mathewhe/aqua_rat huggingface dataset:
Question: In a survey of parents, exactly 3/4 of the mothers and 9/10 of the fathers held full-time jobs. If 40 percent of the parents surveyed were women, what percent of the parents did not hold full-time jobs?
(A) 27%
(B) 21%
(C) 19%
(D) 18%
(E) 16%
Rationale: Let the total number of parents = 100
Number of women = 40
Number of men = 60
Number of mothers who held full time jobs = 3/4*40 = 30
Number of fathers who held full time jobs = 9/10*60 = 54
Total number of parents who held full time jobs = 84
Total number of parents who did not hold jobs = 100 - 84 = 16
Alternatively ,
Percentage of women = 40%
Percentage of women who did not hold full time jobs = (1-3/4)*100 % = 25% of all mothers did not have full time jobs
25% of 40 % --> 10 % of the total parents
Percentage of men = 60%
Percentage of men who held full time jobs = (1-9/10)*100% = 10% of all fathers did not have full time jobs
10 % of 60% --> 6 % of the total parents
Therefore , percentage of parents who did not hold full time jobs = 10+6=16%
Answer E - 16%
Answer: (E) 16%
Question: If the fifth day of a month is two days earlier than Sunday, What day will it be on the tenth day of the month?
(A) Saturday
(B) Monday
(C) Sunday
(D) Wednesday
(E) Friday
Rationale: Explanation:
Given that fifth day of a month is two days earlier than Sunday
=> Fifth day is Friday
=> 12th is Friday
=> 10th is Wednesday
Answer: Option D
Answer: (D) Wednesday
Question: In a group of cows and chickens, the number of legs was 10 more than twice the number of heads. The number of cows was:
(A) 5
(B) 7
(C) 10
(D) 12
(E) 14
Rationale: Let the number of cows be x and their legs be 4x.
Let the number of chicken be y and their legs be 2x.
Total number of legs = 4x + 2y.
Total number of heads = x + y.
The number of legs was 10 more than twice the number of heads.
Therefore, 2 × (x + y) + 10 = 4x + 2y.
or, 2x + 2y + 10 = 4x + 2y.
or, 2x + 10 = 4x [subtracting 2y from both sides].
or, 10 = 4x – 2x [subtracting 2x from both sides].
or, 10 = 2x.
or, x = 5 [dividing by 2 on both sides].
Therefore, the number of cows = 5.
Correct Answer:A)5
Answer: (A) 5
Question: A and B enter into partnership with capitals in the ratio 4 : 3. At the end of 10 months A withdraws,and the profits now are divided in the ratio of 5 : 6. Find how long B remained in the business?
(A) 9 months
(B) 8 months
(C) 16 months
(D) 7 months
(E) None of these
Rationale: Initially A’s investment = 4x and B’s investment = 3x
Let B remain in the business for ‘n’ months.
⇒ 4x × 10 : 3x × n = 5 : 6
∴ 4x × 10 × 6 = 3x × n × 5
⇒ n = 16
Answer C
Answer: (C) 16 months
Question: What is the diagonal of a square field whose perimeter is 64m?
(A) 15 m
(B) 16√2m
(C) 20 m
(D) 25 m
(E) 18 m
Rationale: Sol:
Let the side of the square be xm.
Therefore,
4x=64
x=16
Diagonal of the square is= √2*(16)^2=16√2
Answer: B
Answer: (B) 16√2m
Question: find value for x from below equation? x + 1 = 5
(A) -5
(B) -4
(C) 4
(D) 3
(E) 2
Rationale: 1. Subtract 1 from both sides:
x + 1 - 1 = 5 - 1
2. Simplify both sides:
x = 4
C
Answer: (C) 4
Question: A box contains 20 electric bulbs, out of which 4 are defective. Two bulbs are chosen at random from this box. The probability that at least one of these is defective is
(A) 4/19
(B) 7/19
(C) 12/19
(D) 21/95
(E) None
Rationale: Solution
P( None is defective)
= 16C2 / 20C2
= (16x15/2x1 ×2x1/20x19)
= 12/19.
P( at least one is defective)
= (1- 12/19)
= 7/19.
