mathewhe/aqua_rat huggingface dataset:
Question: A fruit-salad mixture consists of apples, peaches, and grapes in the ratio 6:5:2, respectively, by weight. If 78 pounds of the mixture is prepared, the mixture includes how many more pounds of apples than grapes?
(A) 24
(B) 12
(C) 9
(D) 6
(E) 4
Rationale: We can first set up our ratio using variable multipliers. We are given that a fruit-salad mixture consists of apples, peaches, and grapes, in the ratio of 6:5:2, respectively, by weight. Thus, we can say:
apples : peaches : grapes = 6x : 5x : 2x
We are given that 39 pounds of the mixture is prepared so we can set up the following question and determine a value for x:
6x + 5x + 2x = 78
13x = 78
x = 6
Now we can determine the number of pounds of apples and of grapes.
pounds of grapes = (2)(6) = 12
pounds of apples = (6)(6) = 36
Thus we know that there are 36 -12 = 24 more pounds of apples than grapes.
Answer is A.
Answer: (A) 24
Question: An empty fuel tank is filled with brand Z gasoline. When the tank is half empty, it is filled with brand Y gasoline. When the tank is half empty again, it is filled with brand Z gasoline. When the tank is 1/4 empty again, it is filled with brand Y gasoline. At this time, what percent of the gasoline in the tank is brand Z?
(A) 21%
(B) 24%
(C) 22%
(D) 20%
(E) 18.75%
Rationale: Work with fraction of brand Z in the tank.
1st step: brand Z is 1
2nd step: brand Z is 1/2
3rd step: brand Z is (1/2)*(1/2) + 1/2 = 3/4
4th step: brand Z is (1/4)*(3/4) = 3/16 = 18.75%
Answer (E)
Answer: (E) 18.75%
Question: A number when divided by a divisor leaves a remainder of 24.
When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?
(A) 35
(B) 37
(C) 41
(D) 43
(E) 44
Rationale: Let the original number be 'a'
Let the divisor be 'd'
Let the quotient of the division of aa by dd be 'x'
Therefore, we can write the relation as a/d = x and the remainder is 24.
i.e., a=dx+24 When twice the original number is divided by d, 2a is divided by d.
We know that a=dx+24. Therefore, 2a = 2dx + 48
The problem states that (2dx+48)/d leaves a remainder of 11.
2dx2dx is perfectly divisible by d and will therefore, not leave a remainder.
The remainder of 11 was obtained by dividing 48 by d.
When 48 is divided by 37, the remainder that one will obtain is 11.
Hence, the divisor is 37.
B
Answer: (B) 37
Question: In three years, Janice will be three times as old as her daughter. Six years ago, her age was her daughter’s age squared. How old is Janice's Daughter?
(A) 12
(B) 36
(C) 40
(D) 42
(E) 45
Rationale: Let Jane's age be J and daughters' age be D...
Given J + 3 = 3(D + 3 ) => J - 6 = 3D -> Eq1.
Given J-6 = (D-6)^2 --> Eq 2..
sub J-6 value in eq 2... 3D = D^2 - 12D + 36.
0 = D^2 - 15D + 36 => D = 12 or D = 3.
When D = 12 we get from eq 1... J+3 = 45 => J =42..
When D = 3 ..we get from eq 1.. J+3 = 18 => J = 15..
IMO option A is correct answer..
Answer: (A) 12
Question: The cost of 3 kg of sugar is $12. What will the cost of 8 kg of sugar be?
(A) 32
(B) 48
(C) 64
(D) 120
(E) 180
Rationale: 3 kg costs $12
1 kg costs $4
8 kg costs $32
The answer is A.
Answer: (A) 32
Question: A boat goes 8 km upstream in 24 minutes. The speed of stream is 4 km/hr. The speed of boat in still water is:
(A) 25 km/hr
(B) 26 km/hr
(C) 22 km/hr
(D) 24 km/hr
(E) 28 km/hr
Rationale: rate upstream =8/24*60=20kmph
speed of stream=4kmph
let speed of boat in still water=xkmph
speed upstream=x-4kmph
x-4=20
x=24kmph
ANSWER:D
Answer: (D) 24 km/hr
Question: A person borrows Rs.5000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 5% p.a for 2 years. Find his gain in the transaction per year.
