divelab/Sys2Bench huggingface dataset:
Question: In the accounting branch of a commercial institute, the percentage of male and female workers is 48% and 52% respectively. In this branch, 40% of males and 20% of females are age 25 or older. If one of the workers is selected at random, what is the probability Y that the worker is under 25 years old?
Options:
A) 0.30
B) 0.25
C) 0.45
D) 0.70
E) 0.90
Rationale: Percentage of male worker = 48
Percentage of female worker = 52
Let total number of workers = 1000
number of male workers= 480
number of female workers = 520
Number of male age 25 or older = (4/10)*480 = 192
Number of female age 25 or older =(2/10)*520 = 104
Total number of workers 25 or older = 192+104 = 296
Total number of workers under 25 = 1000 - 296 = 704
Probability that a worker randomly selected is under 25 years old = 704/1000 = .704
Alternatively , since the answer options are not close , we can use estimation here .
Percentage of male worker 25 or older = (4/10)*48 = 20 % approx
Percentage of female worker 25 or older = (2/10)*52 = 10 % approx
Percentage of total worker 25 or older = 30 %
Percentage of total worker under 25 = 70 %
Probability that a worker randomly selected is under 25 years old Y= .7
Answer D
Answer: D
Question: The greatest number of four digits which is divisible by 15, 25, 40 and 75 is:
Options:
A)9000
B)9400
C)9600
D)9800
E)7500
Rationale: Explanation:
Greatest number of 4-digits is 9999.
L.C.M. of 15, 25, 40 and 75 is 600.
On dividing 9999 by 600, the remainder is 399.
Required number (9999 - 399) = 9600.
ANSWER IS C
Answer: C
Question: In an xy-coordinate plane, a line is defined by y = kx + 1. If (4, b), (a, 5), and (a, b+1) are three points on the line, where a and b are unknown, then k = ?
Options:
A) 1/2
B) 1
C) 3/4
D) 2
E) 5/2
Rationale: b=4k+1...(1)
b+1=ak+1...(2)
5=ak+1...(3)
Taking (2) and (3)
5=b+1
b=4
Taking (1)
4=4k+1
k=3/4
Answer :C
Answer: C
Question: A and B are partners in a business. A contributes 1/4 of the capital for 15 months and B received 2/3 of the profit. For how long B’s money was used?
Options:
A)4 months
B)6 months
C)8 months
D)10 months
E)None
Rationale: Sol.
Let the total profit be Rs. z. Then,
B’ share = Rs. 2z/3, A’s share = Rs. [z - 2z/3] = Rs. z/3
∴ A : B = z/3 : 2z/3 = 1 : 2.
Let the total capital be Rs. x and suppose B’s money was used for x months. Then,
[1/4 x * 15] / [3/4 x * y] = 1/2 ⇔ y = [15 * 2 / 3] = 10.
Thus, B’s money was used for 10 months.
Answer D
Answer: D
Question: A searchlight on top of the watchtower makes 2 revolutions per minute. What is the probability that a man appearing near the tower will stay in the dark for at least 6 seconds?
Options:
A)5/6
B)4/5
C)3/4
D)2/3
E)1/2
Rationale: The searchlight completes one revolution every 30 seconds.
The probability that the man's area will be lit up is 6/30=1/5.
The probability that he will stay in the dark is 1-1/5=4/5
The answer is B.
Answer: B
Question: Mr. Jones sold two pipes at $1.20 each. Based on the cost, his profit one was 20% and his loss on the other was 20%. On the sale of the pipes, he:
Options:
A)lost 4 cents
B)broke even
C)gained 4 cents
D)lost 10 cents
E)gained 10 cents
Rationale: B
broke even
20 % profit on $ 1.20
= $ 20/100 × 1.20
= $ 0.20 × 1.20
= $ 0.24
Similarly, 20 % loss on $ 1.20
= $ 20/100 × 1.20
= $ 0.20 × 1.20
= $ 0.24
Therefore, in one pipe his profit is $ 0.24 and in the other pipe his loss is $ 0.24.
Since both profit and loss amount is same so, it’s broke even.
