mathewhe/aqua_rat huggingface dataset:
Question: A, B and C started a business with capitals of Rs. 8000, Rs. 10000 and Rs. 12000 respectively. At the end of the year, the profit share of B is Rs. 1500. The difference between the profit shares of A and C is?
(A) 200
(B) 929
(C) 400
(D) 600
(E) 832
Rationale: Ratio of investments of A, B and C is 8000 : 10000 : 12000 = 4 : 5 : 6
And also given that, profit share of B is Rs. 1500
=> 5 parts out of 15 parts is Rs. 1500
Now, required difference is 6 - 4 = 2 parts
Required difference = 2/5 (1500) = Rs. 600
Answer:D
Answer: (D) 600
Question: The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is?
(A) 6.99%
(B) 6.89%
(C) 6.08%
(D) 6.09%
(E) 6.19%
Rationale: Amount of Rs. 100 for 1 year when compounded half-yearly
= [100 * (1 + 3/100)2]
= Rs. 106.09 Effective rate
= (106.09 - 100) = 6.09%
Answer:D
Answer: (D) 6.09%
Question: Firm A's revenues are described by the equation Ra = 17.12x and its costs by Ca = 12.87x + 2400.
Firm B's revenues are described by the equation Rb = 13.27x and its costs by Cb = 8.77x + 1500.
(x denotes the quantity of sales).
If A's volume of sales increases from 1000 to 3000 over the same period that B's volume increases from 2000 to 3000, the percent increase in profits for the firm with the biggest dollar increase in profits is
(A) 20%
(B) 30%
(C) 60%
(D) 50%
(E) 33%
Rationale: Ok, I do not know whether it is exactly what you want to hear but I did it that way: first look at difference between revenue and variable cost => take the bigger one (b) which gives you: 4.5x-1500 just plug in 2000 and 3000. you get 7500 and 12000 (difference 4500). 4500> 0.5*7500 so 30%
B
Answer: (B) 30%
Question: How many multiples of 4 are less than 6540, and also multiples of 7?
(A) 234
(B) 208
(C) 340
(D) 237
(E) 267
Rationale: LCM of 4 & 7 = 28
Tried dividing 6540 by 28
Got quotient 233.5'So A is answer
Answer: (A) 234
Question: In a 150 member association consisting of men and women, exactly 10% of men and exactly 20 % women are homeowners. What is the least number of members who are homeowners?
(A) 22
(B) 21
(C) 20
(D) 19
(E) 18
Rationale: Solution simple
Out of 150 10% are male i.e 15 and 20% are female i.e 30 , so total homeowner is 45.
Now min number homeowner is 15 and max is 30 so question ask us to find least and 18 has least value among all option.
So ans is 18.
Ans: E
Answer: (E) 18
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) 6
(B) 5
(C) 4
(D) 7
(E) 9
Rationale: 7 * 8 : 9 * x = 8:9 => x= 7
Answer: D
Answer: (D) 7
Question: A cricketer has a certain average for 10 innings. In the eleventh inning, he scored 108 runs, there by increasing his average by 5 runs. His new average is:
(A) 50 runs
(B) 58 runs
(C) 56 runs
(D) 59 runs
(E) 62 runs
Rationale: Let average for 10 innings be x. Then,
(10x + 108)/11 = x + 5
= 11x + 55 = 10x + 108
= x = 53.
New average = (x + 5) = 58 runs.
Answer:B
Answer: (B) 58 runs
Question: An urn contains 15 black and 5 white balls. Two balls are drawn from the urn one after the other
without replacement. What is the probability that both drawn balls are black?
(A) 1/5
(B) 3/7
(C) 2/5
(D) 3/5
(E) 21/38
Rationale: Let E and F denote respectively the events that first and second ball drawn
are black. We have to find P(E n F) or P (EF).
Now P(E) = P (black ball in first draw) = 15/20
Also given that the first ball drawn is black, i.e., event E has occurred, now there are 14 black balls and five white balls left in the urn. Therefore, the probability that the second ball drawn is black, given that the ball in the first draw is black, is nothing but the conditional probability of F given that E has occurred.