(A) 50
(B) 150
(C) 225
(D) 112.5
(E) 212.5
Rationale: Explanation :
The person borrows Rs. 5000 for 2 years at 4% p.a. simple interest
Simple interest that he needs to pay = PRT/100=5000×4×2/100=400
He also lends it at 5% p.a for 2 years
Simple interest that he gets = PRT/100=5000×5×2/100=500
His overall gain in 2 years = Rs.500 - Rs.400 = Rs.100
His overall gain in 1 year = 100/2 = Rs.50
Answer : Option A
Answer: (A) 50
Question: If x is equal to the sum of the integers from 30 to 50, inclusive, and y is the number of even integers from 30 to 50, inclusive, what is the value of x + y ?
(A) 810
(B) 811
(C) 830
(D) 850
(E) x + y=851
Rationale: 21 integers from 30 to 50 inclusive
so 11th integer is mean, it is 40
21*40=840
from 21 integers 11 ones is even
840+11=851
ANSWER:E
Answer: (E) x + y=851
Question: A chair is bought for Rs.500/- and sold at a loss of 20% find its selling price
(A) Rs.500/-
(B) Rs.600/-
(C) Rs.400/-
(D) Rs.700/-
(E) Rs.800/-
Rationale: Loss = 500*20/100 = 100
S.P = C.P - Loss
= 500- 100
=Rs.400/-
Answer :C
Answer: (C) Rs.400/-
Question: In a group of 400 players some are outdoor players, some are indoor players and some plays both. 350 plays outdoors and 110 plays indoor. How many plays indoor as well as outdoor games.
(A) 70
(B) 60
(C) 90
(D) 100
(E) 110
Rationale: Consider total number of players n(O U I) = 400
Players who plays outdoors n(O) = 350
Players who plays indoors n(I) = 110
Players who plays both n(O âˆ© I) = ?
n(O U I) = n(O)+ n(I) - n(O âˆ© I)
400 = 350 + 110 - n(O âˆ© I)
n(O âˆ© I) = 460 - 400
n(O âˆ© I) = 60
SO People read both science fiction and literacy works are 60
ANSWER:B
Answer: (B) 60
Question: A man can row a boat at 26 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 60 km downstream?
(A) 30/83 hours
(B) 80/13 hours
(C) 15/13 hours
(D) 16/19 hours
(E) 15/8 hours
Rationale: Speed downstream = 26 + 6 = 32 kmph.
Time required to cover 60 km downstream
= d/s = 60/32
= 15/8 hours.
Answer:E
Answer: (E) 15/8 hours
Question: Let n~ be defined for all positive integers n as the remainder when (n - 1)! is divided by n.
What is the value of 30~ ?
(A) 1
(B) 0
(C) 2
(D) 8
(E) 31
Rationale: n~ = (n-1)!
so 30~ = (30-1)! = 29!
when 29!/30 we have 16*2 inside 29!
hence 30 gets cancelled and we get remainder as 0
B
Answer: (B) 0
Question: If x^2 − 2x − 15 = (x + r)( x + s) for all values of x, and if r and s are constants, then which of the following is a possible value of (r − s)^2?
(A) 8
(B) 2
(C) 64
(D) − 3
(E) − 5
Rationale: We know that given ax^2 + bx + c = 0, Sum of the roots = -b/a and product of the roots = c/a.
The roots here are -r and -s.
-r - s = -(-2)/1 = r + s = -2
(-r)*(-s) = -15/1 = rs
So one of r and s is -5 and the other is 3. So
(r - s)^2 could be 64.
Answer (C)
Answer: (C) 64
Question: in base 7, a number is written only using digits 0,1,2,3,4,5,6. the number 135 in base 7 is 1*72+3*7+5=75 in base 10. what is the sum of the base 7 numbers 1234 & 6543 in base 7?
