divelab/Sys2Bench huggingface dataset:
Question: A bag contains 3 red, 4 black and 2 white balls. What is the probability of drawing a red and a white ball in two successive draws, each ball being put back after it is drawn?
Options:
A)2/27
B)1/9
C)1/3
D)4/27
E)2/9
Rationale: P=2∗3/9∗2/9=4/27
We are multiplying by 2 as there are two possible wining scenarios RW and WR.
Answer: D.
Answer: D
Question: A car rental company charges for mileage as follows: 9 dollars per mile for the first n miles and 10 dollars per mile for each mile over n miles. How much will the mileage charge be, in dollars, for a journey of d miles, where d > n ?
Options:
A)d-n
B)6d-n
C)10d-n
D)8d-n
E)12d-n
Rationale: Total Distance in miles = d
Millage Charge = 9n + (d-n) 10
9n --> For the first n Miles
(d-n)10--> Total no of miles after traveling the first n miles is d-n and the rate after n miles is 10 .
If we solve the equation , We will get 10d-n
Answer : C
Answer: C
Question: The cost price of a radio is Rs.1500 and it was sold for Rs.1335, find the loss %?
Options:
A)18
B)16
C)26
D)17
E)11
Rationale: Explanation:
1500 ---- 165
100 ---- ? => 11%
Answer:E
Answer: E
Question: In the rectangular coordinate system, what is the x-intercept of a line passing through (10, 3) and (−10, −7)?
Options:
A)4
B)2
C)0
D)−2
E)−4
Rationale: slope = rise/run = 10/20 = 1/2
The equation of the line is y = (1/2)x + b
3 = (1/2)(10) + b
b = -2
The equation of the line is y = (1/2)x - 2
To find the x-intercept, let y = 0:
0 = (1/2)x - 2
x = 4
The answer is A.
Answer: A
Question: Find the 15th term of an arithmetic progression whose first term is 2 and the common difference is 3.
Options:
A)45
B)38
C)44
D)40
E)46
Rationale: n th term of A.P = a +(n-1) *d
= 2+(15-1)*3 , = 2 + 42 = 44.
ANSWER:C
Answer: C
Question: Ravi can do a piece of work in 20 days while Prakash can do it in 40 days. In how many days will they finish it together?
Options:
A)5 7/9 days
B)6 7/9 days
C)5 1/9 days
D)5 7/2 days
E)4 7/9 days
Rationale: 1/20 + 1/40 = 3/40
40/7 = 5 7/9 days
ANSWER:A
Answer: A
Question: In a dairy farm, 46 cows eat 46 bags of husk in 46 days. In how many days one cow will eat one bag of husk ?
Options:
A)34 days
B)40 days
C)46 days
D)50 days
E)None of these
Rationale: Explanation:
Less Cows, More days (Indirect Proportion)
Less bags, Less days (Direct Proportion)
[Cows1 46
Bags 46 1]::46:x
=>x∗46∗1=46∗1∗46
=>x=46
Option C
Answer: C
Question: Tap A runs 3 liters of water per minute into a bucket that has a total volume of 36 liters. Tap B fills a third of the bucket in 20 mins.
Working together how long will it take both taps to fill the bucket ?
Options:
A)10 minutes
B)1.5 hours
C)9 hours and 12 minutes
D)15 hours
E)1 hour and 48 minutes.
Rationale: Pipe A has a rate of 3 liters per minute which equals a rate of 180 liters per hour.
Pipe B has a rate of 36 liters per hour.
180 + 36 (A+B) = Together they have a rate of 2000 liters per hour.
36 (The bucket) / 216 = 1/6 = 10 minutes
Answer -A
Answer: A
Question: A person can row upstream 20 kmph and downstream 30 kmph. Find the person rate in still water and rate of the stream.
Options:
A)25,5
B)10,5
C)5,5
D)10,5
E)1,5
Rationale: Explanation:
Please remember,
If a is rate downstream and b is rate upstream
Rate in still water = 1/2(a+b)
Rate of current = 1/2(a-b)
=> Rate in still water = 1/2(30+20) = 25 kmph
=> Rate of current = 1/2(30-20) = 5 kmph
Option A
Answer: A
Question: The cost price of 18 articles is equal to the selling price of 11 articles. Find the profit percent?
