mathewhe/aqua_rat huggingface dataset:
Question: The sum of the present ages of two persons A and B is 90. If the age of A is twice that of B, find the sum of their ages 5 years hence?
(A) 50
(B) 60
(C) 70
(D) 80
(E) 100
Rationale: A + B = 90, A = 2B
2B + B = 90 => B = 30 then A = 60.
5 years, their ages will be 65 and 35.
Sum of their ages = 65 + 35 = 100.
ANSWER:E
Answer: (E) 100
Question: The area of circle O is added to its diameter. If the circumference of circle O is then subtracted from this total, the result is 10. What is the radius of circle O?
(A) –2/pi
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: pi*r^2 + 2r -2*pi*r = 10
Simplifying the equation: pi*r(r-2)+2r=10
Without much algebraic: We can Test the answers quickly, then 5 is the only possible answer that will eliminate pi from equation.
Answer is E
Answer: (E) 5
Question: On a certain road 10% of the motorists exceed the posted speed limit and receive speeding tickets, but 24% of the motorists who exceed the posted speed limit do not receive speeding tickets. What percent of the motorists on the road exceed the posted speed limit?
(A) 10.5%
(B) 13.2%
(C) 15%
(D) 22%
(E) 30%
Rationale: Answer is B.
This question is in the OG and thus well explained by ets.
those who exceed : X
so X = 10%+0,24X
id est X = 13.2%
Answer: (B) 13.2%
Question: The average age of students in section A of 124 students is 22 years and the average age of students in section B of 145 students is 32 years. Find the average age of students in both sections taken together?
(A) 27 years
(B) 30years
(C) 15years
(D) 25years
(E) 20years
Rationale: The required average = (124*22+145*32)/124+145 = 27 years
Answer is A
Answer: (A) 27 years
Question: How many pieces of 85 cm length can be cut from a rod of 29.75 meters long?
(A) 55
(B) 45
(C) 35
(D) 25
(E) 15
Rationale: Number of pieces = 2975/85 = 35
The answer is C.
Answer: (C) 35
Question: 26 An uneducated retailar marks all its goods at 50% above the cost price and thinking that he will still make 25% profit,offers a discount of 25% on the marked price.what is the actual profit on the sales?
(A) 5%
(B) 10.50%
(C) 9.50%
(D) 12.50%
(E) 10%
Rationale: Let C.P =Rs 100.then ,marked price =Rs100
S.P=75% of Rs 150=Rs112.50
Hence,gain%=12.50%
Answer is D.
Answer: (D) 12.50%
Question: The length of a room is 5.5 m and width is 3.75 m. What is the cost of paying the floor by slabs at the rate of Rs. 800 per sq. meter.
(A) Rs.12000
(B) Rs.19500
(C) Rs.18000
(D) Rs.16500
(E) Rs.17500
Rationale: Explanation:
Area =5.5×3.75 sq. metre.
Cost for 11 sq. metre. = Rs.800
Hence, total cost
=5.5×3.75×800=5.5×3000
= Rs.16500
Answer: Option D
Answer: (D) Rs.16500
Question: In six successive games, a baseball team scored 1 runs once, 4 runs twice, and 5 runs three times.
What was the average (arithmetic mean) number of runs the team scored per game over the six-game period?
(A) 8
(B) 7
(C) 6
(D) 5
(E) 4
Rationale: 1 runs once (one game)
4 runs twice (two game)
5 runs three times (three games)
SO we have (1*1 + 4*2 + 5*3)/6 = 24/6 = 4.
ANS: E.
Answer: (E) 4
Question: Your town has a population of 1260. Every three people have a car. How many cars are in your town?
(A) 400
(B) 410
(C) 420
(D) 430
(E) 450
Rationale: Every three person has a car, then the number of cars in the town could be calculated by the division of number of people over the person-to-car ratio.
the number of cars in the town=1260/(3/1)=1260/3=420 cars
So the correct choice is C
Answer: (C) 420
Question: Tough and Tricky questions: Work/Rate Problems.