Answer B
Answer: (B) 7/19
Question: If @ is a binary operation defined as the difference between an integer n and the product of n and 5, then what is the largest positive integer n such that the outcome of the binary operation of n is less than 21?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: @(n) = 5n - n
We need to find the largest positive integer such that 5n - n < 21.
Then 4n < 21 and n < 5.25.
The largest possible integer is n = 5.
The answer is E.
Answer: (E) 5
Question: Find the L.C.M of the fractions 2/7 , 5/14, and 4/21
(A) 1 1/7
(B) 3 4/7
(C) 2 4/7
(D) 2 6/7
(E) 2 7/7
Rationale: Explanation:
L.C.M = L.C.M of numerator/ H.CF of denominator
L.C.M = L.C.M of 2,5,4 / H.C.F of 7, 14, 21,
L.C.M = 20/7,
L.C.M = 2 6/7
Answer: Option D
Answer: (D) 2 6/7
Question: A fruit seller had some apples. He sells 35% and still has 6500 apples. Originally, he had ?
(A) 650apples
(B) 600 apples
(C) 772 apples
(D) 700 apples
(E) None
Rationale: Answer
âˆµ 65% of N = 800
âˆ´ N = (650 x 100)/65 = 1000
Correct Option: E
Answer: (E) None
Question: 10% of the inhabitants of village having died of cholera.,a panic set in , during which 25% of the remaining inhabitants left the village. The population is then reduced to 4050. Find the number of original inhabitants.
(A) 5000
(B) 6000
(C) 56000
(D) 6500
(E) 7000
Rationale: Let the total number of orginal inhabitants be x.
((75/100))*(90/100)*x)=4050  (27/40)*x=4050
x=((4050*40)/27)=6000.
ANSWER B
Answer: (B) 6000
Question: A candidate appearing for an examination has to secure 55% marks to pass paper I. But he secured only 45 marks and failed by 25 marks. What is the maximum mark for paper I?
(A) 127
(B) 120
(C) 130
(D) 140
(E) 150
Rationale: he secured 45 marks nd fail by 25 marks so
total marks for pass the examinatn=70
let toal marks x
x*55/100=70
x=127
ANSWER:A
Answer: (A) 127
Question: A can do a piece of work in 15 days. When he had worked for 2 days B joins him. If the complete work was finished in 8 days. In how many days B alone can finish the work?
(A) 11 6/7days
(B) 12 6/7days
(C) 13 6/7days
(D) 14 6/7days
(E) 15 6/7days
Rationale: 8/15 + 6/x = 1
X = 12 6/7days
ANSWER:B
Answer: (B) 12 6/7days
Question: The fourth proportional to 10, 14 and 18 is?
(A) 12
(B) 13
(C) 10
(D) 18
(E) 15
Rationale: (10*18)/12 = 15
ANSWER:E
Answer: (E) 15
Question: What is the area of the square with the following coordinates: (x, y), (20, 20), (20, 8), (x, 8)?
(A) 81
(B) 144
(C) 196
(D) 225
(E) 625
Rationale: To find the area of a square, knowing the length of one side is sufficient.
From the coordinates given, we can see that one side equals 12.
The area is 12*12 = 144.
The answer is B.
Answer: (B) 144
Question: Rs. 2780 are invested partly in 4% stock at 75 and 5% stock at 80 to have equal amount of incomes. The investment in 5% stock is:
(A) 1200
(B) 1500
(C) 1280
(D) 1300
(E) 1600
Rationale: Investment Rs 2780
stock - 4% 75 5% at 80%
req 5% stock is -- 1280
ANSWER C
Answer: (C) 1280
Question: A sum of Rs.3000 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years.
(A) 2888
(B) 3120
(C) 2877
(D) 2999
(E) 1950
Rationale: Let A be the amount received at the end of the three years.
A = 3000[1 + 10/100][1 + 20/100][1 + 25/100]
A = (3000 * 11 * 6 * 5)/(10 * 5 * 4)
A = Rs.4950
So the interest = 4950 - 3000 = Rs.1950
Answer: E
Answer: (E) 1950
Question: If 17,777 – n is divisible by 11, and 0 < n < 11, what is n?