Options:
A)68 2/91%
B)63 7/11
C)68 9/11%
D)68 2/91%
E)62 2/11%
Rationale: 18 CP = 11 SP
11 --- 2 CP
100 --- ? =>63 7/11%
Answer:B
Answer: B
Question: Anand and Deepak started a business investing Rs. 12,500 and Rs. 35,000 respectively. Out of a total profit of Rs. 10,800, Deepak's share is?
Options:
A)Rs. 9400
B)Rs. 8900
C)Rs. 8400
D)Rs. 3400
E)Rs. 7957.9
Rationale: Ratio of their shares = 12500 : 35000 = 5:14
Deepak's share = 10800 * 14/19 = Rs. 7957.9
Answer:E
Answer: E
Question: A fruit vendor purchased 20 dozens of bananas at Rs. 15 per dozen. But one-fourth of the bananas were rotten and had to be thrown away. He sold two-third of the remaining bananas at Rs. 22.50 per dozen. At what price per dozen should he sell the remaining bananas to make neither a profit nor a loss?
Options:
A)Rs.18
B)Rs.15
C)Rs.11
D)Rs.19
E)Rs.12
Rationale: CP of 20 dozen of bananas = 15 * 20 = Rs. 300
Number of bananas which are rotten = 1/4 * 20 = 5 dozen.
SP of two-third of remaining bananas = (2/3 * 15) * 22.5 = Rs. 225
SP of remaining 5 dozens of bananas to make no profit and no loss =(300 - 225) = Rs. 75.
SP of 1 dozen bananas = 75/5 = Rs.15.
Answer:B
Answer: B
Question: The diagonals of a rhombus are 14 cm and 18 cm. Find its area?
Options:
A)176
B)190
C)150
D)126
E)292
Rationale: 1/2 * 14 * 18
= 126
Answer:D
Answer: D
Question: Mr. Yutaro’s class contains 4 boys and 12 girls. If two students are chosen, one at a time, from the class, what is the probability that a boy and a girl are chosen?
Options:
A)9/48
B)2/15
C)11/24
D)27/48
E)13/16
Rationale: Probability of a boy being chosen first, then a girl:
4/16 * 12/15
Probability of a girl being chosen first, then a boy:
12/16 * 4/15
Probability of a boy and a girl being chosen:
(4*12+12*4) / (15*16)
=2/15
Answer:B
Answer: B
Question: A tour group of 25 people paid a total of $600 for entrance to a museum. If this price included a 5% sales tax, and all the tickets cost the same amount, what was the face value of each ticket price without the sales tax?
Choices
Options:
A)$22.8
B)$23.94
C)$24
D)$25.20
E)$30
Rationale: A.
Answer: A
Question: Find the missing figures :
?% of 50 = 2.125
Options:
A)8.55
B)6.55
C)8.75
D)7.75
E)4.25
Rationale: (i)	Let x% of 50 = 2.125. Then , (x/100)*50 = 2.125
X = (2.125 * 2) = 4.25
Answer is E.
Answer: E
Question: A diet contains 400 grams of a mixture of two foods, food X and food Y. Food X contains 10 percent protein and food Y contains 15 percent protein. If a diet provides exactly 46 grams of protein daily, how many grams of food X are in the mixture?
Options:
A)280
B)300
C)320
D)340
E)360
Rationale: Let x be the number of grams of food X in the mixture.
0.1x + 0.15(400-x) = 46
0.05x = 14
x = 280
The answer is A.
Answer: A
Question: How many odd factors does 270 have?
Options:
A) 3
B) 4
C) 5
D) 6
E) 8
Rationale: Start with the prime factorization: 270 = 2*3*5
For odd factors, we put aside the factor of two, and look at the other prime factors.
set of exponents = {1, 1}
plus 1 to each = {2, 2}
product = 2*2 = 4
Therefore, there are 4 odd factors of 270.