A group of 4 junior lawyers require 7 hours to complete a legal research assignment. How many hours would it take a group of three legal assistants to complete the same research assignment assuming that a legal assistant works at two-thirds the rate of a junior lawyer?
Source: Chili Hot GMAT
(A) 14
(B) 10
(C) 9
(D) 6
(E) 5
Rationale: # of people times the # of hours:
4*7 = 28 --> 4 lawyers do 28 worksin 7 hours.
3*14/3 = 14 --> 3 assistants do 14worksin 4 hours
So, since the amount of work the assistants do is half the work the lawyers do, the time will be double, soANS A
Answer: (A) 14
Question: The mass of 1 cubic meter of a substance is 500 kg under certain conditions. What is the volume in cubic centimeters of 1 gram of this substance under these conditions? (1 kg =1,000 grams and 1 cubic meter = 1,000,000 cubic centimeters)
(A) 0.1
(B) 0
(C) 1
(D) 2
(E) 3
Rationale: 500 kg - 1 cubic meter;
500,000 g - 1 cubic meter;
500,000 g - 1,000,000 cubic centimeters;
1 g - 1,000,000/500,000 = 10/5 = 2 cubic centimeters.
Answer: D.
Answer: (D) 2
Question: For a road work, a contractor was given a deadline to complete the work in 25 days. Hence, he employed a certain number of workers to accomplish the job. But from the very first day 9 workers were absent and the remaining workers could finish the work in 40 days. What number of workers did the contractor hired in the beginning?
(A) 24
(B) 37
(C) 26
(D) 19
(E) 17
Rationale: Explanation:
Let the number of workers initially hired be x.
Hence, x workers can complete the work in 25 days and (x-9) workers can complete the work in 40 days.
Now, the number of men and the amount of work are in direct proportion and number of men and number of days in indirect proportion.
x*25 = (x – 9)*40
25x = 40x – 360
15x = 360
x = 24
ANSWER:A
Answer: (A) 24
Question: The sale price sarees listed for Rs.400 after successive discount is 10% and 5% is?
(A) 337
(B) 267
(C) 342
(D) 287
(E) 261
Rationale: 400*(90/100)*(95/100) = 342
Answer:C
Answer: (C) 342
Question: Two taps can separately fill a cistern 20 minutes and 20 minutes respectively and when the waste pipe is open, they can together fill it in 18 minutes. The waste pipe can empty the full cistern in?
(A) 22.8
(B) 22.7
(C) 22.6
(D) 22.9
(E) 22.5
Rationale: 1/20 + 1/20 - 1/x = 1/18
x = 22.5
Answer:E
Answer: (E) 22.5
Question: Anna and Carol buy CDs and tapes at a music store that sells each of its CDs for a certain price and each of its tapes for a certain price. Anna spends twice as much as Carol spends, buying three times as many CDs and the same number of tapes. If Carol spends $50.00 on four CDs and five tapes, how much does one tape cost?
(A) $5.00
(B) $6.25
(C) $12.00
(D) $25.00
(E) $100.00
Rationale: CD => C
Type => T
Carol: 4C+5T=50
Anna: 12C+5T=100
12C-4C=50
8C=50
C=6.25
4C+5T=50
25+5T=50
5T=25
T=5
Answer is A
Answer: (A) $5.00
Question: If a/x = 1/3 and a/y =1/ 6, then (x + y) =
(A) A)2a
(B) B)a/2
(C) C)6a
(D) D)7a
(E) E)9a
Rationale: Ratio 1:
3a = x
Ratio 2:
6a = y
x+y = 9a
Answer is E
Answer: (E) E)9a
Question: Jack has two dice, one has six equally probable sides, labeled 1, 2, 3, 4, 5, 6, and the other has seven equally probable sides, labeled 1, 2, 3, 4, 5, 6, 7. If Jack rolls both dice what is the probability that both of the numbers will be 7?