That is P(F|E) = 14/19
By multiplication rule of probability, we have
P (E n F) = P(E) P(F|E)
= 15/20 × 14/19 = 21/38
E
Answer: (E) 21/38
Question: If n is a prime number greater than 17, what is the remainder when n^2 is divided by 12 ?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 5
Rationale: There are several algebraic ways to solve this question, but the easiest way is as follows:since we cannot have two correct answers just pick a prime greater than 17, square it and see what would be the remainder upon division of it by 12.
n=19 --> n^2=361 --> remainder upon division 361 by 12 is 1.
Answer: B.
Answer: (B) 1
Question: The length of a rectangular floor is more than its breadth by 500%. If Rs. 324 is required to paint the floor at the rate of Rs. 6 per sq m, then what would be the length of the floor?
(A) 24.6m.
(B) 23.4m.
(C) 22.5m.
(D) 23.8m.
(E) 25.5m.
Rationale: Let the length and the breadth of the floor be l m and b m respectively.
l = b + 500% of b = l + 5b = 6b
Area of the floor = 324/6 = 54 sq m
l b = 54 i.e., l * l/6 = 108
l2 = 648 => l = 25.5m.
ANSWER:E
Answer: (E) 25.5m.
Question: Anmol can eat 27 pastries in a hour.
Aakriti can eat 2 pastries in 10 minutes.
Divya can eat 7 pastries in 20 minutes.
How long will it take them to eat a 240 pastries ?
(A) 2 hours.
(B) 1 hours.
(C) 5 hours.
(D) 4 hours.
(E) 3 hours.
Rationale: In one hour, Anmol eats 27 pastries, Aakriti eats 12, and Divya eats 21. A total of 60 pastries. Therefore 240 pastries would take 240 ÷ 60 = 4 hours.
ANSWER D
Answer: (D) 4 hours.
Question: How many different 3 digit numbers can be formed from the number 891 by re-arranging its digits so that the odd digits occupy even position
(A) 5
(B) 2
(C) 8
(D) 7
(E) 6
Rationale: There are 2 odd numbers which have to be placed at 2 even places =2!=2 ways
There are 1 even numbers which have to be placed at 1 odd places. So 1! = 1 ways
so total number of ways of arranging all these numbers are 1 * 2 = 2 ways
Answer:B
Answer: (B) 2
Question: Two sets A and B consists only of positive integers such that mean of set A is 55 . If set R consist of all the elements of both A and B such that mean of R is 80 then the mean of set B is =>
(A) [A] 65
(B) [B] 60
(C) [C] 70
(D) [D] 55
(E) [E] cannot be determined
Rationale: For this question, we have zero information about the size of two sets, sets AB. These two sets may have the same size or may be wildly different. Thus, the answer is (E), the mathematical answer cannot be determined. This is a very weak math question. As someone who writes GMAT practice questions, I would give this a grade of anD-as a question.
Answer E
Answer: (E) [E] cannot be determined
Question: What decimal of an hour is a second ?
(A) .0025
(B) .0256
(C) .00027
(D) .000126
(E) None of these
Rationale: Explanation:
Required decimal =	1=	1= .00027
60 x 60=3600
Answer- C
Answer: (C) .00027
Question: A store owner estimates that the average price of type A products will increase by 35% next year and that the price of type B products will increase by 10% next year. This year, the total amount paid for type A products was $4500 and the total price paid for type B products was $8300. According to the store owner's estimate, and assuming the number of products purchased next year remains the same as that of this year, how much will be spent for both products next year?