(A) 11101
(B) 11110
(C) 10111
(D) 11011
(E) 11010
Rationale: 4+3=7 since base is 7 so it will become 0 giving 1 carry to next digits(so 4+7=0)
3+4 + 1 carry from above step= 1 and 1 carry to next digit
2+5 + 1 carry to next digit= 1 and 1 carry
1+6= 11
so ans=11110
ANSWER:B
Answer: (B) 11110
Question: Notebooks are sold in packages of four or seven only. If Wilson bought 69 notebooks exactly, what could be the number of large packs Wilson bought?
(A) 3
(B) 4
(C) 7
(D) 8
(E) 9
Rationale: Let number of packs of four = f
let number of packs of seven = s
4f + 7s = 69
Now , we need to test for values of s .
Since sum 69 is odd and 4f will always be even , e can't be even .
Now , we can test for values e = 3 , 7 and 9
4*5 + 7*7 = 20 + 49 = 69
Answer C
Answer: (C) 7
Question: A and B start walking towards each other at 6pm at speed of 4kmph and 6kmph. They were initially 18km apart. At what time do they meet?
(A) 8pm
(B) 6pm
(C) 7pm
(D) 10pm
(E) 5pm
Rationale: Time of meeting = distance / relative speed = 18/6+3 = 18/9 = 2 hrs after 6pm = 8pm
Answer is A
Answer: (A) 8pm
Question: Which of the following number is divisible by 4 and 9?
(A) 2377
(B) 2736
(C) 2876
(D) 1988
(E) 1192
Rationale: Explanation:
For a number to be divisible by 4, the number formed by the last two digits of that number must be divisible by 4.
For a number to be divisible by 9, the sum of its digits must be divisible by 9.
Among the choices, choices (a) and (b) are divisible by 4 but of the first two choices, only choice (b) is divisible by 9.
Hence choice (b) is divisible by both 4 and 9.
Answer: B
Answer: (B) 2736
Question: Find the perimeter and area of a square of side 13 cm.
(A) 121
(B) 144
(C) 169
(D) 196
(E) 225
Rationale: We know that the perimeter of square = 4 Ã— side
Side= 13 cm
Therefore, perimeter = 4 Ã— 13 cm = 52 cm
Now, area of the square = (side Ã— side) sq. units
= 13 Ã— 13 cmÂ²
= 169 cmÂ²
ANSWER : C
Answer: (C) 169
Question: Tanks A and B are each in the shape of a right circular cylinder. The interior of tank A has a height of 7 meters and a circumference of 8 meters, and the interior of tank B has a height of 8 meters and a circumference of 10 meters. The capacity of tank A is what percent of the capacity of tank B?
(A) 56%
(B) 80%
(C) 100%
(D) 120%
(E) 125%
Rationale: For A, r=8/2pi. Its capacity = (4pi)^2 * 7= 112pi
For B, r=10/pi. Its capacity = (5pi)^2 *8 = 200pi
A/B = 112pi/200pi = 0.56
A
Answer: (A) 56%
Question: The sum of first nine prime numbers is?
(A) 12
(B) 100
(C) 24
(D) 28
(E) 30
Rationale: Required sum = (2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23) = 100.
Note: 1 is not a prime number.
Definition: A prime number (or a prime) is a natural number that has exactly two distinct natural number divisors: 1 and itself.
B
Answer: (B) 100
Question: In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?
(A) 30%
(B) 70%
(C) 100%
(D) 250%
(E) 150%
Rationale: Let C.P.= Rs. 100. Then, Profit = Rs. 320, S.P. = Rs. 420.
New C.P. = 125% of Rs. 100 = Rs. 125
New S.P. = Rs. 420.
Profit = Rs. (420 - 125) = Rs. 295.
Required percentage=295/420x100%=1475/21%= 70%
Answer is B.
Answer: (B) 70%
Question: If 15 percent of the students at a certain school went to a camping trip and took more than $100, and 75 percent of the students who went to the camping trip did not take more than $100, what percentage of the students at the school went to the camping trip?
(A) 95
(B) 90
(C) 85
(D) 80
(E) 60
Rationale: Let x be the number of students in the school. 0.15x students went to the trip and took more than 100$. They compose (100-75)=25% of all students who went to the trip. Therefore the toal of 0.15x/0.25=0.6x students went to the camping which is 60%.