(A) 3/14
(B) 1/7
(C) 0
(D) 1/2
(E) 12/21
Rationale: METHOD-1
Probability that the number on first die is 7 = 0
Probability that the number on Second die is 7 = 1/7 [Because 1 out of 7 faces is 7]
Probability that Both Dice result in odd numbers = (0)*(1/7) = 0
Answer: Option C
Answer: (C) 0
Question: Calculate the average of all the numbers between 18 and 57 which are divisible by 7.
(A) 36.9
(B) 38.5
(C) 18.5
(D) 32.5
(E) 28.5
Rationale: Explanation:
numbers divisible by 7 are 21,28,35,42,49,56,
Average = (21+28+35+42+49+56,) / 6 = 231/6 = 38.5
ANSWER: B
Answer: (B) 38.5
Question: Rajan travelled for 12 hours. He covered the first half of the distance at 60 kmph and remaining half of the distance at 40 kmph. Find the distance travelled by Rajan?
(A) 376
(B) 576
(C) 476
(D) 566
(E) 676
Rationale: Let the distance travelled be x km.
Total time = (x/2)/60 + (x/2)/40 = 12 => x/120 + x/80 = 12 => (2x + 3x)/240 = 12
=> x = 576 km
Answer:B
Answer: (B) 576
Question: 2500 - (1002 / 20.04) = ?
(A) 2984
(B) 2983
(C) 2982
(D) 2450
(E) None of these
Rationale: 2500-50 = 2450
Answer : D
Answer: (D) 2450
Question: A 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?
(A) 230 m
(B) 240 m
(C) 260 m
(D) 320 m
(E) None of these
Rationale: Explanation:
Relative speed = (120 + 80) km/hr
=(200 x5/18)m/sec
=(500/9)m/sec
Let the length of the other train be x metres.
Then,	x + 270 / 9 =500/9
x + 270 = 500
x = 230.
ANSWER IS A
Answer: (A) 230 m
Question: Zachary is helping his younger brother, Sterling, learn his multiplication tables. For every question that Sterling answers correctly, Zachary gives him 3 pieces of candy. For every question that Sterling answers incorrectly, Zachary takes away two pieces of candy. After 7 questions, if Sterling had answered 2 more questions correctly, he would have earned 31 pieces of candy. How many of the 7 questions did Zachary answer correctly?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: i got two equations:
3x-2y=25
x+y=7
3x-2(7-x)=25
3x-14+2x=25
5x=39
x=7.8 or between 7 and 8. (ANS B)
Answer: (B) 7
Question: It is known that no more than 50 guests will be attending a party. What is the smallest number of sweets that must be brought to the party so that each guest receives the same number of sweets?
(A) 115
(B) 100
(C) 56
(D) 87
(E) 15
Rationale: If we assume that the number of guests is no more than 50, the answer is B because only 100 is divisible 50.
Answer: (B) 100
Question: For each color copy, Print Shop X charges $1.20 and Print Shop Y charges $1.70. How much greater is the charge for 70 color copies at Print Shop Y than at Print Shop X?
(A) $27
(B) $29
(C) $31
(D) $33
(E) $35
Rationale: The difference in the two prices is $1.70 - $1.20 = $0.50 for each color copy.
Each color copy will cost an extra $0.50 at Print Shop Y.
70*$0.50 = $35
The answer is E.
Answer: (E) $35
Question: If Rs. 10 be allowed as true discount on bill of Rs. 110 due at the end of a certain time, then the discount allowedon the same sum due at the end of double the time is:
(A) 16
(B) 18.33
(C) 20.21
(D) 26
(E) None
Rationale: Sol.
S.I. on Rs. (110 - 10) for a certian time = Rs. 10.
S.I. on Rs. 100 for double the time = Rs. 20.
T.D. on Rs. 120 = Rs. (120 - 100) = Rs.20
T.D. on Rs. 110 = Rs. [20 /120 * 110] = Rs. 18.33
Answer B
Answer: (B) 18.33
Question: During the last four years, a large truck company purchased diesel at rates of $1.2, $1.4, $1.5 and $2.1 per gallon. What was the mean cost of diesel over the four-year period if the company spends the same amount of dollars on diesel each year?