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
Rationale: 17,777 / 11 = 1616 with a remainder of 1.
We need to subtract the remainder to get a multiple of 11.
The answer is A.
Answer: (A) 1
Question: A vessel contains 20 liters of a mixture of milk and water in the ratio 3:2. 10 liters of the mixture are removed and replaced with an equal quantity of pure milk. If the process is repeated once more, find the ratio of milk and water in the final mixture obtained?
(A) 9.1
(B) 9.0
(C) 9.3
(D) 9.2
(E) 9.7
Rationale: Explanation:
Milk = 3/5 * 20 = 12 liters, water = 8 liters
If 10 liters of mixture are removed, amount of milk removed = 6 liters and amount of water removed = 4 liters.
Remaining milk = 12 - 6 = 6 liters
Remaining water = 8 - 4 = 4 liters
10 liters of pure milk are added, therefore total milk = (6 + 10) = 16 liters.
The ratio of milk and water in the new mixture = 16:4 = 4:1
If the process is repeated one more time and 10 liters of the mixture are removed, then amount of milk removed = 4/5 * 10 = 8 liters.
Amount of water removed = 2 liters.
Remaining milk = (16 - 8) = 8 liters.
Remaining water = (4 -2) = 2 liters.
The required ratio of milk and water in the final mixture obtained = (8 + 10):2 = 18:2 = 9:1.
Answer: Option A
Answer: (A) 9.1
Question: Find the greatest number that will divide 48, 210 and 136 leaving 4, 12 and 4 as remainders respectively
(A) 19
(B) 17
(C) 13
(D) 22
(E) 21
Rationale: Explanation:
Answer will be HCF of (48-4, 210-12, 136-4)
HCF of (44, 198, 132) = 22
Option D
Answer: (D) 22
Question: 3,7,12,18,..............5th terms
(A) 43
(B) 53
(C) 63
(D) 65
(E) 25
Rationale: 3+4=7
7+5=12
12+6=18
18+7=25
ANSWER:E
Answer: (E) 25
Question: A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 120 sq. feet, how many feet of fencing will be required?
(A) 34
(B) 40
(C) 68
(D) 88
(E) 32
Rationale: We have: l = 20 ft and lb = 120 sq. ft.
So, b = 6 ft.
Length of fencing = (l + 2b) = (20 + 12) ft = 32 ft.
ANSWER:E
Answer: (E) 32
Question: Health insurance Plan P requires the insured person to pay $600 but then the insurance pays 70% of the cost over $600. Plan Q requires the insured to pay the initial $400, but then pays 60% of the cost over $400. Which of the following is a cost level for which both insurance plans pay out the same amount?
(A) $1200
(B) $1400
(C) $1600
(D) $1800
(E) $2000
Rationale: 0.7(x-600)=0.6(x-400)
0.1x=420-240
x=1800
The answer is D.
Answer: (D) $1800
Question: 9548 + 7314 = 4362 + (?)
(A) 8300
(B) 8400
(C) 12500
(D) 8700
(E) 9000
Rationale: 9548 16862 = 4362 + x
+ 7314 x = 16862 - 4362
----- = 12500
16862
-----
C)
Answer: (C) 12500
Question: Tom started a new grocery store business. During his first month he bought groceries for $650$650 and sold them for $800$800, while in the second month he bought with $800$800 and sold for $1200$1200. We need to know if Tom made more profit or not and profit or loss percentage
(A) 50 % loss
(B) 50% Profit
(C) 40 % loss
(D) 60 % Profit
(E) None
Rationale: Solution:
We cannot directly tell from these numbers if Tom's profit is increasing or not since his spending and gain are different amounts each month. In order to solve this problem we need to refer all the values to a fixed base value which is 100. Let us express the percent of his profit with respect to his expenditure for the first month:
(800 - 650) ÷ 650 ⋅ 100 = 23.08%
This means that, if Tom spent $100, he would have made a profit of 23.08 in the first month.
Now, let us apply the same for the second month:
(1200 - 800) ÷ 800 ⋅ 100 = 50%
So, for the second month, if Tom spent $100$100 he would have made a profit of $50$50(because $100⋅50%=$100⋅50÷100=$50$100⋅50%=$100⋅50÷100=$50). Now it is clear that Tom's profits are increasing.
