I less than 20 are either a multiple of 2, an odd multiple of 9, or the sum of a positive multiple of 2 and a positive multiple of 9 ?
(A) 19
(B) 18
(C) 17
(D) 16
(E) 15
Rationale: We're asked to deal with the positive integers LESS than 20. There are only 19 numbers in that group (1 to 19, inclusive). We're asked to find all of the numbers that fit one (or more) of the given descriptions. Looking at the answer choices, we have every value form 15 to 19, inclusive, so most (if not all) of the numbers from 1 to 19 fit one (or more) of the descriptions. How long would it take you to find the ones that DON'T fit.....?
The first several should be pretty easy to find - the prompt wants us to focus on multiples of 2 and 9 (and sums of those multiples). So what ODD numbers are less than 9?
1, 3, 5, 7
None of these values fit the given descriptions. That's 4 out of 19 that we know for sure do NOT fit. 19 - 4 = 15 = E
Answer: (E) 15
Question: In Richie's company 60% of the employees earn less than $50,000 a year, 60% of the employees earn more than $40,000 a year, 11% of the employees earn $43,000 a year and 5% of the employees earn $49,000 a year. What is the median salary for the company?
(A) 43.0
(B) 45.5
(C) 46.0
(D) 49.0
(E) 50.0
Rationale: In Richie's company 60% of the employees earn less than $50,000 a year, 60% of the employees earn more than $40,000 a year, 50 and 51 employee will be each 43K. hence median = (43K+43k)/2=A
Answer: (A) 43.0
Question: Souju's age is 1/4th of her father's age. Souju's father's age will be twice Tharak's age after
10 years. If Tharak's eight birthdays was celebrated two years before, then what is Souju's present age.
(A) 6.5
(B) 7.5
(C) 8.5
(D) 8
(E) 9
Rationale: tharak's present age =8+2=10
souju's father's age after 10 years =2(10+10)=40
souju's father's present age =40−10=30
tharak's present age =1/4 *30=7.5
ANSWER:B
Answer: (B) 7.5
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
(B) 781
(C) 767
(D) 277
(E) 266
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
Question: Price of a book increases 15% successively (2times) what is the new price of the book more compared to that of the old price:
(A) 32.25%
(B) 23.34%
(C) 36%
(D) 39%
(E) 29%
Rationale: New price is 1.15*1.15*old price = 1.3225 *old price
Increase in price = 0.3225 * old price
% increase = 100* 0.3225 * old price /old price = 32.25 %
ANSWER:A
Answer: (A) 32.25%
Question: A is 16th position and 29th from down of the people who passed. 5 failed , 6 didn't give . how many boys are there in the class?
(A) 52
(B) 53
(C) 54
(D) 55
(E) 56
Rationale: A is 16th position, means = 15 + A
29th from down, means = A + 28
Total passed = A + 15 + 28 = 44
Total failed = 5
Didn't give = 6
Therefore, total boys = 44 + 5 + 6 = 55
ANSWER:D
Answer: (D) 55
Question: Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is:
(A) 2 : 3
(B) 4 : 3
(C) 6 : 7
(D) 9 : 16
(E) None of these
Rationale: Let us name the trains as A and B. Then,
(A's speed) : (B's speed) = √b : √a = √16 : √9 = 4 : 3.
Answer B
Answer: (B) 4 : 3
Question: 9 men and 2 boys working together can do four times as much work as a man and a boy. Working capacity of man and boy is in the ratio
(A) 1:2
(B) 1:3
(C) 2:1
(D) 2:5
(E) None of these
Rationale: Explanation:
Let 1 man 1 day work = x
1 boy 1 day work = y
then 9x + 2y = 4(x+y)
=> 5x = 2y
=> x/y = 2/5
=> x:y = 2:5
Option D
Answer: (D) 2:5
Question: The speed of a car is 90 km in the first hour and 42 km in the second hour. What is the average speed of the car?
