mathewhe/aqua_rat huggingface dataset:
Question: A bowl of fruit contains 14 apples and 21 oranges. How many oranges must be removed so that 70% of the pieces of fruit in the bowl will be apples?
(A)  3
(B)  15
(C)  14
(D)  17
(E)  20
Rationale: Number of apples = 14
number of oranges = 23
let number of oranges that must be removed so that 70% of pieces of fruit in bowl will be apples = x
Total number of fruits after x oranges are removed = 14+(21-x) = 35-x
14/(35-x) = 7/10
=>20 = 35-x
=>x= 15
Answer B
Answer: (B)  15
Question: A train 210 meters long is running with a speed of 54 kmph. The time taken by it to cross a tunnel 120 meters long is?
(A) 29
(B) 22
(C) 48
(D) 99
(E) 11
Rationale: D = 210 + 120 = 330
S = 54 * 5/18 = 15 mps
T = 330/15 = 22 sec
Answer: B
Answer: (B) 22
Question: An air conditioner can coo the hall in 15 minutes while another takes 20 minutes to cool under similar conditions. if both air conditioners are switched on at same instance then how long will it take to cool the room?
(A) about 5 minutes
(B) about 7 minutes
(C) about 15 minutes
(D) about 19 minutes
(E) about 9 minutes
Rationale: Take LCM of 15 and 20 = 60
15*4=60/ 20*3=60.
So if both are switched on together , room cooled in 60/(4+3)=60/7=8.57 minutes
8.57 can be round to 9 minutes , so about 9 minutes
ANSWER: E
Answer: (E) about 9 minutes
Question: At the store opening, Larry's Grocery had 50 Lemons and 60 Oranges. By closing, the store at 20 Lemons and 40 Oranges left. By approximately what percent did the ratio of Lemons to Orange decrease from opening to closing.
(A) 50.0%
(B) 40.0%
(C) 30.0%
(D) 20.0%
(E) 10.0%
Rationale: Opening: Lemons/Oranges = 50/60 =100/120
Closing: Lemons/Oranges = 20/40 =60/120
ASIDE: It's useful to write both ratios with the same denominator. This allows us to IGNORE the denominator and focus solely on the numerators.
So, our ratio went from 100/120 to 60/120
Ignoring the denominators, we went from 100 to 60
The percent change = 100(difference in values)/(original value)
= (100)(100-60)/100
= (100)(40)/100)
= 40
Answer: B
Answer: (B) 40.0%
Question: .
On dividing a number by 357, we get 40 as remainder. On dividing the same number 17, what will be the remainder ?
(A) 6
(B) 3
(C) 5
(D) 8
(E) 11
Rationale: Let x be the number and y be the quotient. Then,
x = 357 x y + 40
= (17 x 21 x y) + (17 x 2) + 6
= 17 x (21y + 2) + 6)
Required remainder = 6.
Answer: Option A
Answer: (A) 6
Question: A number x is 7 times another number y. The percentage that y is less than x is
(A) 12.5%
(B) 85.7%
(C) 80%
(D) 11%
(E) 1%
Rationale: Say y=1 and x=7.
Then y=1 is less than x=7 by (7-1)/7*100=6/7*100=85.7%.
Answer: B.
Answer: (B) 85.7%
Question: There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is
(A) 100
(B) 110
(C) 120
(D) 140
(E) 150
Rationale: Let the number of students in rooms A and B be x and y respectively.
Then, x - 10 = y + 10 x - y = 20 .... (i)
and x + 20 = 2(y - 20) x - 2y = -60 .... (ii)
Solving (i) and (ii) we get: x = 100 , y = 80.
The required answer A = 100.
Answer: (A) 100
Question: Two varieties of wheat - A and B costing Rs. 9 per kg and Rs. 15 per kg were mixed in the ratio 3 : 7. If 5 kg of the mixture is sold at 25% profit, find the profit made?
(A) 1.2
(B) 3.78
(C) 16.5
(D) 5.84
(E) 7.62
Rationale: Explanation:
Let the quantities of A and B mixed be 3x kg and 7x kg.
Cost of 3x kg of A = 9(3x) = Rs. 27x
Cost of 7x kg of B = 15(7x) = Rs. 105x
Cost of 10x kg of the mixture = 27x + 105x = Rs. 132x
Cost of 5 kg of the mixture = 132x/10x (5) = Rs. 66
Profit made in selling 5 kg of the mixture = 25/100 (cost of 5 kg of the mixture) = 25/100 * 66 = Rs. 16.50
Correct Option : C
Answer: (C) 16.5
Question: From a group of 7 men and 6 women, 4 persons are to be selected to form a committee so that at most 2 men are there in the committee. In how many ways can it be done?
(A) 480
(B) 520
(C) 760
(D) 470
(E) 464
Rationale: Total Men = 7
Total Women = 6
Persons in committee = 4
No. of ways to select at most 2 men = 6C4 + 7C1 * 6C3 + 7C2*6C2
= 470
Ans -D
Answer: (D) 470
Question: 14, 35, 56, 91, 126
In the sequence above, each term is related with the others. Which of the following could not be a term in the sequence?