Answer: B.
Answer: B
Question: There are 99 people that own pets. 15 people own only dogs, 10 people own only cats, 5 people own only cats and dogs, 3 people own cats, dogs and snakes. How many total snakes are there?
Options:
A)2
B)4
C)8
D)69
E)32
Rationale: lets assign variables to all the areas in Venn Diagram of Three.
three different Units are DOG, Cat, Snake= Total = 99
Only Dog= d=15
Only Cat = c=10
Only Snake = s
Exactly Dog and Cat= 5
Exactly Dog and Snake = x
Exactly Cat and Snake = y
all three= 3
so 99=15+10+5+3+x+y+s
we need to know total snakes= x+y+s+3 = 69
answer:D
Answer: D
Question: A garrison of 400 men had a provision for 31 days. After 28 days 280 persons re-enforcement leave the garrison. Find the number of days for which the remaining ration will be sufficient?
Options:
A)227
B)66
C)10
D)99
E)77
Rationale: 400 --- 31
400 --- 3
120 --- ?
400*3 = 120*x => x =10 days
Answer: C
Answer: C
Question: What is the probability of rolling two six-sided dice, and getting a different number on each die?
Options:
A)5/6
B)1/3
C)4/9
D)5/9
E)7/18
Rationale: MAGOOSHOFFICIAL SOLUTION
For the first die, we can roll any one of six numbers. For the second die, we can roll any number save for the number we rolled on the first die, giving us 5 possibilities. For the third die, we can roll four different numbers (we can’t roll the number we rolled on the first or second die.
6 x 5 = 30 possibilities out of 36 total possibilities. (For total possibilities we get 6 x 6 = 36).
30/36 = 5/6
Answer: A.
Answer: A
Question: A box contain Red, Blue and Green colored balls. The number of Red balls is 80 and the number of Blue balls is 60.
The number of Green balls subtracted from the number of Red balls is the same as the number of Green balls added with the number of Blue balls. Then the number of Green balls is?
Options:
A)80
B)green balls = 70
C)60
D)85
E)140
Rationale: Answer
Let the number of Green balls be x.
Then, x - 60= 80 - x
â‡’ 2x = 80+ 60= 140
â‡’ 2x = 140
âˆ´ x = 70
Correct Option: B
Answer: B
Question: The total age of A and B is 20 years more than the total age of B and C. C is how many years younger than A.?
Options:
A)20
B)12
C)15
D)16
E)10
Rationale: (A+B)-(B-C)=20
A-C=20
Answer is A
Answer: A
Question: A man can row with a speed of 40 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?
Options:
A)29
B)378
C)20
D)27
E)45
Rationale: M = 40
S = 5
DS = 40 + 5 = 45
Answer: E
Answer: E
Question: There are 6 ladies and 3 gents to dine at a round table. In how many ways can they seat themselves so that no two gents are seated together.
Options:
A)8540
B)2880
C)8640
D)6560
E)8860
Rationale: First arrange the ladies. This is a circular arrangment. 6 Gents can be arranged in 5! ways.
Now there are 4 spaces (space in between two ladies) and we have to seat 3 gents there.
First select 3 places out of 4 available places. can be done in 4C3 ways. Then arrange 3 gents there in 3! ways.
Total: 5!*4C3*3! = 2880
B is the answer.
Answer: B
Question: A butler stole wine from a butt of sherry which contained
40% of spirit and he replaced,what he had stolen by wine
containing only 16% spirit. The butt was then of 24%
strength only. How much of the butt did he steal?
Options:
A)1/3 OF THE BUTT
B)2/3 OF THE BUTT
C)1/4 OF THE BUTT
D)1/8 OF THE BUTT
E)1/9 OF THE BUTT
Rationale: Wine containing 40%spirit Wine containing 16% spirit
Wine containing 24% spirit
8 16
They must be mixed in the ratio of =1:2.
Thus 1/3 of the butt of sherry was left
hence the butler drew out 2/3 of the butt.