Answer: B
Question: what is the probability of always having x+y>0 ,where y<0
Options:
A)1/2
B)1/8
C)3/4
D)1/4
E)none
Rationale: total value of X can be : 1. X < 0 ; 2. X = 0 ; 3. X > 0 but less than Y in magnitude 4. X > 0 as well as |Y|
so probability of having X + Y > 0 would be 1/4
ANSWER:D
Answer: D
Question: According to the 2001 census,the population growth rate of Lucknow is going to be an increasing AP with first year's rate as 5% and common difference as 5% but simultaneously the migration,rate is an increasing GP with first term as 1% and common ratio of 2.If the population on 31 december 2000 is 1 million,thn find in which year will Lucknow witness its first fall in population?
Options:
A)2006
B)2007
C)2005
D)2008
E)2009
Rationale: population growth rate according to the problem
year 1 = 5%
year 2 = 10%
year 3 = 15%
year 4 = 20%
year 5 = 25%
year 6 = 30%
population decrease due to migration
year 1 = 1%
year 2 = 2%
year 3 = 4%
year 4 = 8%
year 5 = 16%
year 6 = 32%
Thus, the first fall would happen in year 2006
ANSWER:A
Answer: A
Question: In a game of billiards, A can give B 20 points in 60 and he can give C 30 points in 60. How many points can B give C in a game of 100?
Options:
A)43
B)54
C)25
D)86
E)23
Rationale: A scores 60 while B score 40 and C scores 30.
The number of points that C scores when B scores 100
= (100 * 30)/40 = 25 * 3 = 75.
In a game of 100 points, B gives (100 - 75)
= 25 points to C.
Answer: C
Answer: C
Question: For any two numbers X and Y , define X#Y=X+Y -XY . If X,Y>0.5, then X#X < Y#Y if
i. 1>X>Y
ii. 1>Y>X
iii. Y>X>1
Options:
A)i only
B)option ii only
C)i and ii only
D)ii and iii only
E)i and ii only
Rationale: X#X = 2X-X^2 and Y#Y=2Y-Y^2
X#X <Y#X
=> 2X - X^2 < 2Y - Y^2
=> 2(X-Y) < (X-Y)(X+Y)
=> X+Y>2 and X-Y>0 or X+Y<2 and X-Y<0
=> X+Y>2 and X>Y or X+Y<2 and X<Y
Using (i), if 1>X>Y, then the first case applies but X+Y>2 is not satisfied. False.
Using (ii), if 1>Y>X, then the second case applies and X+Y<2 is satisfied. True.
Using (iii), if Y>X>1, then the second case applies but X+Y<2 is not satisfied. False.
Therefore only (ii) is true, and choice (B) is correct.
Answer: B
Question: Car Z travels 50 miles per gallon of gasoline when driven at a constant rate of 45 miles per hour, but travels 20 percent fewer miles per gallon of gasoline when driven at a constant rate of 60 miles per hour. How many miles does car Z travel on 10 gallons of gasoline when driven at a constant rate of 60 miles per hour?
Options:
A)320
B)375.2
C)400
D)408.3
E)440
Rationale: The question stem asks us for the distance possible with 10 gallons of fuel at a constant speed of 60 miles per hour. We therefore first calculate the fuel efficiency at that speed.
The stem tells us that at 50 miles/hour, the car will run 40 miles/gallon and at 60 miles/hour, that distance decreases by 20%. We can therefore conclude that the car will travel 40 miles/gallon at a constant speed of 60 miles/gallon. With 10 gallons of fuel, the car can therefore travel 40 miles/gallon * 10 gallons = 400 miles.
Answer C.
Answer: C
Question: How many positive integers will divide evenly into 310?
Options:
A)4
B)6
C)8
D)12
E)16
Rationale: The question is asking how many factors 310 has.
310 = 2*5*31
The number of factors is 2^3 = 8
The answer is C.
Answer: C
Question: 3,7,12,..............4th terms
Options:
A)43
B)53
C)18
D)65
E)78
Rationale: 3+4=7
7+5=12
12+6=18
ANSWER:C
Answer: C
Question: Divide Rs. 1700 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is?
Options:
A)346
B)425
C)375
D)337
E)639
Rationale: A+B+C = 1700
A = 1/3(B+C); B = 2/3(A+C)
A/(B+C) = 1/3
A = 1/4 * 1700 => 425
Answer:B
Answer: B
Question: A person traveled from his house to office at 30 kmph; then he was late to his office by 5 minutes. If he increases his speed by 10 kmph he would be early by 15 minutes to his office. What should be his speed so that he reaches his office on time ?
