mathewhe/aqua_rat huggingface dataset:
Question: If 70% of an equal to 40% of b, then ratio between a and b is?
(A) 4: 7
(B) 4: 9
(C) 4: 2
(D) 4: 1
(E) 4: 5
Rationale: Explanation:
70 a = 40 b
a: b = 4: 7
Answer:A
Answer: (A) 4: 7
Question: If 2/a + 3/a + 5/a is an integer, which of the following must also be an integer?
(A) 12/a
(B) 3/a
(C) 6/a
(D) 10/a
(E) 15/a
Rationale: 2/a + 3/a + 5/a
=10/a
Answer D
Answer: (D) 10/a
Question: The value of x + x(xx) when x = 2 is:
(A) 36
(B) 16
(C) 18
(D) 64
(E) 10
Rationale: x + x(xx)
Put the value of x = 2 in the above expression we get,
2 + 2(22)
= 2 + 2(2 × 2)
= 2 + 2(4)
= 2 + 8
= 10
Answer: (E) 10
Question: Two partners investede Rs. 1250 and Rs. 850 respectively in a business. They distributed 60% of the profit equally and decide to distribute the remaining 40% as the ratio of their capitals. If one partner received Rs. 30 more than the other, find the total profit?
(A) 393.75
(B) 393.78
(C) 393.72
(D) 393.71
(E) 393.77
Rationale: Let the total profit be Rs.x
60% of the profit = \inline \frac{60}{100}\times x=Rs.\frac{3x}{5}
from this part of the profit each gets = Rs.\inline \frac{3x}{10}
40% of the profit = \inline \frac{40}{100}\times x=Rs.\frac{2x}{5}
Now, this amount of Rs.\inline \frac{2x}{5} has been divided in the ratio of capitals 1250 : 850 = 25 :17
\inline \therefore Share on first capital = \inline (\frac{2x}{5}\times \frac{25}{42})=Rs.\frac{5x}{21}
Share on second capital = \inline (\frac{2x}{5}\times \frac{17}{42})=Rs.\frac{17x}{105}
Total money received by 1st investor = \inline [\frac{3x}{10}+\frac{5x}{21}]= Rs.\frac{113x}{210}
Total money received by 2nd investor = \inline [\frac{113x}{210}+\frac{97x}{210}]=Rs.\frac{97x}{210}
\inline \therefore x = 393.75
Hence total profit = Rs. 393.75
Answer:A
Answer: (A) 393.75
Question: What is the largest integer n such that 2^n is a factor of 20^8 ?
(A) 1
(B) 2
(C) 4
(D) 8
(E) 16
Rationale: 20^8=(2^2∗5)^8=2^16 5^8 Therefore the largest integer n such that 2^n is a factor of 2^165^8 is 16.
Answer: E.
Answer: (E) 16
Question: The difference between a number and its two-fifth is 510. What is 30% of that number?
(A) 158
(B) 200
(C) 255
(D) 400
(E) 280
Rationale: Let the number be x. Then,
x - 2/5 x = 510
x = (510 * 5)/3 = 850
10% of 850 = 255.
Answer:C
Answer: (C) 255
Question: By selling a house for Rs.45000, it was found that 1/8 of the outlay was gained, what ought the selling to price to have been in order to have lost 5 p.c?
(A) 28888
(B) 38000
(C) 28880
(D) 27752
(E) 11222
Rationale: CP + CP/8 = 45000
CP = 40000
SP = 40000*(95/100) = 38000
Answer: B
Answer: (B) 38000
Question: How many arrangements of the letters of the word GRADES can be made, without changing the place of the vowels in the word?
(A) 36
(B) 25
(C) 45
(D) 66
(E) 24
Rationale: A,E fixed. Consonants can be arrangements in 4P4 = 4! = 24 ways
Option 'E'
Answer: (E) 24
Question: The simple interest accrued on an amount of Rs.49500 at he end of three is Rs.17820. What would be the compound interest accured on the same amount at teh same rate in the same period? (Round off your answer to two decimal places?