ANSWER B
Answer: B
Question: If (0.2)x = 2 and log 2 = 0.3010, then the value of x to the nearest tenth is:
Options:
A)-10.0
B)-0.5
C)-0.4
D)-0.2
E)10.0
Rationale: (0.2)x = 2.
Taking log on both sides
log (0.2)x = log 2.
x log (0.2) = 0.3010, [since log 2 = 0.3010].
x log (2/10) = 0.3010.
x [log 2 - log 10] = 0.3010.
x [log 2 - 1] = 0.3010,[since log 10=1].
x [0.3010 -1] = 0.3010, [since log 2 = 0.3010].
x[-0.699] = 0.3010.
x = 0.3010/-0.699.
x = -0.4306….
x = -0.4 (nearest tenth)
correct answer C
Answer: C
Question: Rahul went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
Options:
A)19
B)19.7
C)20
D)21.1
E)23
Rationale: Total cost of the items he purchased = Rs.25
Given that out of this Rs.25, 30 Paise is given as tax
=> Total tax incurred = 30 Paise = Rs.30/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (25−30/100−x)6/100 = 30/100
⇒ 6(25 −0.3 −x) = 30
⇒ (25 − 0.3 − x) = 5
⇒ x = 25 − 0.3 − 5 = 19.7
B)
Answer: B
Question: Calculate the different number of ways 5 boys and 3 girls can sit on a bench?
Options:
A)40120
B)40220
C)40420
D)40320
E)40325
Rationale: npn = n!
8p8 = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 40320
D
Answer: D
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?
Options:
A)9:1
B)9:6
C)9:3
D)9:2
E)9:9
Rationale: 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: A
Answer: A
Question: The radius of the wheel of a bus is 140 cms and the speed of the bus is 66 km/h, then the r.p.m. (revolutions per minutes)of the wheel is
Options:
A)125
B)250
C)300
D)330
E)None of these
Rationale: Radius of the wheel of bus = 140 cm. Then,
circumference of wheel = 2Ï€r = 280Ï€ = 880 cm
Distance covered by bus in 1 minute
= 66â„60 Ã— 1000 Ã— 100 cms
Distance covered by one revolution of wheel
= circumference of wheel
= 880 cm
âˆ´ Revolutions per minute = 6600000/60Ã—880 = 125
Answer A
Answer: A
Question: The number of boys in a class is four times the number of girls. Which one of the following numbers cannot represent the total number of children in the class ?
Options:
A)A)48
B)B)44
C)C)42
D)D)40
E)E)38
Rationale: Explanation:
Let number of girls = x and number of boys = 4x.
Then, 4x + x = 5x = total number of students.
Thus, to find exact value of x, the total number of students must be divisible by 5.
Answer: D
Answer: D
Question: A tradesman by means of his false balance defrauds to the extent of 30%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?
Options:
A)37
B)69
C)65
D)78
E)56
Rationale: Explanation:
g% = 30 + 30 + (30*30)/100
= 69%
Answer: B
Answer: B
Question: If there are twice as many women as men in a group and an equal number of men and women do not own cars - a group that is 40% of the total. What fraction of the total is men who own cars?
Options:
A)3⁄20
B)11⁄60
C)2⁄15
D)1⁄3
E)11⁄20
Rationale: Consider a group of 100 men and 200 women, a total of 300 people. 40% of them, which is 120, form a group of people who don't own a car.
Half of them are men, and the other half are women, more precisely 60.
It means that there are 100 - 60 = 40 men who own a car, and this represents 40/300 = 2/15 of the total.
Answer C
Answer: C
Question: In a railway compartment, there are 2 rows of seats facing each other with accommodation for 5 in each, 4 wish to sit facing forward and 3 facing towards the rear while 3 others are indifferent. In how many ways can the 10 passengers be seated?
Options:
A)172000
B)12600
C)45920
D)43200
E)None
Rationale: Solution:
The four person who wish to sit facing forward can be seated in: 5P4 ways and 3 who wish to sit facing towards the rear can be seated in: 5P3 ways and the remaining 3 can be seated in the remaining 3 seats in 3P3 ways. Total number of ways =5P4 *5P3 *3P3 = 43200.