The answer is E
Answer: (E) 60
Question: How many words can be formed by using all letters of the word â€œBIHARâ€
(A) 320
(B) 200
(C) 420
(D) 120
(E) 300
Rationale: Sol. The word BIHAR contains 5 different letters.
Required number of words = 5p5 = 5! = (5x4x3x2x1) = 120
ANSWER D
Answer: (D) 120
Question: The product of two numbers is 2028 and their H.C.F. is 13. The number of such pairs is:
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: EXPLANATION
Let the numbers 13a and 13b.
Then, 13a x 13b = 2028
ab = 12.
Now, the co-primes with product 12 are (1, 12) and (3, 4).
[Note: Two integers a and b are said to be coprime or relatively prime if they have no common positive factor other than 1 or, equivalently, if their greatest common divisor is 1 ]
So, the required numbers are (13 x 1, 13 x 12) and (13 x 3, 13 x 4).
Clearly, there are 2 such pairs.
Answer B
Answer: (B) 2
Question: K is 50% faster than L. If L starts at 9 A.M. and K starts at 10 A.M. L travels at a speed of 50 km/hr. If L and K are 300 kms apart, The time when they meet when they travel in opposite direction is ?
(A) 12 pm
(B) 22 pm
(C) 72 pm
(D) 92 pm
(E) 23 pm
Rationale: Explanation:
let 't' be the time after which they met since L starts.
Given K is 50% faster than L
50 t + 1.5*50(t-1) = 300
50 t +75 t = 300 + 75
t = 375 / 125 = 3 hrs past the time that L starts
So they meet at (9 + 3)hrs = 12:00 noon.
Answer: A
Answer: (A) 12 pm
Question: A farmer built a fence around his square plot. He used 27 fence poles on each side of the square. How many poles did he need altogether ?
(A) 100
(B) 104
(C) 108
(D) 106
(E) None of these
Rationale: Explanation:
Since each pole at the corner of the plot is common to its two sides, so we have :
Total number of poles needed = 27 x 4 - 4 = 108 - 4 = 104.
Answer: B
Answer: (B) 104
Question: The ratio of the earnings of P and Q is 9:10. If the earnings of P increases by one-fourth and the earnings of Q decreases by one-fourth, then find the new ratio of their earnings?
(A) 4/7
(B) 3 by 2
(C) 3/5
(D) 9/4
(E) 3/1
Rationale: Let the earnings of P and Q be 9x and 10x respectively.
New ratio = [9x + 1/4 (9x)]/[10x - 1/4 (10x)]
=> 9*(1 + 1/4)/10*(1 - 1/4)
=> 9/10 * (5/4)/(3/4) = 3/2
Answer: B
Answer: (B) 3 by 2
Question: A man decided to cover a distance of 80km in 8 hrs. He can walk at a speed of 6 km/hr and cycle at 8 km/hr successively. How long will he walk and how long will he cycle ?
(A) 26.6km,53.3km
(B) 27.6km,53.3km
(C) 26.6km,54.3km
(D) 26.6km,55.3km
(E) 28.6km,53.3km
Rationale: as speed in 80km/8hrs=10 km/hr
as ques solve through mixture and alligation method
6 km/hr and 8km/hr
10km/hr
10-8 10-6
2km/hr 4km/hr
so the ratio is 1:2
ahd we have to find the distance through walk and through cycle
1/3*80=26.6km
2/3*80=53.3km
ANSWER:A
Answer: (A) 26.6km,53.3km
Question: A corporation that had $115.19 billion in profits for the year paid out $230.10 million in employee benefits. Approximately what percent of the profits were the employee benefits? (Note: 1 billion = 10^9)
(A) 50%
(B) 20%
(C) 5%
(D) 2%
(E) 0.2%
Rationale: required answer = [employee benefit/profit] *100
=[(230.10 million)/(115.19 billion)]*100
=[(230.10*10^6)/(115.19*10^9)]*100
=(2/1000)*100
=0.2%
So answer is (E)
Answer: (E) 0.2%
Question: By selling 20 pens for a rupee a man loses 30%. How many for a rupee should he sell in order to gain 30%?