(A) $14,755
(B) $15,205
(C) $16,000
(D) $16,225
(E) $17,155
Rationale: cost of type A products next year = 1.35 * 4500 = 6075
cost of type B products next year = 1.1 * 8300 = 9130
total 6075 + 9130 = 15205 option B
Answer: (B) $15,205
Question: Average of five numbers is 27. If one number is excluded the average becomes 25. The excluded
number is
(A) 35
(B) 45
(C) 55
(D) 65
(E) 75
Rationale: Explanation:
Number is (5*27) - (4*25) = 135-100 = 35
Answer: Option A
Answer: (A) 35
Question: A gambler bought $3,000 worth of chips at a casino in denominations of $20 and $100. That evening, the gambler lost 13 chips, and then cashed in the remainder. If the number of $20 chips lost was 3 more or 3 less than the number of $100 chips lost, what is the largest amount of money that the gambler could have received back?
(A) $2,040
(B) $2,120
(C) $2,240
(D) $1,920
(E) $1,400
Rationale: In order to maximize the amount of money that the gambler kept, we should maximize # of $20 chips lost and minimize # of $100 chips lost, which means that # of $20 chips lost must be 2 more than # of $100 chips lost.
So, if # of $20 chips lost is x then # of $100 chips lost should be x-2. Now, given that total # of chips lost is 13: x+x-3=13 --> x=8: 8 $20 chips were lost and 8-2=6 $100 chips were lost.
Total worth of chips lost is 8*20+6*100=$760, so the gambler kept $3,000-$760=$2,240.
Answer: C.
Answer: (C) $2,240
Question: An article is bought for Rs.675 and sold for Rs.900, find the gain percent?
(A) 33 1/8%
(B) 33 8/3%
(C) 33 1/3%
(D) 35 1/3%
(E) 32 1/3%
Rationale: 675 ---- 225
100 ---- ? => 33 1/3%
Answer: C
Answer: (C) 33 1/3%
Question: The measures of the 2 acute angles of a triangle are in the ratio of 2:7. What are the measures of the 2 angles?
(A) 40°
(B) 70°
(C) 80°
(D) 100°
(E) 180°
Rationale: If the ratio of the two angles is 2:7, then the measures of two angles can be written as 2x and 7x. Also the two acute angles of a triangle is equal to 90°. Hence
2x + 7x = 90
9x = 90
x = 10
Measures of the two acute angles are
2x = 2 × 10 = 20°
7x = 7 × 10 = 70°
B
Answer: (B) 70°
Question: Find the area of a parallelogram with base 22 cm and height 14 cm?
(A) 298 cm2
(B) 384 cm2
(C) 308 cm2
(D) 286 cm2
(E) 276 cm2
Rationale: Area of a parallelogram = base * height = 22 * 14
= 308 cm2
Answer:C
Answer: (C) 308 cm2
Question: Find √? /20 = 4 ?
(A) 76
(B) 6400
(C) 304
(D) 1296
(E) None
Rationale: Answer
Let √N/20= 4
Then √N = 20 x 4 = 80
∴ N = 80 x 80= 6400.
Correct Option: B
Answer: (B) 6400
Question: 24 oz of juice P and 25 oz of juice V are mixed to make smothies M and Y . The ratio of p to V in smothie M is 4 is to 1 and that in Y is 1is to 5.How many ounces of juice P are contained in the smothie M?
(A) 5
(B) 10
(C) 15
(D) 20
(E) 25
Rationale: The ratio of p to V in smothie M is 4 is to 1 and that in Y is 1is to 5.p1 + p2 = 24
v1 + v2 = 25
p1 = 4v1
p2 = v2/5
4v1 + v2/5 = 24
v1 + v2 = 25
4v2 - v2/5 = 76
19v2/5 = 76 => v2 = 20
=> v1 = 5
=> p1 = 20
Answer - D
Answer: (D) 20
Question: If n = 30! + 27, then n is divisible by which of the following?
I. 25
II. 27
III. 29
(A) None
(B) I only
(C) II only
(D) I and II
(E) II and III
Rationale: 27 divides 30! so 27 also divides 30! + 27.
25 and 29 divide 30! so they do not divide 30! + 27.
The answer is C.