Answer B
Answer: (B) 50% Profit
Question: Sarah's grade was 50th percentile of the 20 grades for her class. Of the 30 grades from another class, 10 were higher than Sarah's, and the rest were lower. If no other grade was the same as Sarah's grade, then Sarah's grade was what percentile of the grades of the two classes of two classes combined?
(A) 52nd
(B) 56th
(C) 60th
(D) 70th
(E) 82nd
Rationale: 52nd/56th/60th/70th/82nd
Correct option: C
Answer: (C) 60th
Question: eleven family members: 5 grandchildren (3 brothers and 2 sisters) and their 6 grandparents are to be seated around a circular table. How many different seating arrangements are possible so that 2 sisters are seated between any two of the three brothers?
(A) 120
(B) 60480
(C) 1440
(D) 2880
(E) 8640
Rationale: Answer: B.
Answer: (B) 60480
Question: In a car wheel, four spokes cover 40 degree. Then for the entire car,how many spokes are there?
(A) 120
(B) 144
(C) 158
(D) 200
(E) 328
Rationale: given, 4 spokes cover 40degrees,
so for 360 degrees.---->360*4/40=36..
so, for entire car, 4*36=144
ANSWER:B
Answer: (B) 144
Question: A pipe can empty 2/3rd of a cistern in 10mins. In 8 mins, what part of the cistern will be empty?
(A) 2/3
(B) 3/7
(C) 8/15
(D) 3/8
(E) 4/7
Rationale: 2/3 ---- 10
? ----- 8 ==> 8/15
C
Answer: (C) 8/15
Question: In an election between the two candidates, the candidates who gets 70% of votes polled is winned by 200 vote’s majority. What is the total number of votes polled?
(A) 750
(B) 500
(C) 800
(D) 850
(E) None of these
Rationale: Explanation:
Note: majority (40 %) = difference in votes polled to win (70 %) & defeated candidates (30 %)
40 % = 70 % - 30 %
40% -----> 200 (40*5 = 200)
100% -----> 500 (100*5 = 500)
Answer: Option B
Answer: (B) 500
Question: (112 x 5^4) = ?
(A) 60000
(B) 70000
(C) 80000
(D) 64000
(E) 65000
Rationale: (112 x 5^4) = 112 x (10/2)^4 =112 x 10^4 / 2^4 =	1120000 /6 = 70000
ANSWER:B
Answer: (B) 70000
Question: If a * b * c =(√(a + 2)(b + 3)) / (c + 1), find the value of 6 * 15 * 2.
(A) 8
(B) 5
(C) 11
(D) 3
(E) 4
Rationale: 6 * 15 * 2 = (√(6 + 2)(15 + 3) )/ (2 + 1)
= (√8 * 18) / 3
= (√144) / 3
= 12 / 3 = 4.
Answer is E
Answer: (E) 4
Question: A cab on its way to Bangalore overtakes an auto also going in the same direction at 11 am. The cab reaches Bangalore at 1.30 pm and starts the return journey after taking a break of 1 hour. On its way back it meets the auto at 3 pm. At what time will the auto reach Bangalore?
(A) 3 p.m.
(B) 3.30 p.m.
(C) 5 p.m
(D) 4 p.m
(E) 5 p.m
Rationale: Explanation:
The time interval is shown below with an interval of half hour.
11 am ------- 11:30 ------- 12 ------- 12:30 ------- 1-------1:30
At 11 the cab overtakes the auto and reaches Bangalore at 1:30. Hence, the cab travels 5 segments in two and a half hour assuming the cab to be travelling at constant
speed.
On its way back, the cab commences its journey at 2:30 and meets the auto at 3 p.m. In half an hour the cab travels one segment and hence the auto in one segment away
from Bangalore.
Therefore, the auto travels 4 segments from 11 am to 3 pm assuming it to be travelling at a constant speed. Hence, the speed of auto is 4/4 = 1 segment per hour.