(A) 89 kmph
(B) 92 kmph
(C) 75 kmph
(D) 65 kmph
(E) 66 kmph
Rationale: S = (90 + 42)/2 = 66 kmph
E
Answer: (E) 66 kmph
Question: How many five digit numbers can be formed using digits 0,1,2,3,4,5, Which are divisible by 12, without any of the digits repeating?
(A) 100
(B) 98
(C) 81
(D) 96
(E) 72
Rationale: 0,1,2,3,4,5
One digit will have to remain out for all 5 digit numbers;
if 0 is out; Leftover digits will be 1,2,3,4,5 = Sum(1,2,3,4,5)=15. Ignore
if 1 is out; Leftover digits will be 0,2,3,4,5 = Sum(0,2,3,4,5)=14. Ignore
if 3 is out; Leftover digits will be 0,1,2,4,5 = Sum(0,1,2,4,5)=12.
4*4! = 4*24 = 96
if 4 is out; Leftover digits will be 0,1,2,3,5 = Sum(0,1,2,3,5)=11. Ignore
if 5 is out; Leftover digits will be 0,1,2,3,4 = Sum(0,1,2,3,4)=10. Ignore
Total count of numbers divisible by 12 = 96
Ans:D
Answer: (D) 96
Question: 6 people meet for a business lunch. Each person shakes hands once with each other person present. How many handshakes take place?
(A) 30
(B) 21
(C) 18
(D) 15
(E) 10
Rationale: the formula to count handshakes is n(n−1)2n(n−1)2
Where n is the number of people
=> 6(6-1)/2 = 6*5/2 = 30/2 = 15
=> the answer is D(15)
Answer: (D) 15
Question: How many 3-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 repeated?
(A) 10
(B) 5
(C) 15
(D) 20
(E) 25
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.
The tens place can now be filled by any of the remaining 5 digits (2, 3, 6, 7, 9). 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.
Required number of numbers = (1 x 5 x 4) = 20.
Answer is D.
Answer: (D) 20
Question: Which of the following correctly lists the data sets in order of greatest to least standard deviation?
I. 4, 12, 15, 17, 19, 25
II. 42, 42, 42, 42, 42, 42
III. 57, 58, 59, 50, 51, 52
(A) II, I, III
(B) I, III, II
(C) I, II, III
(D) II, III, I
(E) III, II, I
Rationale: out of three given sets,
II has all numbers same, so it has zero standard deviation hence it is Least
only answer choices C and D have II in least position.
Out of I ans III
III has consecutive numbers , hence all are closedly spaced hence std deviation will be less
while in I,numbers are spread widely hence std deviation should be more than III
hence order should be II, III, I
IMO C
Answer: (C) I, II, III
Question: If Rs. 782 be divided into three parts, proportional to 1/2:2/3 :3/4, then the first part is:
(A) 202
(B) 201
(C) 205
(D) 206
(E) 204
Rationale: Given ratio = 1/2: 2/3:3/4
= 6 : 8 : 9.
Therefore, 1st part = Rs. (782 x 6/23)= Rs. 204.
Answer is E.
Answer: (E) 204
Question: X, Y, and Z are consecutive numbers and X > Y > Z. Also, 2X + 3Y + 3Z = 5Y + 11. What is the value of Z?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: If X, Y, and Z are consecutive numbers and X > Y > Z, then Y = Z+1 and X = Z+2.
2X + 3Y + 3Z = 5Y + 11
2Z+4+3Z+3+3Z = 5Z+5+11
3Z = 9
Z = 3
The answer is B.
Answer: (B) 3
Question: The population of a town increased from 1,75,000 to 2,97,500 in a decade. The average percent increase of population per year is
(A) 4.37%
(B) 5%
(C) 6%
(D) 8.75%
(E) 7%
Rationale: Solution
Increase in 10 years	= (297500 - 175000)
= 122500
Increase%	= (122500/175000Ã—100)%
= 70%.
Required average	= (70/10)%
= 7%.
Answer E
Answer: (E) 7%
Question: The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1600 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?