(A) Rs.20043.94
(B) Rs.20043.99
(C) Rs.20043.95
(D) Rs.20043.98
(E) Rs.20043.91
Rationale: Let the rate of interest be R% p.a.
(49500)(3)(R)/100 = 17820
495R = 5940
R = 12
CI on Rs.49500 at 12% p.a. for three years
= 49500{[1 + 12/100]3 - 1} = 69543.936 - 49500 = Rs.20043.94
when rounded off to two decimal places.
Answer:A
Answer: (A) Rs.20043.94
Question: How many zeros does 500! end with?
(A) 201
(B) 240
(C) 124
(D) 125
(E) 180
Rationale: According to above 500! has 500/5+500/25+500/125=100+20+4=124 trailing zeros.
Answer: C.
Answer: (C) 124
Question: If the sides of a triangle are 36 cm, 34 cm and 20 cm, what is its area?
(A) 320 cm2
(B) 360 cm2
(C) 340 cm2
(D) 310 cm2
(E) 300 cm2
Rationale: The triangle with sides 36 cm, 34 cm and 20 cm is right angled, where the hypotenuse is 36 cm.
Area of the triangle
= 1/2 * 34 * 20
= 340 cm2
Answer: C
Answer: (C) 340 cm2
Question: Sachin can cover a distance in 1hr 24 min by covering 2/3 of the distance at 4 kmph and the rest at 5 kmph. The total distance is?
(A) 8 km
(B) 7 km
(C) 5 km
(D) 6 km
(E) 4 km
Rationale: dist travelled at 4 kmph speed = 2/3
dist at 5 kmph speed = (1-2/3)d=(1/3)d
tot time = 1 hr 24 min =(64+24) min=84/60hr=>21/15 hr
time = dist/speed
21/15=2/3/4d+1/3/5d
d=6 km
ANSWER D
Answer: (D) 6 km
Question: The length of the bridge, which a train 170 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) 388
(B) 267
(C) 205
(D) 288
(E) 261
Rationale: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (170 + X)/30 = 25/2 ==> 2(170 + X) = 750 ==> X = 205 m.
Answer: C
Answer: (C) 205
Question: The membership of a committee consists of 3 English teachers, 4 Mathematics teachers, and 3 Social Studies teachers. If 2 committee members are to be selected at random to write the committee’s report, what is the probability that the two members selected will both be English teachers?
(A) 2/3
(B) 1/3
(C) 2/9
(D) 1/12
(E) 1/24
Rationale: Probability of first member an English teacher = 3/10
Probability of second member an English teacher = 2/10
Probability of both being english teacher = 3/9 x 2/8 =3/5(D)
Answer: (D) 1/12
Question: An object travels at fifteen feet per minute. How many feet does it travel in 24 minutes and 40 seconds?
(A) 220
(B) 156
(C) 370
(D) 420
(E) 519
Rationale: Convert speed from feet/minute into feet/seconds.
15 feet / mn = 15 feet / 60 sec
In 24 minutes 40 seconds, there are
24*60 + 40 = 1480 seconds
We now multiply speed by time to find distance
1480*15/60 = 370 feet
correct answer C
Answer: (C) 370
Question: What is the are of an equilateral triangle of side 16 cm?
(A) 64√3
(B) 64√5
(C) 64√9
(D) 64√2
(E) 64√1
Rationale: Area of an equilateral triangle = √3/4 S2
If S = 16, Area of triangle = √3/4 * 16 * 16
= 64√3 cm2;
Answer:A
Answer: (A) 64√3
Question: The least number of complete years in which a sum of money put out at 20% C.I. will be more than doubled is?
(A) 5
(B) 4
(C) 7
(D) 1
(E) 2
Rationale: P(1 + 20/100)n > 2P or (6/5)n > 2
Now, (6/5 * 6/5 * 6/5 * 6/5) > 2. So, n
= 4 years.
Answer:B
Answer: (B) 4
Question: Given that there are 11 cricket players per team, how many ways can you select 10 cricket players from 2 teams if no more than 7 players can be selected from each team?