(A) 8.76
(B) 10.76
(C) 8.76
(D) 9.76
(E) 5.76
Rationale: 70% --- 20130% --- ?70/130 * 20 = 10.76Answer: B
Answer: (B) 10.76
Question: A mixture contains alcohol and water in the ratio 4 : 3. If 5 litres of water is added to the mixture, the ratio becomes 4: 5. Find the quantity of alcohol in the given mixture
(A) 15 litres
(B) 10 litres
(C) 30 litres
(D) 22 litres
(E) 8 litres
Rationale: Let the quantity of alcohol and water be 4x litres and 3x litres respectively
4x/(3x+5)=4/5
20x=4(3x+5)
8x=20
x=2.5
Quantity of alcohol = (4 x 2.5) litres = 10 litres.
Answer is B.
Answer: (B) 10 litres
Question: 3,6,9,12,15....
(A) 58
(B) 60
(C) 18
(D) 62
(E) 63
Rationale: 1*3=3
2*3=6
3*3=9
4*3=12
5*3=15
6*3=18
ANSWER:C
Answer: (C) 18
Question: A man spend 1/5 of his salary on food , 1/10 of his salary on house rent and 3/5 salary on clothes. he still has $18000 left with him. find salary..
(A) $10800
(B) $18000
(C) $180000
(D) $1800
(E) None
Rationale: [1/(x1 / y1 + x2/y2 + x3/y3)] * Total amount= Balance amount
[1-(1/5 + 1/10 + 3/5)} * total salary= $18000, = [1-9/10] * Total salary = $18000, Total salary = $18000*10 = $180000, correct answer (C)
Answer: (C) $180000
Question: For an agricultural experiment, 300 seeds were planted in one plot and 200 were planted in a second plot. If exactly 25 percent of the seeds in the first plot germinated and exactly 35 percent of the seeds in the second plot germinated, what percent of the total number of seeds germinated?
(A) 12%
(B) 26%
(C) 29%
(D) 30%
(E) 60%
Rationale: In the first plot 25% of 300 seeds germinated, so 0.25 x 300 = 75 seeds germinated.
In the second plot, 35% of 200 seeds germinated, so 0.35 x 200 = 70 seeds germinated.
Since 75 + 70 = 145 seeds germinated out of a total of 300 + 200 = 500 seeds, the percent of seeds that germinated is (145/500) x 100%, or 29%.
Answer: C.
Answer: (C) 29%
Question: The cost C, in dollars, to remove p percent of a certain pollutant from a pond is estimated by using the formula C = 100,000p/(100 - p). According to this estimate, how much more would it cost to remove 90 percent of the pollutant from the pond than it would cost to remove 50 percent of the pollutant?
(A)  $400,000
(B)  $100,000
(C)  $50,000
(D)  $10,000
(E)  $5,000
Rationale: To remove 90% of pollutant
C= 100,000(90)/(100-90) = 900,000
To remove 50% of pollutant
C' = 100,000(80)/(100-80) = 500,000
Difference = C - C' = 400,000
Answer - A
Answer: (A)  $400,000
Question: Which of the following is not a leap year?
(A) 700
(B) 800
(C) 1000
(D) 1100
(E) 1200
Rationale: The century divisible by 400 is a leap year.
The year 700 is not a leap year. ANSWER : A
Answer: (A) 700
Question: The average age of 8 men is increased by years when two of them whose ages are 21 years and 23 years are replaced by two new men. The average age of the two new men is
(A) 38
(B) 30
(C) 39
(D) 12
(E) 11
Rationale: Explanation:
Total age increased = (8 * 2) years = 16 years.
Sum of ages of two new men = (21 + 23 + 16) years = 60 years
Average age of two new men = (60/2) years = 30 years.
Answer: B
Answer: (B) 30
Question: Working, independently X takes 10 hours to finish a certain work. He works for 9 hours. The rest of the work is finished by Y whose rate is 1/10 th of X. In how much time does Y finish his work?
(A) 2hrs
(B) 4hrs
(C) 6hrs
(D) 8hrs
(E) 10hrs
Rationale: machine X will do 9/10 in 9 hrs, so X does 9/10 of the work ..
Therefore, Y will do the remaining 1/10 th work alone..
As the speed of Y is 1/10 rate of X, Y will do the 1/10 th work in same time that X takes to complete full job...
ans 10
E
Answer: (E) 10hrs
Question: The probability that A speaks truth is 3/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact?