(A) $2.5
(B) $2.55
(C) $1.49
(D) $3.25
(E) $3.0
Rationale: finding the Harmonic mean here.
HM = 4/(1/12 + 1/14 + 1/15 + 1/21) = 14.87
C
Answer: (C) $1.49
Question: Find the least number when successively divided by 2, 3 and 7 leaves remainders 1, 2 and 3 respectively?
(A) 22
(B) 65
(C) 28
(D) 27
(E) 19
Rationale: Explanation:
2) 65 (32 3) 32 (10 7) 10 (1
64 30 7
-------- -------- - -----
1 2 3
=> 65
Answer: B
Answer: (B) 65
Question: 1. Internet: $80, with no sales tax, plus $10 shipping fee
2. Store X: $90, a 10% discount, plus 10% tax on discounted price
3. Store Y: $90, no tax
4. Store Z: $80, a 20% sales tax, and $10 rebate after tax
Isaac can purchase a certain item in four different ways, as shown in the table. What is the lowest price for which he can purchase this item?
(A) 88.1
(B) 86.0
(C) 89.1
(D) 89.5
(E) 90.0
Rationale: Option 2 = (90 - 9) + 0.1 * 81
= 81 + 8.1 = 89.10
Option 4 = 80 + 0.2 * 80 - 10
= 86
So the OA is correct - B
Answer: (B) 86.0
Question: Carl can wash all the windows of his house in 8 hours. His wife Maggie can wash all the windows in 4 hours. How many hours will it take for both of them working together to wash all the windows?
(A) 2
(B) 2 1/4
(C) 3 2/2
(D) 4 1/2
(E) 5
Rationale: Work hrs=AB/(A+B)= 32/12 =3 2/2
Answer is C
Answer: (C) 3 2/2
Question: A train 110 metres long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going ?
(A) 5 sec
(B) 6 sec
(C) 7 sec
(D) 10 sec
(E) None
Rationale: Solution
Speed of train relative to man =(60+6) km/hr= 66km/hr
=(66x5/18) m/sec =(55/3) m/sec
∴ Time taken to pass the man = (110x3/55)sec = 6sec
Answer B
Answer: (B) 6 sec
Question: Jeevan bought an article with 30 per cent discount on the labelled price. He sold the article with 12 per cent profit on the labelled price. What was his per cent profit on the price he bought?
(A) 40
(B) 50
(C) 60
(D) Data inadequate
(E) None of these
Rationale: Let the labelled price of the article = ₹ 100 then
CP = ₹ 70 and SP = ₹ 112.
∴ Read profit percent = 112−70/70×100
= 42/7×10=60
Answer C
Answer: (C) 60
Question: Which of the following fractions is greater than 3/4 and less than 5/6?
(A) 4/5
(B) 2/5
(C) 1/5
(D) 3/5
(E) None of them
Rationale: 3/4 = 0.75, 5/6 = 0.833, 1/2= 0.5, 2/3= 0.66, 4/5= 0.8, 9/10= 0.9.
Clearly, 0.8 lies between 0.75 and 0.833.
Therefore, 4/5 lies between 3/4 and 5/6.
Answer is A.
Answer: (A) 4/5
Question: Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 15 cm
(A) 178 cm2
(B) 179 cm2
(C) 285 cm2
(D) 167 cm2
(E) 197 cm2
Rationale: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)
= 1/2 (20 + 18) * (15)
= 285 cm2
Answer: C
Answer: (C) 285 cm2
Question: What least number must be added to 1056, so that the sum is completely divisible by 23 ?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: 23) 1056 (45
92
---
136
115
---
21
---
Required number = (23 - 21)
= 2.
A)
Answer: (A) 2
Question: Each week a restaurant serving Mexican food uses the same volume of chili paste, which comes in either 25-ounce cans or 15-ounce cans of chili paste. If the restaurant must order 40 more of the smaller cans than the larger cans to fulfill its weekly needs, then how many larger cans are required to fulfill its weekly needs?