Answer: Option D
Answer: D
Question: The 8 spokes of a custom circular bicycle wheel radiate from the central axle of the wheel and are arranged such that the sectors formed by adjacent spokes all have different central angles, which constitute an arithmetic series of numbers (that is, the difference between any angle and the next largest angle is constant). If the largest sector has a central angle of 87°, what fraction of the wheel’s area is represented by the smallest sector?
Options:
A)1/120
B)1/100
C)1/80
D)1/60
E)1/40
Rationale: The largest angle is 87.
Let d be the difference between any two angles in the progression.
The sum of all the angles will be:
87 + (87-d) + (87-2d) + ... + (87-7d) = 696 - 28d
The sum of all the central angles in a circle = 360
696 - 28d = 360
d = 336/28 = 12
The smallest sector is (87-7d) = 87-7*12 = 3
3/360 = 1/120
The answer is A.
Answer: A
Question: If the numerator of a fraction be increased by 15% and its denominator be diminished by 8% , the value of the fraction is 15/16. Find the original fraction.
Options:
A)3/4
B)1/4
C)1/2
D)1
E)None of them
Rationale: Let the original fraction be x/y.
Then (115%of x)/(92% of y)=15/16 => (115x/92y)=15/16
=((15/16)*(92/115))=3/4
Answer is A.
Answer: A
Question: The average age of a group of 5 members is 20 years. Two years later, a new member joins the group. The average age of the group becomes 21.5 years. What is the age of the new member ?
Options:
A)20 years
B)19 years
C)22 years
D)23 years
E)24 years
Rationale: The average age of the 5 members is 20 years
=> The sum of the ages of the 5 members is 20*5 = 100 years
Once the new member joins, the average age becomes 21.5 years.
Let the age of the new member be x.
Then (110+x)/6 = 21.5
=> x = 19 years
Answer B
Answer: B
Question: A man covered a certain distance at some speed. If he had moved 3 kmph faster, he would have taken 40 minutes less. If he had moved 2 kmph slower, he would have taken 40 minutes more. What is the the distance in km?
Options:
A)33
B)37
C)40
D)38
E)27
Rationale: Let the distance be x km ,
the speed in which he moved = v kmph
Time taken when moving at normal speed - time taken when moving 3 kmph faster = 40 minutes
⇒xv−xv+3=4060⇒x[1v−1v+3]=23⇒x[v+3−vv(v+3)]=23⇒2v(v+3)=9x................(Equation1)
Time taken when moving 2 kmph slower - Time taken when moving at normal speed = 40 minutes
⇒xv−2−xv=4060⇒x[1v−2−1v]=23⇒x[v−v+2v(v−2)]=23⇒x[2v(v−2)]=23⇒x[1v(v−2)]=13⇒v(v−2)=3x................(Equation2)Equation1Equation2⇒2(v+3)(v−2)=3⇒2v+6=3v−6⇒v=12Substituting this value of v in Equation 1⇒2×12×15=9x=>x=2×12×159=2×4×153=2×4×5=40Hence distance = 40 km
Answer :C
Answer: C
Question: If an article is sold at 5% gain instead of 5% loss,the seller gets Rs 6.72 more. The C.P of the article is?
Options:
A)132.82
B)138.55
C)148.81
D)150.45
E)None
Rationale: Sol.
100 * 10/6.72 = 148.81 answer
Answer C
Answer: C
Question: 4 DICE ARE THROWN AND THE SUM OF THE NUMBERS NOTED IS 10. FIND THE PROBABILITY THAT ALL THE NUMBERS LIE BETWEEN 2 AND 5 (both inclusive)?