(A) 140
(B) 99
(C) 88
(D) 160
(E) 12
Rationale: Given that the area of the square = 1600 sq.units
=> Side of square = √1600 = 40 units
The radius of the circle = side of the square = 40 units Length of the rectangle = 2/5 * 40 = 16 units
Given that breadth = 10 units
Area of the rectangle = lb = 16 * 10 = 160 sq.units
Answer: D
Answer: (D) 160
Question: If a tap could fill entire tank in 20 hrs due to leakage, then in how much time
tank can be emptied by leakage if tap can fill entire tank in 16 hrs without leakage
(A) 12hrs
(B) 24hrs
(C) 36hrs
(D) 80hrs
(E) 52hrs
Rationale: time take to fill[withleakage] =20hrs so workdone in 1hr=1/20
time tkae to fill[without leakage]=16hrs so workdone in 1hr=1/16
if u subtract both u'll get time taken by leakage to empty...
1/20-1/16=1/80 so 80hrs
ANSWER:D
Answer: (D) 80hrs
Question: A man can row a distance of 5 km in 60 min with the help of the tide. The direction of the tide reverses with the same speed. Now he travels a further 20 km in 10 hours. How much time he would have saved if the direction of tide has not changed?
(A) 2
(B) 8
(C) 1
(D) 6
(E) 5
Rationale: Explanation:
He covered 5 km in 1 hour , so he might cover 20 km in 4 hours.
But he took 10 hours.
He would have saved 10 – 4 = 6 hours.
Answer: D
Answer: (D) 6
Question: Look at this series: 544, 509, 474, 439, 404, 369 ... What number should come next?
(A) 334
(B) 408
(C) 306
(D) 507
(E) 404
Rationale: 334
This is a simple subtraction series. Each number is 35 less than the previous number.
A
Answer: (A) 334
Question: The cost of type 1 rice is Rs 15 per Kg and type 2 rice
is Rs 20 per Kg. If both type1 and type 2 are mixed in the
ratio of 2:3,then the price per Kg of the mixed variety
of rice is?
(A) 15
(B) 17
(C) 19
(D) 18
(E) 16
Rationale: Let the price of the mixed variety be Rs x per Kg.
Cost of 1 Kg of type 1 rice Rs 15 Cost of 1 Kg of type 2 rice Rs 20
Mean Price Rs x
20-x x-15
(20-x) /( x-15) = 2/3
=> 60-3x = 2x-30
5x = 90=>x=18.
ANSWER : D 18
Answer: (D) 18
Question: The salary of a worker is first increased by 30% and afterwards reduced by 30%. What is net change in his salary?
(A) 3% decrease
(B) 5% decrease
(C) 9% decrease
(D) 4% decrease
(E) 8% decrease
Rationale: (30 * 30)/100 = 9% decrease
Answer:C:
Answer: (C) 9% decrease
Question: A money lender lent Rs. 1000 at 4% per year and Rs. 1400 at 5% per year. The amount should be returned to him when the total interest comes to Rs. 350. Find the number of years.
(A) 3.2
(B) 3.75
(C) 4
(D) 4.25
(E) 4.5
Rationale: (1000xtx4/100) + (1400xtx5/100) = 350 â†’ t =3.2 answer A
Answer: (A) 3.2
Question: If d is the standard deviation x, y, and z, what is the standard deviation of x + 4, y + 4, z + 4 ?
(A) 4d
(B) d
(C) 5d
(D) d+4
(E) d+16
Rationale: CONCEPT: Standard Deviation is Defined as Average Deviation of Terms in the set from the Mean value of the set. i.e.
1) It depends on the separation between the successive terms of the set
2) If a Constant Value is Added/Subtracted in every terms of set then the Separation between successive terms does NOT change Hence S.D. remains Constant
e.g.{1, 2, 3, 4, 5} will have same standard Deviation as {1+10, 2+10, 3+10, 4+10, 5+10}
3) If a Constant Value is Multiplied in every terms then the Separation between succesive terms gets multiplied by the constant Hence S.D. remains gets multiplied by same Number
e.g. {0.7, 1.4, 2.1, 2.8, 3.5} will have Standard Deviation = 0.7* Standard deviation of set {1, 2, 3, 4, 5}
When 4 is added in each term of set {x, y, z} then the new set {x+4, y+4, z+4} will remain same as the previous standard deviation i.e. d
Answer: B
Answer: (B) d
Question: A batsman makes a score of 100 runs in the 11th inning and thus increases his average by 5. Find his average after 11th inning.