(A) 40
(B) 30
(C) 60
(D) 45
(E) 55
Rationale: let x be the number of 25 ounce cans. Therefore (x+40) is the number of 15 ounce cans.
Total volume is same, therefore
25x=15(x+40)
10x=600
x=60
ans is C
Answer: (C) 60
Question: Pascal has 96 miles remaining to complete his cycling trip. If he reduced his current speed by 4 miles per hour, the remainder of the trip would take him 16 hours longer than it would if he increased his speed by 50%. What is his current speed X?
(A)  6
(B)  8
(C)  10
(D)  12
(E)  16
Rationale: Let the current speed be x miles per hour.
Time taken if speed is 50% faster (i.e. 3x/2 = 1.5x) = 96/1.5x
Time taken if speed is reduced by 4 miles/hr (i.e. (x-4)) = 96/(x-4)
As per question, 96/(x-4) - 96/1.5x = 16
Solving this X we get x = 8.
B.
Answer: (B)  8
Question: A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that all the four bulbs are defective.
(A) 1/187
(B) 1/127
(C) 1/178
(D) 1/129
(E) 1/126
Rationale: Out of nine, five are good and four are defective. Required probability
= ⁴C₄/⁹C₄
= 1/126
Answer:E
Answer: (E) 1/126
Question: A committee that includes 6 members is about to be divided into 2 subcommittees with 3 members each. On what percent of the possible subcommittees that Michael is a member of is David also a member?
(A) 10%
(B) .20%
(C) 25%
(D) 40%
(E) 50%
Rationale: there are only 2 possibility : either they both are in same team or in another team.
so probability to be in same team = 50 percernt
hence E
Answer: (E) 50%
Question: A and B enter into partnership with capital as 7:9. At the end of 8 months, A withdraws. If they receive the profits in the ratio of 8:9 find how long B's capital was used?
(A) months
(B) months
(C) months
(D) months
(E) months
Rationale: 7 * 8 : 9 * x = 8:9 => x= 7
ANSWER:D
Answer: (D) months
Question: An amount of money lent against simple interest at 4 1/2 % per annum amounts to Rs.381 after 6 years. Find the sum.
(A) 100
(B) 200
(C) 300
(D) 400
(E) 500
Rationale: GIVEN SI+P=381
SI=381-P
SI=PTR/100
381-P=P*6*4.5/100
P=300
ANSWER:C
Answer: (C) 300
Question: The perimeter of a square is equal to the perimeter of a rectangle of length 19 cm and breadth 14 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)
(A) 22.78
(B) 23.54
(C) 23.5
(D) 24.55
(E) 25.93
Rationale: Let the side of the square be a cm.
Perimeter of the rectangle = 2(19 + 14) = 66 cm
Perimeter of the square = 66 cm
i.e. 4a =66
A = 16.5
Diameter of the semicircle = 16.5 cm
Circumference of the semicircle
= 1/2(∏)(16.5)
= 1/2(22/7)(16.5) = 25.93 cm to two decimal places
Answer: E
Answer: (E) 25.93
Question: Amar takes as much time in running 24 meters as a car takes in covering 60 meters. What will be the distance covered by Amar during the time the car covers 2.2 km?
(A) 700 m
(B) 500 m
(C) 870 m
(D) 880 m
(E) 840 m
Rationale: Distance covered by Amar
= 24/60 (2.2km)
= 2/5(2200) = 880 m
Answer: D
Answer: (D) 880 m
Question: A can contains a mixture of two liquids A and B in the ratio 7:5. When 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7:9. How many litres of liquid A was contained by the can initially?
(A) 25
(B) 21
(C) 20
(D) 10
(E) 15
Rationale: Suppose the can initially contains 7x and 5x litres mixtures A and B
respectively
Quantity of A in mix. left =[7x –7/12 * 9 ] =[7x –21/4]
Quantity of B in mix. left =[5x –5/12 *9 ] = [ 5x - 15/4 ]
Therefore [ 7x-21/4 ] =7/9 or 28x-21 = 7/9
[5x-15/4]+9 20x+21
252x -189 =140x+147 or 112x =336 , x = 3.