(A) 108900
(B) 457845
(C) 145256
(D) 356586
(E) 213444
Rationale: Now from each group we have to select 5 persons only: 11C7 * 11C7= 330 * 330 = 108900
Total ways=108900 ways.
Answer A
Answer: (A) 108900
Question: A, B and C can do a work in 8 days, 8 days and 12 days respectively. In how many days can all three of them working together, complete the work?
(A) 3
(B) 2 2/8
(C) 2 2/0
(D) 2 2/2
(E) 2 2/1
Rationale: Work done by all three of them in one day = 1/8 + 1/8 + 1/12 = 1/3
The number of days required = 3 days.
Answer:A
Answer: (A) 3
Question: A boat goes 100 km downstream in 10 hours, and 75 m upstream in 15 hours. The speed of the stream is?
(A) 22 1/9
(B) 22 1/7
(C) 22 1/1
(D) 22 1/2
(E) 32 1/2
Rationale: 100 --- 10 DS = 10
? ---- 1
75 ---- 15 US = 5
? ----- 1 S = (10 - 5)/2
= 22 1/2 kmph.Answer:D
Answer: (D) 22 1/2
Question: Two stations A and B are 110 km apart on a straight line. One train starts from A at 2 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
(A) 15 a.m
(B) 10 a.m
(C) 12 a.m
(D) 02 a.m
(E) 05 a.m
Rationale: Suppose they meet x hours after 2 a.m.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x - 1) hours = 25(x - 1) km.
Therefore 20x + 25(x - 1) = 110
45x = 135
x = 3.
So, they meet at 5 a.m.
Answer:E
Answer: (E) 05 a.m
Question: If the average (arithmetic mean) of five consecutive negative integers is 4k – 1, what is the difference between the greatest and least of the five integers?
(A) 4K
(B) 4k^2 -4k
(C) 4-4k
(D) 4
(E) 4k+4
Rationale: (n-2 + n - 1 + n + n + 1 + n + 2)/5 = 4k - 1
=> n = 20k - 5
Greatest = n + 2 = 20k - 5 + 2 = 20k - 3
Least = n - 2 = 20k - 5 - 2
=> Difference = 20k - 3 - (20k - 7)
= 4
Answer - D
Answer: (D) 4
Question: How long does a train 120 meters long running at the rate of 54 kmph take to cross a bridge 660 meters in length?
(A) 33
(B) 72
(C) 52
(D) 82
(E) 62
Rationale: Explanation:
T = (660 + 120)/54 * 18/5
T = 52
Answer: Option C
Answer: (C) 52
Question: There are a total of 10 students in Mr. Schmidt's gym class. Over the course of a badminton unit, each of the 10 students will compete exactly once against every other student in the class. How many total games of badminton will be played?
(A) 48
(B) 47
(C) 45
(D) 41
(E) 46
Rationale: there are 10 students , if each play with all other members .
then total games can be calculated as 9+8....+1 = 45.
alternate approach is to choose 2 distinct out of 10 = 10c2 = 45
Answer is C.
Answer: (C) 45
Question: What is x if x + 5y = 24 and y = 2?
(A) 1
(B) 3
(C) 5
(D) 7
(E) 14
Rationale: Substitute y by 2 in x + 5y = 24
x + 5(2) = 24
x + 10 = 24
If we substitute x by 14 in x + 10 = 24, we have 14 + 10 = 24. Hence
x = 14 correct answer E
Answer: (E) 14
Question: In a race of 400 m, A can beat B by 40 m and C by 20 m. In how many meter race, C will beat B by 50m ?
(A) 1000m
(B) 1200m
(C) 800m
(D) 950m
(E) 600m
Rationale: Explanation:
A:B = 400 : 360
A:C = 400 : 380
=>B:C = 360:380 = 18:19
When C covers 380 m , B Covers 360 m
When C covers x m , B Covers
=> x - 50 m
18x/19 = x - 50
x = 950 m
Answer: D
Answer: (D) 950m
Question: The population of a town increases 22% and 25% respectively in two consecutive years. After the growth the present population of the town is 1220. Then what is the population of the town 2 years ago?