As the auto is one segment away from Bangalore, it will take another 1 hour for the auto to reach Bangalore and hence the auto will reach Bangalore at 4 p.m.
ANSWER: D
Answer: (D) 4 p.m
Question: The cost of one photocopy is $0.02. However, a 25% discount is offered on orders of more than 100 photocopies. If Steve and Dennison have to make 80 copies each, how much will each of them save if they submit a single order of 160 copies?
(A) $0.32
(B) $0.40
(C) $0.45
(D) $0.48
(E) $0.54
Rationale: If Steve and Dennison submit separate orders, each would be smaller than 100 photocopies, so no discount. Each would pay (80)*($0.02) = $1.60, or together, a cost of $3.20 --- that's the combined no discount cost.
If they submit things together as one big order, they get a discount off of that $3.20 price ---- 25% or 1/4 of that is $0.80, the discount on the combined sale. They each effective save half that amount, or $0.40. Answer =(B).
Answer: (B) $0.40
Question: The equation (M +)/36 = (p – 7)/21 relates two temperature scales, where M is the number of degrees on one scale and P is the number of degrees on the other scale. Which of the following equations can be used to convert temperatures from the P scale to the M scale?
(A) (P-7)*12/7
(B) (P-7)*13/7
(C) (P-7)*15/7
(D) (P-7)*16/7
(E) (P-7)*17/7
Rationale: M/36 =(P-7)/21
M = (P-7)*36/21
=(P-7)*12/7
A
Answer: (A) (P-7)*12/7
Question: An equilateral triangle is described on the diagonal of a square. What is the ratio of the area of the triangle to that of the square?
(A) 2292
(B) 2298
(C) 2788
(D) 2662
(E) 2998
Rationale: Explanation:
By selling Rs. 100 stock , cash realised =
By selling Rs. 2400 stock, cash realised = = Rs 2298.
Answer: B) 2298
Answer: (B) 2298
Question: A dealer purchased an article at 3/4 of its list price and sold 50% more than the list price. Find his gain percent?
(A) 107%
(B) 180%
(C) 100%
(D) 140%
(E) 109%
Rationale: MP = 100
CP = 75
SP = 150
------
75 ---- 75
100 ---- ? => 100%
Answer:C
Answer: (C) 100%
Question: A boy has 9 trousers and 20 shirts. In how many different ways can he select a trouser and a shirt?
(A) 180
(B) 102
(C) 104
(D) 108
(E) 110
Rationale: The boy can select one trouser in nine ways.
The boy can select one shirt in 12 ways.
The number of ways in which he can select one trouser and one shirt is 9 * 20 = 180 ways.
A
Answer: (A) 180
Question: If a-b= 9 and a^2+b^2=281, find the value of ab
(A) 100
(B) 12
(C) 15
(D) 18
(E) 19
Rationale: 2ab = (a^2 + b^2) - (a - b)^2
= 281 - 81 = 200
=> ab = 100
ANSWER:A
Answer: (A) 100
Question: An error 5% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is:
(A) 10.01
(B) 9.25
(C) 10.25
(D) 8.25
(E) 6.25
Rationale: Explanation:
100 cm is read as 105 cm.
A1 =(100 × 100)cm2 = 10000
and A2= (105 × 105)cm2= 10816
(A2 - A1) = 11025-10000 = 1025
=> 1025/10000*100 =10.25
Answer : C
Answer: (C) 10.25
Question: How many 7's are present in the following sequence of numbers which are both preceded and followed by perfect square numbers ?
8 6 3 7 9 7 4 3 6 9 7 2 1 7 4 9 5 2 5 4 7 9 5 2 9 7 1 4 7 1
(A) 5
(B) 6
(C) 7
(D) 8
(E) 0
Rationale: Explanation:
8 6 3 7 9 7 4 3 6 9 7 2 1 7 4 9 5 2 5 4 7 9 5 2 9 7 1 4 7 1
ANSWER:A
Answer: (A) 5
Question: Tom, who has 50 math questions, will get 6 points per question if he chooses a correct answer. If he chooses a wrong answer to a question or skips one, he will lose 3 points per question. Then, which of the following can be the score if he solves all the 50 questions?