(A) 40
(B) 50
(C) 62
(D) 45
(E) 56
Rationale: Let the average after 11th inning = x
Then, average after 10th inning = x-5
10(x-5)+100 = 11x
x = 100-50 = 50
Answer is B
Answer: (B) 50
Question: At a certain supplier, a machine of type A costs $20,000 and a machine of type B costs $50,000. Each machine can be purchased by making a 20 percent down payment and repaying the remainder of the cost and the finance charges over a period of time.If the finance charges= 40 percent of the remainder the cost, how much less would 2 machines of type A cost than 1 machine of type B?
(A) $10,000
(B) $11,200
(C) $12,000
(D) $12,800
(E) $13,200
Rationale: 1 machine of type B will cost: 20% down payment of 50,000 = 10,000 plus remaining sum (50,000-10,000=40,000) with 40% of finance charges 40,000*1.4=56,000 --> 10,000+56,000=66,000;
2 machine of type A will cost: 20% down payment of 2*20,000 = 8,000 plus remaining sum (40,000-8,000=32,000) with 40% of finance charges 32,000*1.4=44,800 --> 8,000+44,800=52,800;
Difference = 66,000 - 52,800 = 13,200.
Answer: E.
Answer: (E) $13,200
Question: If simple interest on a certain sum of money for 8 years at 4% per annum is same as the simple interest on Rs. 560 for 8 years at the rate of 12% per annum then the sum of money is
(A) Rs.1820
(B) Rs.1040
(C) Rs.1120
(D) Rs.1680
(E) None of these
Rationale: Explanation:
Let the sum of money be x
then
(x × 4 × 8)/100 = (560 × 12 × 8)/100
x × 4 × 8 = 560 × 12 × 8
x × 4 = 560 × 12x = 560 × 3 = 1680
Answer: Option D
Answer: (D) Rs.1680
Question: The average age of a group of persons going for tour is 16 years. Twenty new persons with an average age of 15 years join the group on the spot due to which their average age becomes 15.5 years. The number of persons initially going for tour is:
(A) 5
(B) 10
(C) 20
(D) 30
(E) 40
Rationale: Explanation :
Let the initial number of persons be x. Then,
=> 16x + 20 x 15 -15.5 (x + 20)
=> 0.5x = 10
=> x = 20
Answer : C
Answer: (C) 20
Question: A mixture of 70 liters of wine and water contains 10% water. How much water must be added to make water 12 ½% of the total mixture?
(A) 8
(B) 7
(C) 5
(D) 2
(E) 1
Rationale: 70 * (10/100) = 7
Wine Water
87 1/2% 12 1/2%
87 1/2% ------- 63
12 1/2% -------? => 9-7=2
Answer: D
Answer: (D) 2
Question: Which of the following are roots of an equation (x^-2)-(x^-1)-30=0
(A) 1/5 and -1/6
(B) -1/5 and 1/6
(C) 1/5 and 1/6
(D) -1/5 and -1/6
(E) -5/2 and -1/6
Rationale: Given: (x^-2) - (x^-1) - 30 = 0
Rewrite as: 1/(x²) - 1/x - 30 = 0
Remove fractions by multiplying both sides by x² to get: 1 - 1x - 30x² = 0
Rearrange to get: 30x² + x - 1 = 0
Factor to get: (5x + 1)(6x - 1) = 0
So, EITHER 5x + 1 OR 6x - 1 = 0
If 5x + 1 = 0, then x = -1/5
If 6x - 1 = 0, then x = 1/6
So, the roots (solutions) are -1/5 and 1/6
The answer is B.