Answer: (C) II only
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 6400 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) 320 sq.units
(C) 367sq.units
(D) 178sq.units
(E) 176sq.units
Rationale: Given that the area of the square = 6400 sq.units
=> Side of square = √6400 = 80 units
The radius of the circle = side of the square = 80 units Length of the rectangle = 2/5 * 80 = 32 units
Given that breadth = 10 units
Area of the rectangle = lb = 32 * 10 = 320 sq.units
Answer:B
Answer: (B) 320 sq.units
Question: The least number,which when divided by 48,60,72,108 and 140 leaves 38,50,62,98 and 130 as remainder respectively, is :
(A) 11115
(B) 15110
(C) 15120
(D) 15210
(E) 12510
Rationale: Solution
Here (48 - 38) = 10 , (60 - 50) = 10,(72 - 62) = 10,(108 - 98) = 10 & (140 - 130) = 10.
So, Required number = (L.C.M. of 48,60,72,108,140) - 10 = 15120 - 10 = 15110. Answer B
Answer: (B) 15110
Question: A buffet costs rs300. owner reduced the price 20% less. he got profit of 25% on its revenue. what is the percentage increase in number of customers?
(A) 56%
(B) 57%
(C) 58%
(D) 45%
(E) 35%
Rationale: let assume he sells 1 buffet daily,
now
then 300*1 = revenue (eq -1)
if he reduced his price by 20% then ,
240*(customer) = 125/100*revenue
customer = 1.25*300/240 = 1.56
means 56 % increase in customer.
ANSWER:A
Answer: (A) 56%
Question: The population of a village is 10000. It increases annually at the rate of 20% p.a. What will be its population after 2 years?
(A) 10000
(B) 12000
(C) 13000
(D) 14000
(E) 14400
Rationale: Formula :
( After =100 denominator
Ago = 100 numerator)
10000 × 120/100 × 120/100 = 14400
E
Answer: (E) 14400
Question: For any integer k greater than 1, the symbol k* denotes the product of all the fractions of the form 1/t, where t is an integer between 1 and k, inclusive. What is the value of 5*/6* ?
(A) 5
(B) 5/4
(C) 4/5
(D) 1/4
(E) 1/5
Rationale: When dealing with 'Symbolism' questions, it often helps to 'play with' the Symbol for a few moments before you attempt to answer the question that's asked. By understanding how the Symbol 'works', you should be able to do the latter calculations faster.
Here, we're told that K* is the PRODUCT of all the fractions of the form 1/T, where T is an integer between 1 and K, inclusive.
Based on this definition....
IF....
K = 2
K* = (1/1)(1/2) = 1/2
IF....
K = 3
K* = (1/1)(1/2)(1/3) = 1/6
We're asked to find the value of 5*/4*
Now that we know how the Symbol 'works', solving this problem shouldn't be too difficult. You can actually choose to do the math in a couple of different ways....
5* = (1/1)(1/2)(1/3)(1/4)(1/5)
Don't calculate this just yet though....since we're dividing by 4*, many of those fractions will 'cancel out.'
4* = (1/1)(1/2)(1/3)(1/4)
We're looking for the value of:
(1/1)(1/2)(1/3)(1/4)(1/5) / (1/1)(1/2)(1/3)(1/4)
Since the first four fraction in the numerator and denominator cancel out, we're left with just one fraction:
1/4
D
Answer: (D) 1/4
Question: A man can row upstream at 25 kmph and downstream at 41 kmph, and then find the speed of the man in still water?
(A) 33
(B) 67
(C) 30
(D) 15
(E) 17
Rationale: US = 25
DS = 41
M = (41 + 25)/2
= 33
Answer: A
Answer: (A) 33
Question: Let the polynomials be:
P1(x)=3x2−7x+4,
P2(x)=−5x2−4x+2,
P1(x)+P2(x)=
(A) 2x2 + 11x - 7
(B) -2x2 - 11x + 6
(C) -2x2 - 11x + 6
(D) 2x2 - 9x + 7
(E) None of these
Rationale: Solution:
P1(x)+P2(x)=(3x2−7x+4)+(−5x2−4x+2)=P1(x)+P2(x)=(3x2−7x+4)+(−5x2−4x+2)=
3x2−7x+4−5x2−4x+2=3x2−7x+4−5x2−4x+2=
−2x2−11x+6
Answer B
Answer: (B) -2x2 - 11x + 6
Question: A certain galaxy is known to comprise approximately 10^11 stars. Of every 50 million of these stars, one is larger in mass than our sun. Approximately how many stars in this galaxy are larger than the sun?