Quantity of A in the can initially =7*3 =21
ANSWER:B
Answer: (B) 21
Question: A sum of Rs.4800 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) 2987
(B) 3120
(C) 2798
(D) 2689
(E) 2761
Rationale: Let A be the amount received at the end of the three years.
A = 4800[1 + 10/100][1 + 20/100][1 + 25/100]
A = (4800 * 11 * 6 * 5)/(10 * 5 * 4)
A = Rs.7920
So the interest
=7920 - 4800
= Rs.3120
Answer:B
Answer: (B) 3120
Question: In a bag, there are 2400 ball, and their colors are red, green blue.. The ratio of the balls are 15:13:17.Then how many red color balls are available in the bag?
(A) 900
(B) 1600
(C) 750
(D) 890
(E) 1010
Rationale: Red:green:blue = 15+13+17=45; Ratio of the red balls= 15/40 simplify =3/8*2400=900.Answer =A
Answer: (A) 900
Question: By mixing two brands of coffee and selling the mixture at the rate of Rs. 177 per kg. a shopkeeper makes a profit of 18%. If to every 2 kg of one brand costing Rs. 200 per kg, 3 kg of the other brand is added, then how much per kg does the other brand cost?
(A) 12.66
(B) 23
(C) 116.66
(D) 10.66
(E) 43.2
Rationale: E
C
Let the cost of the brand be Rs. X per kg.
C.P. of 5 kg = (2 * 200 + 3 * x) = Rs. (400 + 3x)
S.P of 5 kg = Rs. (5 * 177) = Rs. 885
[885 - (400 + 3x)]/(400 + 3x) * 100 = 18
24250 - 150x = 3600 + 27x
177x = 20650 => x = 116 2/3
So, cost of the other brand = Rs. 116.66.
Answer: (C) 116.66
Question: In how many ways can a committee consisting of 4 men and 5 women be formed from a group of 8 men and 9 women?
(A) 8C4 9C5
(B) 4C8 5C9
(C) 7C5 9C4
(D) 9C4 7C5
(E) NONE
Rationale: Group consisting of 8 men and 9 women
4 men can be selected from 8 men in 8C4 ways
5 women can be selected from 9 women in 9C5 ways
Therefore, Total number of ways= 8C4 9C5
ANSWER:A
Answer: (A) 8C4 9C5
Question: If x < y < 0, which of the following must be true?
(A) x+y is a positive integer
(B) x+y is a negative integer
(C) xy is a negative integer
(D) x/y is a negative integer
(E) 2x/y is a negative integer
Rationale: Given x, y are less than 0. So both will be negative integers
negative + negative = negative
negative * negative = positive
negative / negative = positive
So, option B is true and all others are false.
Answer : B
Answer: (B) x+y is a negative integer
Question: There is a total of 120 marbles in a box, each of which is red, green, blue, or white. If one marble is drawn from the box at random, the probability that it will be white is 1/4 and the probability that it will be green is 1/3. What is the probability that the marble will be either red or blue ?
(A) 1/6
(B) 1/4
(C) 2/7
(D) 1/3
(E) 5/12
Rationale: Total marbles in the box=120
white marbles=120/4=30
green marbles=120/3=40
w+g=70
red+blue=50
p(red or blue)=50/120=5/12
ANSWER:E
Answer: (E) 5/12
Question: Ramu bought an old car for Rs. 42000. He spent Rs. 15000 on repairs and sold it for Rs. 64900. What is his profit percent?
(A) 12%
(B) 13.85%
(C) 18%
(D) 82%
(E) 23%
Rationale: Total CP = Rs. 42000 + Rs. 15000 = Rs. 57000 and SP
= Rs. 64900
Profit(%) = (64900 - 57000)/57000 * 100
= 13.85%
Answer:B
Answer: (B) 13.85%
Question: Seven cards numbered from 1 to 7 are placed in an empty bowl. First one card is drawn and then put back into the bowl, and then a second card is drawn. If the cards are drawn at random and if the sum of the numbers on the cards is 10, what is the probability that one of the two cards drawn is numbered 4?