Options:
A)11/79
B)10/79
C)12/79
D)13/79
E)14/79
Rationale: Sum of numbers noted on 4 dice(with six faces) to be 10 will include combinations:
( 1,1,2,6)(1,1,3,5)(1,1,4,4)(1,1,5,3)(1,1,6,2)(1,2,1,6)(1,2,2,5)(1,2,3,4)(1,2,4,3)(1,2,5,2)(1,2,6,1)(1,3,1,5)(1,3,2,4)(1,3,3,3)(1,3,4,2)(1,3,5,1)(1,4,1,4)(1,4,2,3)(1,4,3,2)(1,4,4,1)(1,5,1,3)(1,5,2,2)(1,5,3,1)(1,6,1,2)(1,6,2,1)
(2,1,1,6)(2,1,2,5)(2,1,3,4)(2,1,4,3)(2,1,5,2)(2,1,6,1)(2,2,1,5)(2,2,2,4)(2,2,3,3)(2,2,4,2)(2,2,5,1)(2,3,1,4)(2,3,2,3)(2,3,3,2)(2,3,4,1)(2,4,1,3)(2,4,2,2)(2,4,3,1)(2,5,1,2)(2,5,2,1)(2,6,1,1)
(3,1,1,5)(3,1,2,4)(3,1,3,3)(3,1,4,2)(3,1,5,1)(3,2,1,4)(3,2,2,3)(3,2,3,2)(3,2,4,1)(3,3,1,3)(3,3,2,2)(3,3,3,1)(3,4,1,2)(3,4,2,1)(3,5,1,1)
(4,1,1,4)(4,1,2,3)(4,1,3,2)(4,1,4,1)(4,2,1,3)(4,2,2,2)(4,2,3,1)(4,3,1,2)(4,3,2,1)(4,4,1,1)
(5,1,1,3)(5,1,2,2)(5,1,3,1)(5,2,1,2)(5,2,2,1)(5,3,1,1)
(6,1,1,2)(6,1,2,1) ------- Total 79
Combinations with all the numbers lie between 2 and 5 are (2,2,2,4)(2,2,3,3)(2,2,4,2)(2,3,2,3)(2,3,3,2)(2,4,2,2)(3,2,2,3)(3,2,3,2)(3,3,2,2)(4,2,2,2) ------Total 10
So probability=10/79
ANSWER:B
Answer: B
Question: If the area of a square with sides of length 4 centimeters is equal to the area of a rectangle with a width of 8 centimeters, what is the length of the rectangle, in centimeters?
Options:
A)4
B)8
C)2
D)16
E)18
Rationale: Let length of rectangle = L
4^2 = L*8
=> L = 16/8 = 2
Answer C
Answer: C
Question: If the sum of two numbers is 30 and the sum of their squares is 840, then the product of the numbers is
Options:
A)40
B)44
C)80
D)88
E)30
Rationale: Sol.
Let the numbers be x and y.
Then, (x+y) = 30 and x2 + y2 = 840.
Now, 2xy = (x+y)2 - (x2 + y2)
= (30)2 - 840= 900 - 840= 60
xy = 30.
Answer E
Answer: E
Question: The 40 parents participating in the Smithville PTA have been assigned to at least 1 of 3 committees: festival planning, classroom aid, and teacher relations. 21 parents are assigned to the festival planning committee, 18 parents are assigned to the classroom aid committee, and 19 parents are assigned to the teacher relations committee. If 5 parents are assigned to all 3 committees, how many parents are assigned to exactly 2 committees?
Options:
A)4
B)6
C)8
D)9
E)10
Rationale: The formula is Total = A+B+C - sum of exactly two + 2*all three + neither
21+18+19-x-2*5=40
solving for x you get 8
Answer C
Answer: C
Question: Write 330,000,000,000 in scientific notation
Options:
A)3.3 * 10 11
B)3.30 * 10 11
C)3.300 * 10 11
D)3.3000 * 10 11
E)30.3000 * 10 11
Rationale: a * 10 n , where a is a real number such that 1 * |a| < 10 and n is an integer.
330,000,000,000 = 3.3 * 100,000,000,000 = 3.3 * 10 11**
correct answer A
Answer: A
Question: If x + y = 13 and x – y = 3, then x^2 - y^2 =
Options:
A)-4
B)4
C)10
D)39
E)40
Rationale: The fastest approach has already been shown. Here's one more option.