(A) 800
(B) 1,250
(C) 2,000
(D) 12,000
(E) 80,000
Rationale: 10^11
50 mln = 5*10^7
we divide 10^11 by 10^7 and we get 10^4=10,000 and divide by 5. the result is 2,000
C
Answer: (C) 2,000
Question: A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length?
(A) 30
(B) 50
(C) 40
(D) 60
(E) 70
Rationale: Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
= 500 * (2/25) = 40 seconds
Answer: Option C
Answer: (C) 40
Question: In a race of 200 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) 225 m
(B) 285 m
(C) 200 m
(D) 250 m
(E) 150 m
Rationale: Explanation:
A:B = 100 : 60
A:C = 100 : 80
=>B:C = 60:80 = 3:4
When C covers 80 m , B Covers 60 m
When C covers x m , B Covers
=> x - 50 m
3x/4 = x - 50
x = 200 m
Answer: C
Answer: (C) 200 m
Question: There are two numbers. If 20% of the first number is added to the second number, then the second number increases to its five-fourth. What is the ratio of the first number to the second number?
(A) 2 : 9
(B) 3 : 8
(C) 8 : 5
(D) 5 : 4
(E) 7 : 3
Rationale: Let the two numbers be x and y.
(2/10) * x + y = (5/4) * y
(2/10) * x = (1/4) * y
x/y = 10/8 = 5/4
The answer is D.
Answer: (D) 5 : 4
Question: Of 55 players on a cricket team, 37 are throwers. The rest of the team is divided so one third are left- handed and the rest are right handed. Assuming that all throwers are right handed, how many right- handed players are there total?
(A) 49
(B) 55
(C) 59
(D) 71
(E) 92
Rationale: Total = 55
Thrower = 37
Rest = 55 - 37 = 18
Left Handed = 18/3 = 6
Right handed = 12
If all Thrower are right handed then total right handed is 37 + 12 = 49
so A. 49 is the right answer
Answer: (A) 49
Question: When the smallest of 3 consecutive odd integers is added to four times the largest, it produces a result 730 more than 4times the middle integer. Find the numbers?
(A) 650
(B) 678
(C) 698
(D) 710
(E) 730
Rationale: x + 4 (x + 4) = 730 + 4 (x + 2)
Solve for x and find all three numbers
x + 4 x + 16 = 730 + 4 x + 8
x = 722
x + 2 = 724
x + 4 = 726
Check: the smallest is added to four times the largest
722 + 4 * 726 = 3626
four times the middle
4 * 724 = 2896
3626 is more than 2896 by
3626 - 2896 = 730
E
Answer: (E) 730
Question: What is the smallest number which when increased by 3 is divisible by 18, 70, 25 and 21?
(A) 2327
(B) 2757
(C) 3147
(D) 3587
(E) 3997
Rationale: When increased by 3, the number must include at least 2*3^2*5^2*7 = 3150
The answer is C.
Answer: (C) 3147
Question: A can do a piece of work in 30 days. He works at it for 5 days and then B finishes it in 20 days. In what time can A and B together it?
(A) 14 1/7 days
(B) 15 1/7 days
(C) 16 2/3 days
(D) 17 1/7 days
(E) 18 1/7 days
Rationale: 5/10 + 20/x = 1
x = 40
1/30 + 1/40 = 7/120
120/7 = 17 1/7 days
ANSWER:D
Answer: (D) 17 1/7 days
Question: In a fuel station the service costs $1.75 per car, every liter of fuel costs 0.85$. Assuming that a company owns 12 cars and that every fuel tank contains 55 liters and they are all empty, how much money total will it cost to fuel all cars?