(A) A)600
(B) B)700
(C) C)800
(D) D)900
(E) E)1000
Rationale: Explanation:
Formula: (After =100 denominator
Ago = 100 numerator)
1220 * 100/122 * 100/125 = 800
Answer: Option C
Answer: (C) C)800
Question: Find large number from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder
(A) 1245
(B) 1435
(C) 2345
(D) 3543
(E) 1635
Rationale: Let the smaller number be x. Then larger number = (x + 1365).
x + 1365 = 6x + 15
5x = 1350
x = 270
Large number = 270+1365 = 1635
E
Answer: (E) 1635
Question: During a trip on an expressway, Kon drove a total of x miles. His average speed on a certain 5-mile section of the expressway was 30 miles per hour, and his average speed for the remainder of the trip was 60 miles per hour. His travel time for the x-mile trip was what percent greater than it would have been if he had traveled at a constant rate of 60 miles per hour for the entire trip?
(A) 8.5%
(B) 50%
(C) x/12%
(D) 60/x%
(E) 500/x%
Rationale: so Kon drove (x-5) miles at 60mph and 5 miles at 30mph:
(x-5)/60 + (10/60) = (X+5)/60 - current time to drive the whole distance
if the entire trip @60mph than time = x/60
so to get percent [(X+5)/60 ]/[x/60] x100
=(x+5)/x *100
=100+500/x
so increase of 500/x%[/u]=E
Answer: (E) 500/x%
Question: If 30!/10! is written as the product of consecutive integers, the largest of which is 30, what is the smallest of the integers?
(A) 1
(B) 3
(C) 7
(D) 11
(E) 20
Rationale: 30!/10!=30∗29∗28...........11∗10!/10!
Smallest integer = 11
Answer = D
Answer: (D) 11
Question: How many 3-digit integers between 100 and 200 have a digit that is the average (arithmetic mean) of the other 2 digits?
(A) 1
(B) 7
(C) 9
(D) 11
(E) 19
Rationale: Since the number is between 100 and 200, the hundreds digit has to be 1.
And since the answer choices are small enough, it won't hurt just to write them out. 102, 111, 120, 123, 132, 135, 147, 153, 159, 174, 195.
Answer D
Answer: (D) 11
Question: A sells a bicycle to B at a profit of 20%. B sells it to C at a profit of 25%. If C pays Rs. 225 for it, the cost price of the bicycle for A is
(A) 627
(B) 297
(C) 127
(D) 150
(E) 181
Rationale: Explanation:
125% of 120% of A = 225
125/100 * 120/100 * A = 225
A = 225 * 2/3 = 150.
Answer: D
Answer: (D) 150
Question: Ramu bought an old car for Rs. 40000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent?
(A) 12%
(B) 16%
(C) 18%
(D) 82%
(E) 22.45%
Rationale: Total CP = Rs. 40000 + Rs. 13000 = Rs. 53000 and SP
= Rs. 64900
Profit(%) = (64900 - 53000)/53000 * 100
= 22.45%
Answer:E
Answer: (E) 22.45%
Question: If x, y, and z are positive integers and x = 4y = 7z, then the least possible value of x - y - z is
(A) 33
(B) 17
(C) 49
(D) 16
(E) 23
Rationale: x - y - z = x - x/4 - x/7
= (28 - 7 - 4 )x/28 = 17x/28
17 is not divisible by 28(it's a prime #), so for least value, x = 28
Answer - B
Answer: (B) 17
Question: If 3 persons can do 3 times of a particular work in 3 days, then, 7 persons can do 7 times of that work in
?
(A) 3 days
(B) 7 days
(C) 9 days
(D) 11 days
(E) 15 days
Rationale: That is, 1 person can do one time of the work in 3 days.
Therefore, 7 persons can do 7 times work in the same 3 days itself.
Option 'A'
Answer: (A) 3 days
Question: Insert the missing number. 2, 7, 10, 22, 18, 37, 26
(A) 42
(B) 32
(C) 52
(D) 62
(E) 50
Rationale: There are two series here
2, 10, 18, 26, ... (Increase by 8)
7, 22, 37, ... (Increase by 15)
Hence, next term is 37+15 = 52
Answer is C.