Answer: (B) -1/5 and 1/6
Question: A drink vendor has 80 liters of Mazza, 144 liters of Pepsi, and 368 liters of Sprite. He wants to pack them in cans, so that each can contains the same number of liters of a drink, and doesn't want to mix any two drinks in a can. What is the least number of cans required?
(A) 35
(B) 36
(C) 37
(D) 38
(E) 39
Rationale: If we want to pack the drinks in the least number of cans possible, then each can should contain the maximum numbers of liters possible.As each can contains the same number liters of a drink, the number of liters in each can is a comman factor for 80,144 and 368; and it is also the highest such factor, as we need to store the maximum number of liters in each can.
So, the number of liters in each can = HCF of 80,144 and 368 = 16 liters.
Now, number of cans of Maaza = 80/16 = 5
Number of cans of Pepsi = 144/16 = 9
Number of cans of Sprite = 368/16 = 23
Thus, the total number of cans required = 5 + 9 + 23 = 37 Answer: C
Answer: (C) 37
Question: Two trains move in the same direction at speeds 50 kmph and 32 kmph respectively. A man in the slower train observes that 15 seconds elapse before the faster train completely passes by him. What is the length of faster train?
(A) 100m
(B) 75m
(C) 120m
(D) 50m
(E) 70m
Rationale: since both trains move in same direction so:
average speed=50-32=18kmph=5mps
speeed=length of train /time
length of train=5*15=75m
ANSWER:B
Answer: (B) 75m
Question: Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. The marks obtained by them are:
(A) 39, 30
(B) 41, 32
(C) 42, 33
(D) 43, 34
(E) 42, 34
Rationale: Let their marks be (x + 9) and x.
Then, x + 9 = 56/100(x + 9 + x)
25(x + 9) = 14(2x + 9)
3x = 99
x = 33
So, their marks are 42 and 33.
answer :C
Answer: (C) 42, 33
Question: Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 60 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
(A) 21
(B) 88
(C) 40
(D) 99
(E) 22
Rationale: Relative speed = 60 + 30 = 90 km/hr.
90 * 5/18 = 25 m/sec.
Distance covered = 500 + 500 = 1000 m.
Required time = 1000 *1/25 = 40 sec
Answer: C
Answer: (C) 40
Question: There are n members in a certain department, including Michael. Two representatives are to be selected to attend a company conference. If there are 55 possible combinations in which Michael is not selected, what is the value of n?
(A) 11
(B) 12
(C) 15
(D) 18
(E) 22
Rationale: Combinations of two persons, in which Michael was not selected = 55
number of ways two persons can be selected from m people = m*(m-1)/2
Let m be the number of people excluding Michael, then m*(m-1) = 110 => m=11
Thus, n = m + 1(Michael) = 12
option B
Answer: (B) 12
Question: Jim is now twice as old as Fred, who is nine years older than Sam. Six years ago, Jim was six times as old as Sam. How old is Jim now?
(A) 30
(B) 34
(C) 38
(D) 42
(E) 46
Rationale: J = 2F = 2(S+9) = 2S+18
J-6 = 6*(S-6)
(2S+18)-6 = 6S-36
S = 12 and so J = 42
The answer is D.
Answer: (D) 42
Question: The average of 11 numbers is 9.9. If the average of the first six numbers is 10.5 and that of the last six numbers is 11.4, then the middle number is
(A) 71.5
(B) 11.5
(C) 81.5
(D) 11.5
(E) 22.5
Rationale: Explanation:
Middle numbers = [(10.5 x 6 + 11.4 x 6) - 9.9 x 11] = 22.5.
Answer: E
Answer: (E) 22.5
Question: A man has Rs. 80 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
(A) 15
(B) 60
(C) 75
(D) 90
(E) 105
Rationale: Answer : A
Let number of notes of each denomination be x.
Then, x + 5x + 10x = 80
16x = 80
x =5.
Hence, total number of notes = 3x = 15.