(A) 192
(B) 193
(C) 194
(D) 195
(E) 196
Rationale: Let x be the correctly answered questions. y be the wrongly answered/ skipped ones.
We have x + y = 50;
Score = 6x-3y
3x+3y = 150; 6x-3y = Score;
==> 9x = 150+Score;
check for answer choices where 150+Score is divisible by 9
Choice (A) 192 fits the equation !
Answer: (A) 192
Question: If y exceeds x by 40%, then x is less than y by?
(A) 16 2/9%
(B) 16 3/3%
(C) 16 2/3%
(D) 12 2/3%
(E) 28 4/7%
Rationale: X=100	y=140
140------40
100-------? => 28 4/7%
Answer:E
Answer: (E) 28 4/7%
Question: If 8 Men or 10 Women take 8 days to complete some work, how many days will 10 Men and 6 Women working together take to complete the work?
Can anyone explain please?
(A) 1. 3/2 days
(B) 2. 2 Days
(C) 3. 9/4 days
(D) 4.5/2 days
(E) 5.64/37 days
Rationale: 8 men or 10 women takes 6 days to complete the work
So 8M = 10W
W = 4/5M
1 man in 1 day does 1 unit of work
so 8 M in 8 M = 64 units of work
now 10 M and 6 W = 10 M + 6(4/5)M
= 10M + 24M/5
= 37M
Since both set do the same work
37M in n Days = 64 units of work
n = 64/37 days.
E
Answer: (E) 5.64/37 days
Question: The length of the rectangular field is double its width. Inside the field there is square shaped pond 6m long. If the area of the pond is 1/8 of the area of the field. What is the length of the field?
(A) 24
(B) 32
(C) 75
(D) 28
(E) 11
Rationale: A/8 = 6 * 6 => A = 6 * 6 * 8
x * 2x = 6 * 6 * 8
x = 12 => 2x = 24
Answer:A
Answer: (A) 24
Question: Two trains are moving at 50 kmph and 70 kmph in opposite directions. Their lengths are 150 m and 100 m respectively. The time they will take to pass each other completely is?
(A) 7 1/9
(B) 7 1/8
(C) 7 1/3
(D) 7 1/2
(E) 7 1/1
Rationale: 70 + 50 = 120 * 5/18 = 100/3 mps
D = 150 + 100 = 250 m
T = 250 * 3/100 = 15/2 = 7 1/2 sec
Answer:D
Answer: (D) 7 1/2
Question: For the positive integers x, x + 2, x + 4, x + 7, and x + 27, the mean is how much greater than the median?
(A) 0
(B) 1
(C) 2
(D) 4
(E) 7
Rationale: Mean = (x + x+2 + x+4 + x+7 + x+27)/5
=(5x+40)/5
=x+8
Median = x+4
Thus Mean - Median = x+8 - (x+4)
=4
Answer = D
Answer: (D) 4
Question: What sum of money put at C.I amounts in 2 years to Rs.8000 and in 3 years to Rs.9261?
(A) 5969.72
(B) 8877.72
(C) 2877.72
(D) 2678.72
(E) 1011.72
Rationale: 8000 ---- 1261
100 ---- ? => 15.76%
x *115.76/100 * 115.76/100 = 8000
x*1.34=8000
x=8000/1.34 =>5969.72
Answer: A
Answer: (A) 5969.72
Question: If the time is currently 1:30pm, what time will it be in exactly 650 hours?
(A) 12:30am
(B) 1:30am
(C) 12:30pm
(D) 2:30pm
(E) 3:30pm
Rationale: Every 24 hours will bring us to the same 1:30pm. 648 is divisible by 24 (27*24=648), so if it were 648 hours we would have 1:30pm, but since it's 649 hours then it will be 2 hour more, so 3:30pm.
Answer: E.
Answer: (E) 3:30pm
Question: A pineapple costs Rs. 7 each. A watermelon costs Rs. 5 each. X spends Rs. 38 on these fruits. The number of pineapples purchased is
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: 7P+5W= 38
As P and W are integers, only possible value of P is 4.
ANSWER:C
Answer: (C) 4
Question: What is the remainder when 15487^(62177037) is divided by 5?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: We need to find the units digit of the number.