Given:
x + y = 13
x – y = 3
Add the two equations to get: 2x = 16, which means x = 8
If x = 8, we can plug that value into either equation, to conclude that y = 5
If x = 8 and y = 5, then x² - y² = 39
Answer: D
Answer: D
Question: The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ Rs. 26.50 per metre is Rs. 6625, what is the length of the plot in metres?
Options:
A)333
B)250
C)288
D)276
E)1999
Rationale: Let length of plot = L meters, then breadth = L - 20 meters
and perimeter = 2[L + L - 20] = [4L - 40] meters
[4L - 40] * 26.50 = 6625
[4L - 40] = 6625 / 26.50 = 250
4L = 290
L = 240/4= 72.5 meters.
Answer: B
Answer: B
Question: $400 is divided amongst A,B and C so that A may get 2/3 as much as B and C together, B may get 6/9 as much as A and C together, then the share of A is
Options:
A)$100
B)$150
C)$160
D)$200
E)$250
Rationale: A:(B+C) = 2:3
A's share = 400*2/5 = $160
Answer is C
Answer: C
Question: In how many W ways can a four-letter password be chosen, using the letters A, B, C, D, E, and/or F, such that at least one letter is repeated within the password?
Options:
A)720
B)864
C)900
D)936
E)1,296
Rationale: Total number of four letter passwords = 6*6*6*6= 1296 ------(1)
Total number of passwords in which no letter repeats = 6C4*4!= 15*24=360------(2)
therefore required value W= (1)-(2)= 1296-360=936.D
Answer: D
Question: It is currently 8:12 PM. At what time in the morning was it exactly 205,106 minutes ago?
Options:
A)9:14
B)9:16
C)9:42
D)9:44
E)9:46
Rationale: Convert 205,106 minutes to hours by dividing by 60: 205,106/60 = 3,418 R26. That is 3,418 hours and 26 minutes. Convert 3,418 hours to days by dividing by 24: 3,418/24 = 142 R10. That is 142 days and 10 hours. Now, 142 days previous was 8:12 PM. Another 10 hours previous was 10:12 AM. Another 26 minutes previous was 9:46 AM (Subtract the 12 minutes of 10:12 from 26 to get 14. Then subtract 14 from 60 to get 46). E
Answer: E
Question: A sum of money becomes Rs 13,380 in 3 years and Rs 20,070 in 6 years at compound interest. The initial sum is?
Options:
A)Rs 8927
B)Rs 8922
C)Rs 89298
D)Rs 8920
E)Rs 8921
Rationale: Use the formula Amount = Principal Amount(1 + R/100)n
Where r is rate and t is time in years
=>13,380 = P(1+R/100)2 --(1)
=>20,070 = P(1+R/100)6 --(2)
=> 1.5 = (1+R/100)4
=> P = Rs 8920
ANSWER:D
Answer: D
Question: In a factory, an average of 50 TV's are produced per day for the fist 25days of the months. A few workers fell ill for the next 5days reducing the daily avg for the month to 48 sets/day . The average production per day for day last 5days is ?
Options:
A)20
B)36
C)48
D)38
E)59
Rationale: Production during these 5 days = Total production in a month - production in first 25 days.
= 30 x 48 - 25 x 50
= 190
∴ Average for last 5 days = 190 / 5
= 38
D
Answer: D
Question: A money lender lent a total of $1800 to two of his customers. He charged at the rate of 5%p.a. to one of them and 6% p.a. to the other. If he earned an average of 5.67% on $1800, how much did he lend to each of the two customers?
Options:
A)700; 1100
B)1200; 600
C)1000; 800
D)1200; 800
E)None of the above
Rationale: The method given above is the one given in the book.
However the method I used was
(1*x*5)/100 + (1800-x)*6/100 = 1800*5.67/100
Simplifying we get x=594
Though the actual answer is 600
ANSWER:B
Answer: B
Question: A brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 28 m * 2 m * 0.75 m?
Options:
A)28000
B)27908
C)78902
D)25000
E)27991
Rationale: 28 * 2 * 0.75 = 20/100 * 10/100 * 7.5/100 * x
28 = 1/100 * x => x
= 28000
Answer: A
Answer: A