(A) 320$
(B) 420$
(C) 582$
(D) 650$
(E) 780$
Rationale: 12*1.75 + 0.85*12*55 = 582 hence - C
Answer: (C) 582$
Question: An iron cube of side 10 cm is hammered into a rectangular sheet of thickness 0.5 cm. If the sides of the sheet are in the ratio 1 : 5, the sides are :
(A) 10 cm20 cm
(B) 2 cm10 cm
(C) 100 cm20 cm
(D) 30 cm100 cm
(E) None
Rationale: Sol.
Let the sides of the sheet be x and 5x. Then,
⇒ x * 5x * 1/2 = 10 * 10 * 10 ⇒ 5x² = 2000 ⇒ x² = 400 ⇒ x = 20.
∴ The sides are 20 cm and 100 cm.
Answer A
Answer: (A) 10 cm20 cm
Question: In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together ?
(A) 120960
(B) 135650
(C) 115850
(D) 142560
(E) 185260
Rationale: In the word 'MATHEMATICS' we treat the two vowels AEAI as one letter. Thus,we have MTHMTCS (AEAI)
Now, we have to arranged 8 letters, out of which M occurs twice, T occurs twice and the rest are different.
Number of ways of arranging these letters= 8!/(2!)(2!)=10080.
Now AEAI has 4 letters in which A occurs 2 times and the rest are different.
number of ways of arranging these letters =4!/2!=12.
Required number of ways =(10080*12)=120960.
Answer is A
Answer: (A) 120960
Question: The average age of 15 students of a class is 15 years. Out of these, the average age of 4 students is 14 years and that of the other 10 students is 16 years, The age of the 15th student is
(A) 11
(B) 12
(C) 9
(D) 14
(E) 15
Rationale: Explanation:
Age of the 15th student = [15 * 15 - (14 * 5 + 16 * 9)] = 9 years. Answer: C
Answer: (C) 9
Question: In one hour, a boat goes 19 km/hr along the stream and 11 km/hr against the stream. The speed of the boat in still water (in km/hr) is:
(A) 12 kmph
(B) 13 kmph
(C) 14 kmph
(D) 15 kmph
(E) 16 kmph
Rationale: Explanation:
Let the speed downstream be a km/hr and the speed upstream be b km/hr, then
Speed in still water =1/2(a+b) km/hr
Rate of stream = 1/2(a−b) km/hr
Speed in still water = 1/2(19+11) kmph = 15 kmph.
Answer: Option D
Answer: (D) 15 kmph
Question: A runs twice as fast as B and gives B a start of 71m.How long should the racecourse be so that A and B might reach in the same time?
(A) 75 m.
(B) 80 m.
(C) 150 m.
(D) 142 m.
(E) None of the above
Rationale: ratio of speeds of a and b is 2:1
b is 71m away from a but we know that a covers 1 meter(2-1) more in every second than b
the time taken for a to cover 71m is 71/1=71m
so the total time taken by a and b to reach =2*71=142m
ANSWER:D
Answer: (D) 142 m.
Question: On a weekend, 11 college friends went to the beach and evenly split the cost of their beach house. If the amount paid by each person was an integer, which of the following could not have been the cost of the beach house?
(A) $121
(B) $568
(C) $484
(D) $363
(E) $319
Rationale: Each of the seven persons evenly splitting the cost is an integer amount, therefore check the divisibility by 11 for all answer choices.
121/11 = 11
568/11 = 51.64
484/11 = 44
363/11 = 33
319/11 = 29
B is not an integer amount.
Answer:B
Answer: (B) $568
Question: How many four-digit numbers are there such that all three digits are different and the first digit and last digit is not zero?
(A) 2128
(B) 3458
(C) 4207
(D) 5184
(E) 8104
Rationale: All three digits are different and first digit is not zero.
So first digit can be filled in 8 ways.
And, second digit can be filled in 9 ways.
And, third digit can be filled in 9 ways.