Answer: (A) 15
Question: (128.5 x 32) + (13.8 x 30) = ? x 25
(A) 524.48
(B) 556.02
(C) 574.36
(D) 181.04
(E) 595.46
Rationale: Explanation :
? = (128.5 x 32) + (13.8 x 30)/25
= 4112 + 414/25 = 181.04
Answer : Option D
Answer: (D) 181.04
Question: Two pipes A and B can fill a cistern in 37 ½ min and 45 minutes respectively. Both the pipes are opened. The cistern will be filled in just half an hour, if the pipe B is turned off after
(A) 6 minutes
(B) 9 minutes
(C) 45 minutes
(D) 3 minutes
(E) 4 minutes
Rationale: If pipe B is turned off after x mins, then
(2*30)/75 + x/45 =1
x/45 = 1-60/75 = 1/5
x= 45/5= 9 mins
ANSWER:B
Answer: (B) 9 minutes
Question: If a(a - 6) = 27 and b(b - 6) = 27, where a ≠ b, then a + b =?
(A) −48
(B) 6
(C) −2
(D) 46
(E) 48
Rationale: i.e. if a =-3 then b = 9
or if a = 9 then b =-3
But in each case a+b = -3+9 = 6
Answer: option B
Answer: (B) 6
Question: Nine persons went to a hotel for taking their meals. Eight of them spent 14 each on their meals and the ninth spend 8 more than the average expenditure of all the nine. What was the total money spent by them?
(A) 115
(B) 117
(C) 119
(D) 122
(E) 135
Rationale: Let the average expenditure of all the nine be x.
Then, 14 × 8 + (x + 8) = 9x or 8x = 120 or x = 15.
∴ Total money spent = 9x = (9 × 15) = 135.
Answer E
Answer: (E) 135
Question: What is the greater of the two numbers whose product is 2048, given that the sum of the two numbers exceeds their difference by 64?
(A) A)90
(B) B)32
(C) C)64
(D) D)70
(E) of these
Rationale: Let the greater and the smaller number be g and s respectively.
gs = 2048
g + s exceeds g - s by 64 i.e., g + s - (g - s) = 64
i.e., 2s = 64 => s = 32.
g = 2048/s = 64.
ANSWER:C
Answer: (C) C)64
Question: For an upcoming charity event, a male vocalist has agreed to sing 5 out of 8 “old songs” and 3 out of 7 “new songs.” How many ways can the singer make his selection?
(A) 25
(B) 50
(C) 150
(D) 217.78
(E) 600
Rationale: =8C5*7C3
=8*7/3*7*5/3
=217.78
Ans = D
Answer: (D) 217.78
Question: On 8th Dec, 2007 Saturday falls. What day of the week was it on 8th Dec, 2006?
(A) Saturday
(B) Friday
(C) Monday
(D) Tuesday
(E) Surday
Rationale: Explanation:
The year 2006 is an ordinary year. So, it has 1 odd day.
So, the day on 8th Dec, 2007 will be 1 day beyond the day on 8th Dec, 2006.
But, 8th Dec, 2007 is Saturday
S0, 8th Dec, 2006 is Friday.
Answer: B) Friday
Answer: (B) Friday
Question: [( 3.242 x 10 ) / 100] = ?
(A) 0.045388
(B) 4.5388
(C) 0.03242
(D) 473.88
(E) None of these
Rationale: Answer
Multiplying 3.242 x 10=3.242
Now divide 3.242 by 100
So, 3.242 ÷ 100= 0.03242
∴ Shift the decimal two places to the left as 100
Correct Option: C
Answer: (C) 0.03242
Question: Profit selling 10 candles equals selling price of 3 bulbs. While loss on selling 10 bulbs equal selling price of 4 candles. Also profit percentage equals to the loss percentage and cost of a candle is half of the cost of a bulb. What is the ratio of selling price of candles to the selling price of a bulb?