(A) 18/35
(B) 18/22
(C) 18/29
(D) 18/12
(E) 18/33
Rationale: If both agree stating the same fact, either both of them speak truth of both speak false.
Probability = 3/5 * 4/7 + 2/5 * 3/7
= 12/35 + 6/35
= 18/35
Answer:A
Answer: (A) 18/35
Question: The sum of two numbers is 20 and their product is 375. What will be the sum of their reciprocals?
(A) 1/40
(B) 4/75
(C) 75/4
(D) 75/8
(E) 75/6
Rationale: (1/a)+(1/b)=(a+b)/ab=20/375=4/75
ANSWER:B
Answer: (B) 4/75
Question: 31, 29, 24, 22, 17, ?
(A) 12
(B) 14
(C) 15
(D) 17
(E) 20
Rationale: C
15
This is a simple alternating subtraction series, with a pattern -2, -5, -2, -5 ....
Answer: (C) 15
Question: A straight fence is to be constructed from posts 5 inches wide and separated by lengths of chain 5 feet long. If a certain fence begins and ends with a post, which of the following couldnotbe the length of the fence in feet? (12 inches = 1 foot)
(A) 17
(B) 28
(C) 34
(D) 39
(E) 50
Rationale: The fence begins and ends with a post: {post = 0.5 feet}{chains = 5 feet}{post = 0.5 feet}...{chains = 5 feet}{post = 0.5 feet}
The minimum length is with 2 posts = 0.5 + 5 + 0.5 = 6 feet. To increase the fence, each time we should add{post = 0.5 feet}{chains = 5 feet}, so 5.5 feet. Thus, the lengths could be:
6 feet;
5 + 5.5 = 10.5 feet;
11.5 + 5.5 = 16 feet;
17 + 5.5 = 21.5 feet;
22.5 + 5.5 = 27 feet;
28 + 5.5 = 32.5 feet;
33.5 + 5.5 = 38 feet.
...
We skipped 34 feet.
Answer: C.
Answer: (C) 34
Question: How many arrangements of the letters of the word DEFEATED are there in which the three E are separated?
(A) 840
(B) 750
(C) 770
(D) 760
(E) 820
Rationale: Total arrangements-Three E's together-Exactly Two E's together
Total arrangement= 8!/3!2!
Three E's together= 6!/2!
Exactly Two E's together= Two E's together - Three E's together = 7!/2!−6/!2!=6∗6!/2!
8!/3!2!−6!/2!−6∗6!/2!
8!/3!2!−7!/2!=7!/2!∗13=840
Ans: "840"	A
Answer: (A) 840
Question: In the coordinate plane, points (x, 1) and (18, y) are on line k. If line k passes through the origin and has slope 1/2, then x + y =
(A)  4.5
(B)  7
(C)  8
(D)  11
(E)  12
Rationale: Line k passes through the origin and has slope 1/2 means that its equation is y=1/2*x.
Thus: (x, 1)=(2, 1) and (18, y) = (18,9) --> x+y=2+9=11.
Answer: D.
Answer: (D)  11
Question: David obtained 76, 65, 82, 67 and 85 marks (out in 100) in English, Mathematics, Physics, Chemistry and Biology.What are his average marks?
(A) 65
(B) 69
(C) 72
(D) 75
(E) 79
Rationale: add all those marks and divide it by 5 becz they gave us 5 subjects for finding average marks we need to divide them
add them 76+65+82+67+85/5=375/5=75
ANSWER:D
Answer: (D) 75
Question: In how many ways can the letters of the word ABACUS be rearranged such that the vowels always appear together?
(A) 6!/2!
(B) 3!*3!
(C) 4!/2!
(D) 4! *3!/2!
(E) 3!*3!/2
Rationale: In the word ABACUS , there are 3 vowels - 2 A's and U
Number of ways the letters of word ABACUS be rearranged such that the vowels always appear together
= (4! * 3! )/2!
We can consider the the 3 vowels as a single unit and there are 3 ways to arrange them . But since 2 elements of vowel group are identical we divide by 2! .
The entire vowel group is considered as a single group .