Answer: (C) 52
Question: What is the total number of positive integers that are less than 800 and that have no positive factor in common with 800 other than 1?
(A) 200
(B) 320
(C) 480
(D) 500
(E) 600
Rationale: Since 800=2^5*5^2 then a number can not have 2 and/or 5 as a factor.
The odd numbers do not have 2 as a factor and there are 400 odd numbers from 1 to 800.
We then need to eliminate the 80 numbers that end with 5, that is 5, 15, 25,...,795.
There are a total of 400 - 80 = 320 such numbers between 1 and 800.
The answer is B.
Answer: (B) 320
Question: Eighteen years ago, a father was three times as old as his son. Now the father is only twice as old as his son. Then the sum of the present ages of the son and the father is
(A) 54.
(B) 72
(C) 105
(D) 108
(E) None
Rationale: Solution
Let the present ages of Father and Son be 2x years and x years respectively.
Then	(2x-18)=3(x-18)
2x-18=3x-54
x=54-18
x=36.
Required sum	= (2x+x)
=3x
=3x36
=108 years.
Answer D
Answer: (D) 108
Question: The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 900 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?
(A) 140 sq.units
(B) 120 sq.units
(C) 187 sq.units
(D) 607 sq.units
(E) 815 sq.units
Rationale: Given that the area of the square = 900 sq.units
=> Side of square = √900 = 30 units
The radius of the circle = side of the square = 30 units
Length of the rectangle = 2/5 * 30 = 12 units
Given that breadth = 10 units
Area of the rectangle = lb = 12 * 10 = 120 sq.units
Answer: B
Answer: (B) 120 sq.units
Question: Twenty-four men can complete a work in sixteen days. Thirty-two women can complete the same work in twenty-four days. Sixteen men and sixteen women started working and worked for twelve days. How many more men are to be added to complete the remaining work in 2 days?
(A) 48
(B) 24
(C) 36
(D) 16
(E) None of the above
Rationale: 24 men complete the work in 16 days
∴ 16 men complete (16⁄24 × 12⁄16) = 1⁄2 part of work in 12 days
32 women complete the work in 24 days
∴ 16 women complete 16⁄32 × 14⁄24) = 7⁄24 part of work in (12 + 2 ) = 14 days
So, the remaining part of the work which is done by sixteen men + sixteen women and the reqd additional no. of men in 2 days
= 1 - (1⁄2 + 7⁄24) = 1⁄2 - 7⁄24 = 5⁄24 (part)
Now, in 2 days 5⁄24 part of the work is done by
24 × 16⁄2 × 5⁄24 = 40 men
Hence, the reqd. additional no. of men
= 40 – 16 = 24 men.
Answer B
Answer: (B) 24
Question: In a shop, the cost of 4 shirts, 4 pairs of trousers and 2 hats is $560. The cost of 9 shirts, 9 pairs of trousers and 6 hats is $1,290. What is the total cost of 1 shirt, 1 pair of trousers and 1 hat?
(A) $150
(B) $545
(C) $214
(D) $332
(E) $199
Rationale: Let x be the price of one shirt, y be the price of one pair of trousers and z be the price of one hat.
4x + 4y + 2z = 560 :
9x + 9y + 6z = 1,290
3x + 3y + 2z = 430 : divide all terms of equation C by 3
x + y = 130 : subtract equation D from equation B
3(x + y) + 2z = 430 : equation D with factored terms.
3*130 + 2z = 430
z = 20 : solve for z
x + y + z = 130 + 20 = $150
correct answer A
Answer: (A) $150
Question: If Ryan has 20% more notebook than justin.and Ryan have 18 notebook then Justin have how many notebooks?
(A) 16
(B) 14
(C) 12
(D) 15
(E) 10
Rationale: lets Justin have x notebook.
(18-x)*100/x=20
1800-100x=20x
120x=1800
x=1800/120
x=15
answer D
Answer: (D) 15
Question: In a recent survey at a local deli, it was observed that 3 out of 5 customers bought a bagel and 5 out of 7 customers bought a coffee. Some customers bought both. If 6 customers are selected, what are the chances that at least 1 customer bought a coffee and a bagel?