(A) 5:4
(B) 3:2
(C) 4:5
(D) 3:4
(E) NONE
Rationale: Solution:
Price	Candle	Bulb
SP	A(let)	C(let)
CP	B	D
and, C = 2A
Profit = 10 (B-A) = 3D
Loss = 10 (C-D) = 4B
Profit % = (3D*100)/10A
Loss % = (4B*100)/10C
Now, By the questions,
(3D*100)/10A = (4B*100)/10C
B/D = 3/2.
Answer: Option B
Answer: (B) 3:2
Question: A room 3 m 21 cm long and 7m 77 cm broad is to be paved with square tiles. Find the least number of square tiles required to cover the floor.
(A) 27636
(B) 27640
(C) 27647
(D) 27713
(E) 27675
Rationale: Explanation:
Area of the room = (321 x 777) cm2.
Size of largest square tile = H.C.F. of 321 cm and 777 cm = 3 cm.
Area of 1 tile = (3 x 3) cm2.
Number of tiles required =(321×777)/(3×3)=27713
Answer: Option D
Answer: (D) 27713
Question: Jill has 42 gallons of water stored in quart, half-gallon, and one gallon jars. She has equal numbers of each size jar holding the liquid. What is the total number of water filled jars?
(A) 3
(B) 6
(C) 9
(D) 72
(E) 14
Rationale: Let the number of each size of jar = wthen 1/4w + 1/2w + w = 42 1 3/4w = 42w=24The total number of jars = 3w =72Answer: D
Answer: (D) 72
Question: A man can row with a speed of 15 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?
(A) 21
(B) 25
(C) 20
(D) 29
(E) 24
Rationale: M = 15
S = 5
DS = 15 + 5 = 20
Answer: C
Answer: (C) 20
Question: The greatest number of four digits which is divisible by 10, 20, 15 and 60 is:
(A) 9200
(B) 9300
(C) 9400
(D) 9600
(E) 9900
Rationale: Greatest number of 4-digits is 9999.
L.C.M. of 10, 20, 15 and 60 is 300.
On dividing 9999 by 300, the remainder is 99.
Required number (9999 - 99) = 9900.
ANSWER :E
Answer: (E) 9900
Question: A,B,C invested the capitals in a business. If A invested Rs. 30,000 more thanC and B invested Rs.10,000 more than A, then how should a profit of Rs.15,000 be divided among A,B and C? Given : Capital of C is Rs.10,000
(A) 6000, 4500, 4500
(B) 6200, 5800, 3000
(C) 6000, 7500, 1500
(D) 6500, 5500, 3000
(E) 6000, 5250, 3750
Rationale: A==40,000
B==50,000
C==10,000
so, ration are 4:5:1
profit 15000
so,, 15000/10==1500
so,, A==6000, B==7500,, C==1500
ANSWER:C
Answer: (C) 6000, 7500, 1500
Question: A train travelled from station P to Q in 8 hours and came back from station Q to P is 6 hours. What would be the ratio of the speed of the train while traveling from station P to Q to that from station Q to P?
(A) 3 : 6
(B) 3 : 9
(C) 3 : 3
(D) 3 : 4
(E) 3 : 1
Rationale: Since S # 1/t
S1 : S2 = 1/t1 : 1/t2 = 1/8 : 1/6 = 3 : 4
Answer:D
Answer: (D) 3 : 4
Question: The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age will be twice that of his son. The ratio of their present ages is:
(A) 5 : 2
(B) 7 : 3
(C) 9 : 2
(D) 13 : 4
(E) 15 : 8
Rationale: Explanation:
Let the ages of father and son 10 years ago be 3x and x years respectively.
Then, (3x + 10) + 10 = 2[(x + 10) + 10]
3x + 20 = 2x + 40
x = 20.
Required ratio = (3x + 10) : (x + 10) = 70 : 30 = 7 : 3.
Answer: B
Answer: (B) 7 : 3
Question: What is the greatest positive integer T such that 3^T is a factor of 9^10?
(A) 5
(B) T=9
(C) T=10
(D) T=20
(E) 30
Rationale: What is the greatest positive integer T such that 3^T is a factor of 9^10?
9^10 = (3^2)^10 = 3^20
D. 20
Answer: (D) T=20