Answer D
Answer: (D) 4! *3!/2!
Question: The average price of 10 oranges is Rs. 12 while the average price of 8 of these oranges is Rs. 11.75. Of the remaining two oranges, if the price of one orange is 50% more than the price of the other, what is the price of each of these two oranges?
(A) Rs 5, Rs 7.50
(B) Rs 10.4, Rs 15.6
(C) Rs 10, Rs 16
(D) Rs 12, Rs 14
(E) None of these
Rationale: Explanation :
Total price of the two oranges = Rs. [(12 x 10) (11.75 x 8)]
= Rs. (120 - 94) = Rs. 26.
Let the price of one orange be Rs. x.
Then, the price of other orange = Rs. (x + 50% of x) = Rs. x + 1/2x = Rs. 3x/2
So, x + 3x/2 = 26
5x = 52
x = 10.4
The prices of the two oranges are Rs. 10.4 and Rs. 15.6
Answer : B
Answer: (B) Rs 10.4, Rs 15.6
Question: 4!/(4-3)!=?
(A) 24
(B) 34
(C) 35
(D) 36
(E) 39
Rationale: 4!/(4-3)!=4!/1!=4*3*2=24. Hence, the correct answer is A.
Answer: (A) 24
Question: A chain smoker had spent all the money he had. He had no money to buy his cigarettes. Hence, he resorted to join the stubs and to smoke them. He needed 4 stubs to make a single cigarette. If he got a pack of 10 cigarettes as a gift, then how many cigarettes could he smoke in all?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Rationale: Explanation :
10 cigarettes will produce 10 stubs.
Since, out of 10 cigarettes,
=>8 cigarettes' stubs gives 2 cigarette and, 2 stubs are still left.
=>these 2 gigarette will give 2 stubs.
Now, he will make 1 more cigarette by using 2stubs + 2 stubs.
Hence, total number of cigarettes will be 10 + 2 + 1 i.e 13.
Answer : D
Answer: (D) 13
Question: Score Interval Number of Scores
50-59 2
60-69 10
70-79 14
80-89 27
90-99 18
The table shows a distribution of test scores. Which score interval contains the median of the 71 scores?
(A) a) 60-69
(B) b) 70-79
(C) c) 80-89
(D) d) 90-99
(E) e) Cannot determine.
Rationale: 36th person
80-89 C
Answer: (C) c) 80-89
Question: The sector of a circle has radius of 21 cm and central angle 135o. Find its perimeter?
(A) 91.5
(B) 92
(C) 93
(D) 94
(E) 95
Rationale: Perimeter of the sector = length of the arc + 2(radius)
= (135/360 * 2 * 22/7 * 21) + 2(21)
= 49.5 + 42 = 91.5 cm
Answer: Option A
Answer: (A) 91.5
Question: If a truck is traveling at a constant rate of 36 kilometers per hour, how many seconds will it take the truck to travel a distance of 600 meters? (1 kilometer = 1000 meters)
(A) 18
(B) 24
(C) 60
(D) 36
(E) 48
Rationale: Speed =36 Km/hr => 36,000 m/hr
In one minute => 36000/60 = 600 meters
In one sec => 600/60 = 10 meters
Time = Total distance need to be covered / Avg. speed
=> 600/ 10 =60 and hence the Answer : C
Answer: (C) 60
Question: A fast food company plans to build 4 new restaurants. If there are 14 sites that satisfy the company's criteria for location of new restaurant, in how many different ways can company select the 4 sites needed for the new restaurant if the order of selection doesn't matter.
(A) 1001
(B) 495
(C) 364
(D) 2002
(E) 756
Rationale: The number of ways of choosing 4 sites out of 14 are counted by = 14C4 ways = 1001
Answer: Option A
Answer: (A) 1001
Question: Rs.1170 is divided so that 4 times the first share, thrice the 2nd share and twice the third share amount to the same. What is the value of the third share?
(A) 229
(B) 277
(C) 202
(D) 540
(E) 223
Rationale: A+B+C = 1170
4A = 3B = 2C = x
A:B:C = 1/4:1/3:1/2 = 3:4:6
6/13 * 1170 = Rs.540
Answer:D
Answer: (D) 540