The units digit of powers of seven repeats 7, 9, 3, and 1 cyclically.
Since 62177037 has the form 4a+1, the units digit is 7.
Then the remainder when dividing by 5 is 2.
The answer is C.
Answer: (C) 2
Question: Four car rental agencies A, B, C and D rented a plot for parking their cars during the night. A parked 15 cars for 12 days, B parked 12 cars for 20 days, C parked 18 cars for 18 days and D parked 16 cars for 15 days. If A paid Rs. 1305 as rent for parking his cars, what is the total rent paid by all the four agencies?
(A) Rs. 4500
(B) Rs. 4800
(C) Rs. 5250
(D) Rs. 7134
(E) None of these
Rationale: The ratio in which the four agencies will be paying the rents = 15 * 12 : 12 * 20 : 18 * 18 : 16 * 15
= 180 : 240 : 324 : 240 = 45 : 60 : 81 : 60
Let us consider the four amounts to be 45k, 60k, 81k and 60k respectively.
The total rent paid by the four agencies = 45k + 60k + 81k + 60k= 246k
It is given that A paid Rs. 1305
45k = 1305 => k = 29
246k = 246(29) = Rs. 7134
Thus the total rent paid by all the four agencies is Rs. 7134.
ANSWER:D
Answer: (D) Rs. 7134
Question: The number of stamps that P and Q had were in the ratio of 9:2 respectively. After P gave Q 33 stamps, the ratio of the number of P's stamps to the number of Q's stamps was 6:5. As a result of the gift, P had how many more stamps than Q?
(A) 11
(B) 33
(C) 45
(D) 67
(E) 80
Rationale: P started with 9k stamps and Q started with 2k stamps.
(9k-33)/(2k+33) = 6/5
45k - 12k = 178 + 165
33k = 343
k = 11
P has 9(11) - 33 = 66 stamps and Q has 2(11)+33 = 55 stamps.
The answer is A.
Answer: (A) 11
Question: Gill drives 120 miles from Los Angeles to San Diego to fetch a package. On her way there she drives at 40 miles per hour. On her way back she drives 50% faster. What is Gill's average velocity T for the round trip?
(A) 24 miles per hour
(B) 48 miles per hour
(C) 50 miles per hour
(D) 53 1/3 miles per hour
(E) 68 miles per hour
Rationale: Here's an Average Speed question in which the prompt gives you almost all of the immediate numbers needed to work with.
Driving from LA to SD, we have a distance of 120 miles and a speed of 40 miles/hour.
D = (R)(T)
120 = (40)(T)
120/40 = 3 = T
3 hours to drive to SD
On the way back, she drives 50% FASTER. Gill's return speed is (1.5)(40) = 60 miles/hour.
D = (R)(T)
120 = (60)(T)
120/60 = 2 = T
2 hours to drive to SD
Total Distance = 240 miles
Total Time = 3+2 = 5 hours
Average Speed = 240/5 = 48 miles/hour
Final Answer:
B
Answer: (B) 48 miles per hour
Question: Harold works at a resort from the beginning of March to the end of September. During the month of August this past year, he made 6 times the average (arithmetic mean) of his monthly totals in tips for the other months. His total tips for August were what fraction of his total tips for all of the months he worked?
(A) 1/3
(B) 2/5
(C) 3/7
(D) 1/2
(E) 4/7
Rationale: The time from beginning of March to the end of September is 7 months.
If x is the average monthly tip for all months other than August then his August month tip will be 6*x
His total tip for the 7 months = 6*(average tip for the months other than August) + 6x
=12x
August tips as a fraction of total tips = 6x/12x =1/2. So D
Answer: (D) 1/2
Question: A certain sum amounts to Rs.1725 in 3 years and Rs.1875 in 5 years. Find the rate % per annum?
(A) 7%
(B) 5%
(C) 2%
(D) 1%
(E) 6%
Rationale: 3 --- 1725
5 --- 1875
--------------
2 --- 150
N = 1 I = 75 R = ?
P = 1725 - 225 = 1500
75 = (1500*1*R)/100
R = 5%
Answer:B
Answer: (B) 5%