(A) 27/343
(B) 3/7
(C) 27/125
(D) 776/965
(E) 9/125
Rationale: Let us take 7*5=35 as the total number of customers. So 7*3=21 customers bought a bagel and 5*5=25 customers bought a coffee.
chances that at least 1 customer bought a coffee and a bagel = 1 - chances that no customer bought a coffee and a bagel
chances that no customer bought a coffee and a bagel= 24/35*23/34*22/33*21/32*20/31*19/30=189/965
chances that at least 1 customer bought a coffee and a bagel= 1 -189/965 = 776/965
Answer D.
Answer: (D) 776/965
Question: A can do a piece of work in 10 days, B in 15 days. They work for 5 days. The rest of work finished by C in 2 days. If they get Rs 1500 for the whole work, the daily wages of B and C are?
(A) 275
(B) 250
(C) 225
(D) 300
(E) 335
Rationale: Part of work done by A = 5/10 = 1/2
Part of work done by B = 1/3
Part of work done by C = (1- (1/2 + 1/3)) = 1/6
A’s share : B’s share : C’s share = 1/2 : 1/3 : 1/6 = 3 : 2 : 1.
A’s share = (3/6) x 1500 = 750
B’s share = (2/6) x 1500 = 500
C’s share = (1/6) x 1500 = 250
A’s daily wages = 750/5 = 150/-
B’s daily wages = 500/5 = 100/-
C’s daily wages = 250/2 = 125/-
Daily wages of B & C = 100 + 125 = 225/-
ANSWER:C
Answer: (C) 225
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are picked at random, what is the probability that they are either blue or yellow?
(A) 2/29
(B) 2/20
(C) 2/21
(D) 2/28
(E) 2/23
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability that both marbles are blue = ³C₂/¹⁵C₂ = (3 * 2)/(15 * 14) = 1/35
Probability that both are yellow = ²C₂/¹⁵C₂
= (2 * 1)/(15 * 14) = 1/105
Probability that one blue and other is yellow
= (³C₁ * ²C₁)/¹⁵C₂ = (2 * 3 * 2)/(15 * 14)
= 2/35
Required probability = 1/35 + 1/105 + 2/35
= 3/35 + 1/105 = 1/35(3 + 1/3)
= 10/(3 * 35)
= 2/21
Answer:C
Answer: (C) 2/21
Question: A rectangular field is to be fenced on three sides leaving a side of 80 feet uncovered.If the area of the field is 680 sq.ft, how many feet of fencing will be required?
(A) 44ft
(B) 97ft
(C) 22ft
(D) 11ft
(E) 66ft
Rationale: Given that length and area, so we can find the breadth.
Length x Breadth = Area
80 x Breadth = 680
Breadth = 8.5 feet
Area to be fenced = 2B + L = 2 (8.5) + 80 = 97 feet
Answer: B) 97ft
Answer: (B) 97ft
Question: How many 8 ′ s are there in the given sequence which are not immediately preceded by 09 and not immediately followed by 90?
9 0 8 0 9 0 9 8 9 0 8 9 0 8 0 9 8 9 0 9 8 0 9 8 9 0 8 9 0
(A) 3
(B) 1
(C) 2
(D) More than 3
(E) None of these
Rationale: the given logic is executed 3 times for 8's occuring at 2nd eight,5th eight and 7th eight in the sequence.
ANSWER:A
Answer: (A) 3
Question: The factorial expression 11!/2! is not divisible by which of the following integers?
(A) 3
(B) 5
(C) 6
(D) 7
(E) None of these
Rationale: 11!/2! => 11 x 10 x 9 x 8x7x6x5x4x3
(A) 3 Can divide 3,12 or 9
(B) 5 Can divide 10
(C) 6 Can divide 12
(D) 7 can divide 7, 21, 42
Hence answer will be (E)
Answer: (E) None of these
Question: A product when sold with 10% rebate on the listed price gave a profit of Rs.70. What was its cost price?