(A) 2/7
(B) 1/10
(C) 1/7
(D) 1/5
(E) 2/5
Rationale: There are 5 ways to get a total sum of 10.
2 of these ways include the number 4.
The probability that one of the cards is a 4 is 2/5
The answer is E.
Answer: (E) 2/5
Question: How many litres of pure acid are there in 10 litres of a 25% solution
(A) 1.5
(B) 1.6
(C) 2.5
(D) 1.8
(E) 1.9
Rationale: Explanation:Question of this type looks a bit typical, but it is too simple, as below... It will be 10 * 25/100 = 2.5 Answer: Option C
Answer: (C) 2.5
Question: Last year, Bill's farm produced 768,000 oranges. If Bill distributed his apples evenly across 9 different retail shops, how many apples remained with him.
(A) 1 orange
(B) 2 oranges
(C) 3 oranges
(D) 4 oranges
(E) 5 oranges
Rationale: This is equivalent to finding the first number that is divisible by 9 that occurs before 768,000 oranges.
In order to divide the sum in 9 parts, the amount must be divisible by 9
Divisibility rule of 9: The sum of the digits must be divisible by 9
Sum of digits of 768,000 = 21 and 18 is divisible by 9.
Hence, we need to remove 3 to this number for it to be divisible by 9
Correct Option: C
Answer: (C) 3 oranges
Question: Sara's mother is 6 times older than Sara. Next year, however, she will be only 5 times older than her daughter. How old is Sara's mother.
(A) 24 years
(B) 25 years
(C) 26 years
(D) 27 years
(E) 28 years
Rationale: At the present,
Sara's age is x.
Sara's mother's age is y=6x.
Next year,
Sara's age will be x+1.
Sara's mother's age will be y+1=5(x+1).
From the two equations, we can calculate Sara's age:
y=6x
y+1=5 (x+1)
6x+1=5x+5
6x-5x=5-1
x=4
If Sara is currently 4 years old, and her mother is 6 times older, then her age is
6x=6×4=24.
ANSWER: A
Answer: (A) 24 years
Question: 48 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?
(A) 10
(B) 16
(C) 13
(D) 18
(E) 19
Rationale: Let the required number of days be x.
Less persons, More days (Indirect Proportion)
More working hours per day, Less days (Indirect Proportion)
Persons 30 : 48 :: 12 : x
Working hours/day 6 : 5
30 x 6 x x = 48 x 5 x 12
x = (48 x 5 x 12)/(30 x 6)
x = 16
ANSWER B
Answer: (B) 16
Question: 5,7,11,19,35, (...)
(A) 12
(B) 67
(C) 5
(D) 64
(E) 32
Rationale: 5
5Ã— 2 - 3 = 7
7 Ã— 2 - 3 = 11
11 Ã— 2 - 3 = 19
19 Ã— 2 - 3 = 35
35 Ã— 2 - 3 = 67
Answer is B
Answer: (B) 67
Question: If 6^q is a factor of (10!)^2, What is the greatest possible value of q ?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Rationale: q 10!= 10*9*8*7*6*5*4*3*2*1 = 2*5*3*3*2*2*2*7*2*3*5*2*2*3*2 = 2^8*3^4*5^2*7
6= 2*3
Therefore only the exponents of 2 and 3 are relevant, 2^8 or 3^4 -> higher number counts = 8 -> Answer Choice D
Answer: (D) 8
Question: Find the area of the quadrilateral of one of its diagonals is 20 cm and its off sets 9 cm and 6 cm?
(A) 328
(B) 150
(C) 279
(D) 277
(E) 267
Rationale: 1/2 * 20(9 + 6) = 150 cm2
Answer:B
Answer: (B) 150
Question: How many 3-digit even numbers are possible such that if one of the digits is 5, the next/succeeding digit to it should be 6
(A) 5
(B) 305
(C) 365
(D) 405
(E) 495
Rationale: 560, 562, 564, 566, and 568, so total 5. Hence Option A.
Answer: (A) 5