And, fourth digit can be filled in 8 ways.
Total ways = 8*9*9*8
= 5184
Hence option (D).
Answer: (D) 5184
Question: A bus 75 m long is running with a speed of 21 km/hr. In what time will it pass a woman who is walking at 3 km/hr in the direction opposite to that in which the bus is going?
(A) 5.75
(B) 7.62
(C) 11.25
(D) 4.25
(E) 3.25
Rationale: Speed of bus relative to woman = 21 + 3 = 24 km/hr.
= 24 * 5/18 = 20/3 m/sec.
Time taken to pass the woman = 75 * 3/20
= 11.25 sec.
Answer: C
Answer: (C) 11.25
Question: Find the fourth proportion to 2,5,12
(A) 18
(B) 12
(C) 40
(D) 30
(E) 24
Rationale: Explanation:
2:5 :: 12:x
=> 2/5 = 12/x
=> x = 60/2
=> x = 30
Option D
Answer: (D) 30
Question: A container contains 40 litres of milk.From this container 4 litres of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container.
(A) 29.19 litres
(B) 29.96 litres
(C) 99.16 litres
(D) 29.16 litres
(E) 23.16 litres
Rationale: Answer: D) 29.16 litres
Answer: (D) 29.16 litres
Question: A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of A?
(A) 30229
(B) 3000
(C) 278
(D) 274
(E) 287
Rationale: 60*5:36*6:75*3
100: 72: 75
100/247 * 7410 = 3000
Answer:B
Answer: (B) 3000
Question: The area of sector of a circle whose radius is 18 metro and whose angle at the center is 42Â° is?
(A) 52.6
(B) 52.9
(C) 52.8
(D) 118.8
(E) 52.2
Rationale: 42/360 * 22/7 * 18 * 18 = 118.8 m2
Answer: D
Answer: (D) 118.8
Question: There are 10 slate rocks, 11 pumice rocks, and 4 granite rocks randomly distributed in a certain field. If 2 rocks are chosen at random and without replacement, what is the probability that both rocks will be slate rocks?
(A) 3/20
(B) 5/26
(C) 7/34
(D) 9/37
(E) 11/49
Rationale: 10/25*9/24 = 3/20
The answer is A.
Answer: (A) 3/20
Question: In a box, there are 8 orange, 7 black and 6 white balls. If one ball is picked up randomly. What is the probability that it is neither orange nor white?
(A) 2/3
(B) 3/4
(C) 7/19
(D) 8/21
(E) 10/21
Rationale: total balls are 21
and neither black nor white .
so favor case will be only 8C1
and total case 21C1
probability will be 8C1/21C1=8/21
ANSWER:D
Answer: (D) 8/21
Question: Two trains 110 meters and 200 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet?
(A) 4.85
(B) 7.69
(C) 6.85
(D) 5.85
(E) 6.15
Rationale: T = (110+ 200)/ (80 + 65) * 18/5
T = 7.69
ANSWER:B
Answer: (B) 7.69
Question: Given f(x) = 3x – 5, for what value of x does 2*[f(x)] – 7 = f(3x – 6)
(A) 0
(B) 2
(C) 6
(D) 7
(E) 13
Rationale: Answer = B = 2
f(x) = 3x – 5
2*[f(x)] – 7 = f(3x – 6)
2(3x-5) -7 = 3 (3x-6) - 5
6x - 17 = 9x - 23
x = 2
Answer: (B) 2
Question: A and B enter into partnership with capitals in the ratio 1 : 2. At the end of 10 months A withdraws,and the profits now are divided in the ratio of 5 : 6. Find how long B remained in the business?
(A) 9 months
(B) 8 months
(C) 6 months
(D) 7 months
(E) None of these
Rationale: Initially A’s investment = 1x and B’s investment = 2x
Let B remain in the business for ‘n’ months.
⇒ 1x × 10 : 2x × n = 5 : 6
∴ 1x × 10 × 6 = 2x × n × 5
⇒ n = 6
Answer C
Answer: (C) 6 months