(A) Rs. 200
(B) Rs. 250
(C) Rs. 300
(D) Cannot be determined
(E) None
Rationale: Solution
Since the marked price is not given, so the cost price cannot be determined.
Answer D
Answer: (D) Cannot be determined
Question: The cash difference between the selling prices of an book at a profit of 12% and 20% is $3. The ratio of the two selling prices is:
(A) 55:23
(B) 52:33
(C) 52:53
(D) 45:53
(E) 14:15
Rationale: Let C.P. of the book be $x.
Then, required ratio = 112% of x / 120% of x
= 112/120 = 14/15 = 14:15
E
Answer: (E) 14:15
Question: Find the result of equation of the ellipse whose foci are at (0 , -5) and (0 , 5) and the length of its major axis is 14.
(A) 5
(B) 4
(C) 3
(D) 2
(E) 1
Rationale: From the coordinates of the foci, c = 5 and the major axis is the y axis. From the length of the major axis, we obtain a = 7. Also b 2 = a 2 - c 2 = 24.
The equation of the ellipse is given by
x 2 / 24 + y 2 / 49 = 1
correct answer is E) 1
Answer: (E) 1
Question: The average of first 10 natural numbers is?
(A) 5.7
(B) 5.5
(C) 5.6
(D) 5.4
(E) 5.2
Rationale: Sum of 10 natural no. = 110/2 = 55
Average = 55/10 = 5.5
Answer: B
Answer: (B) 5.5
Question: If 18 bindres bind 900 books in 10 days , How many binders will be required to bind 660 books in 12 days?
(A) 17
(B) 77
(C) 12
(D) 11
(E) 91
Rationale: Explanation:
Let the required no of binders be X.
Less books , Less binders (Direct Proportion)
More days, Less binders (Indirect proportion)
\inline \fn_jvn \left.\begin{matrix} Books\: 900:600\\ Days\: \: 12:10 \end{matrix}\right\}::18:x
\inline \fn_jvn \therefore \inline \fn_jvn (900\times 12\times x)=(600\times 10\times 18) \inline \fn_jvn \Leftrightarrow x= \inline \fn_jvn \frac{600\times 10\times 18}{900\times 12} = 11
Answer: D
Answer: (D) 11
Question: In the line xy plane line m has the equation y = 3x - 3, then the line m passes through which of the following points?
(A) (3, 1)
(B) (3, 4)
(C) (4, 2)
(D) (6, 9)
(E) (6, 15)
Rationale: Yes it is y=3x-8....extremely sorry for mistake....
IF that's the case then answer is E
y=3x-8
15=3X6-3
15=18-3
15=15 (satisfied)
Answer: (E) (6, 15)
Question: How many Books each of Volume 100 meter cube can be packed into a crate of volume 3000 meter cube?
(A) 50
(B) cannot be determined
(C) 150
(D) 300
(E) 350
Rationale: Gud question with a simple concept.
In geo if we want to insert one shape into another we need to know the dimensions of the two shapes.
In above with volume given , we can come up with different shapes, so we cant know the answer
For ex :3000 m3 can be 300*10 or 30*100 or just 3000*1 we don't know , so we cant calculate
Answer : B
Answer: (B) cannot be determined
Question: The average of 6 observations is 16. A new observation is included and the new average is decreased by 1. The seventh observation is?
(A) 1
(B) 3
(C) 9
(D) 6
(E) 7
Rationale: Let seventh observation = X.
Then, according to the question we have
=> (96 + X) / 7 = 15
=> X = 9
Hence, the seventh observation is 9.
ANSWER:C
Answer: (C) 9
Question: A zoo has an average of 510 visitors on Sundays and 480 on Saturday, 210 on other days and Wednesday is holiday. The average number of visitors in a month of 30 days starting with Saturday is
(A) 252
(B) 268
(C) 277
(D) 295
(E) 310
Rationale: Number of saturdays and sundays in that month is 5 and number of wednesdays in that month is 4.
Total number of visitors=(510x5)+(480x5)+((20-4)x210)=8310
Average visitor per day= 8310/30 = 277
Answer: C
Answer: (C) 277