Options:
A)36 kmph
B)32 kmph
C)34 kmph
D)35 kmph
E)37 kmph
Rationale: Let the distance between house and office be x km
(x/30) – (x/40) = 20/40; x/120 = 1/3 x = 40 km
Travlling at 40 kmph, he reaches office in 1 hour i.e. 15 minutes early
So required speed = 40/ 5/4 = 40 * 4/5
= 160/5
= 32 kmph
ANSWER:B
Answer: B
Question: Which of the options below is the lowest interger divisible by all the numbers below: 1,2,3,4,5,6,7,8,9,10
Options:
A)234
B)1222
C)2520
D)2894
E)1430
Rationale: To get the least positive integer that can be divided by each of these numbers 1,2,3,4,5,6,7,8,9,10 you calculate the lowest common denominator of all the numbers. Express each number as a product of their prime factors and multiply the set of prime numbers from each set with the highest exponent value.
LCM=2^3*3^2*5*7
The answer is C)
Answer: C
Question: If two numbers, a and b, are to be chosen from a set of 4 consecutive integers starting with 1 and a set of three consecutive even integers starting with 12, respectively, what is the probability that b/a will not be an integer?
Options:
A)2/12
B)3/12
C)4/12
D)1/2
E)2/3
Rationale: a is from the following set {1,2,3,4}
b is from the following set {12,14,16}
The total number of ways of choosing 2 integers, one from each set is 4*3 = 12 ways.
The possibilities where b/a is not an integer is for the following outcomes:
{b,a} = {14,3},{14,4},{16,3} = 3 ways
Thus the probability is 3/12 = 1/4
The answer is B.
Answer: B
Question: If def < 0 and ef > 0, which of the following must be positive?
Options:
A) xy
B) xz
C) (d^2)ef
D) d(e^2)f
E) xy(z^2)
Rationale: Given that ef is positive and def is negative, you can say that a MUST be negative. As for e and f either they are both positive or both negative.
Option (C) has d^2 which is positive and ef which is positive. So (C) must be positive.
Answer: C
Question: Jim bought edging to go around a circular garden with a radius of 10 feet. Later he decided to
double the diameter of the garden. How many more feet of edging must he buy?
Options:
A)28.84' additional edging
B)48.84' additional edging
C)38.84' additional edging
D)62.80' additional edging
E)58.84' additional edging
Rationale: circumference of small garden = 2 x 3.14 x 10 = 62.80'
double of the circumference of small garden = 2 x 62.80' = 125.60'
More feet to be buy =125.60 - 62.80 = 62.80
Answer :D
Answer: D
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?
Options:
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
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?
Options:
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
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?
Options:
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
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?
Options:
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
Question: How many pieces of 85 cm length can be cut from a rod of 29.75 meters long?
Options:
A)55
B)45
C)35
D)25
E)15
Rationale: Number of pieces = 2975/85 = 35
The answer is C.
Answer: C
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?
Options:
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
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.
Options:
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
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?
Options:
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
Question: Your town has a population of 1260. Every three people have a car. How many cars are in your town?
Options:
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
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
Options:
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
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)
Options:
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
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?
Options:
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
Question: The sale price sarees listed for Rs.400 after successive discount is 10% and 5% is?
Options:
A)337
B)267
C)342
D)287
E)261
Rationale: 400*(90/100)*(95/100) = 342
Answer:C
Answer: C
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?
Options:
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
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?
Options:
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
Question: If a/x = 1/3 and a/y =1/ 6, then (x + y) =
Options:
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
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?
Options:
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
Question: Calculate the average of all the numbers between 18 and 57 which are divisible by 7.
Options:
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
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?
Options:
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
Question: 2500 - (1002 / 20.04) = ?
Options:
A)2984
B)2983
C)2982
D)2450
E)None of these
Rationale: 2500-50 = 2450
Answer : D
Answer: D
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?
Options:
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
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?
Options:
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
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?
Options:
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
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?
Options:
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
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:
Options:
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
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?
Options:
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
Question: Find the least number when successively divided by 2, 3 and 7 leaves remainders 1, 2 and 3 respectively?
Options:
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
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?
Options:
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
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?
Options:
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
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 ?
Options:
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
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?
Options:
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
Question: Which of the following fractions is greater than 3/4 and less than 5/6?
Options:
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
Question: Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 15 cm
Options:
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
Question: What least number must be added to 1056, so that the sum is completely divisible by 23 ?
Options:
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
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?
Options:
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
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?
Options:
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
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.
Options:
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