(A) 407
(B) 259
(C) 322
(D) 686
(E) 847
Rationale: Simplifying the question into easier words we just need to find which of the numbers is not divisible by 7
clearly the answer is 407 because if we divide 407 by 4 we get a remainder of 1
Correct answer - A
Answer: (A) 407
Question: Jones covered a distance of 50 miles on his first trip. On a later trip he traveled 300 miles while going three times as fast. Find out his new time compared with the old time.
(A) twice as much
(B) three times as much
(C) the same
(D) half as much
(E) a third as much
Rationale: Let speed of the 1st trip x miles / hr. and speed of the 2nd trip 3x / hr.
We know that
Speed = Distance/Time.
Or, Time = Distance/Speed.
So, times taken to covered a distance of 50 miles on his first trip = 50/x hr.
And times taken to covered a distance of 300 miles on his later trip = 300/3x hr.
= 100/x hr.
So we can clearly see that his new time compared with the old time was: twice as much.
Answer is A.
Answer: (A) twice as much
Question: When x is divided by 7, the remainder is 5. When m is divided by 13, the remainder is 6. If 1 < x< 200, what is the greatest possible value of x?
(A) 5
(B) 19
(C) 61
(D) 74
(E) 110
Rationale: Answer is E.
I started with E.110 and it fits the bill . 105 is divisible by 7 and 104 is divisible by 13. so its E.
Modular approach would be the proper way, but this worked at first attempt. E
Answer: (E) 110
Question: The age of Ritu's mother is 6 times that of Ritu's age. After 6 years it will be 3 times that of Ritu's age. what is Ritu's mother present age?
(A) 24 years
(B) 26 years
(C) 28 years
(D) 10 years
(E) None of the above
Rationale: Let present age of Ritu=x
then, present age of ritu's mother=6x
A/c
after 6 years
=>6x+6=3(6+x)
x=4
so, Ritu mother present age is 24 years
ANSWER:A
Answer: (A) 24 years
Question: Every letter in the alphabet has a number value that is equal to its place in the alphabet. Thus, the letter A has a value of 1, the letter B has a value of 2, the letter C has a value of 3, etc... The number value of a word is obtained by adding up the value of the letters in the word and then multiplying that sum by the length of the word. What is the number value of the word "RAT"?
(A) 108
(B) 111
(C) 114
(D) 117
(E) 120
Rationale: "RAT" = (18+1+20)*3=117.
The answer is D.
Answer: (D) 117
Question: For any non-zero a and b that satisfy |ab| = -ab and |a| = a, a^2+b^2+2|ab| =?
(A) ab-4
(B) (a+b)^2
(C) (a-b)^2
(D) a^2-|ab+ab^2|
(E) 4-ab
Rationale: Given: |ab| = -ab and |a| = a
Question: a^2+b^2+2|ab| =?
**** Looking at |ab| = -ab tells us that a and b are either positive or negative
**** Looking at |a| = a tells us that a must be positive
**** Combine two observations: a is positive, b is negative
so a^2+b^2+2|ab| = a^2+b^2-2ab.
as we know : (a-b)^2= a^2+b^2-2ab.
hence option c is correct.
Answer: (C) (a-b)^2
Question: A boat crossed a lake from West to South at the speed of 8 km/h, entered a river and covered twice as much distance going upstream at 7 km/h. It then turned around and stopped at the south shore of the lake. If it averaged 3.8 km/h that day, what was its approximate downstream speed?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 9
Rationale: One way of solving this is:
Speed of boat on still water (lake)=8kmph
Speed upstream = 7kmph = speed in still water - speed of river => speed of river = 1kmph
=>Speed downstream = speed in still water + speed of river = 8+1 =9kmph
Ans is E
Answer: (E) 9
Question: A train speeds past a pole in 15 seconds and a platform 100 meter long in 25 seconds. What is length of the train ?
(A) 140 meter
(B) 145 meter
(C) 150 meter
(D) 155 meter
(E) None of these
Rationale: Explanation:
Let the length of the train is x meter and Speed of the train is y meter/second
Then x/y = 15 [because distance/speed = time]
=> y = 15/x
=>x+100/25=x/15
x=150 meters
So length of the train is 150 meters
Option C
Answer: (C) 150 meter
Question: The ratio of the length and the breadth of a rectangle is 4 : 3 and the area of the rectangle is 6912 sq cm. Find the ratio of the breadth and the area of the rectangle?
(A) 1: 96.
(B) 1: 99
(C) 1: 94
(D) 1: 93
(E) 1: 72
Rationale: Explanation:
Let the length and the breadth of the rectangle be 4x cm and 3x respectively.
(4x)(3x) = 6912
12x2 = 6912
x2 = 576 = 4 * 144 = 22 * 122 (x > 0)
=> x = 2 * 12 = 24
Ratio of the breadth and the areas = 3x : 12x2 = 1 : 4x = 1: 96.
Answer: Option A
Answer: (A) 1: 96.
Question: A sequence of positive and negative numbers contain q numbers. If the sequence begins with a negative number and q is an odd number how many positive numbers are in it.
(A) q/(2+1)
(B) (q+1)/2
(C) (q-1)/2
(D) q/(2-1)
(E) q/(2+2)
Rationale: Lets put values for x, say q=7 since it's odd
and first number is neg so sequence will be {neg,pos,neg,pos,neg,pos,pos} we can see that it has 3 positive terms
so putting q=7 in the options,
option C = (q-1)/2 => 7-1/2 = 3 , the number of positive integers
So, C is the answer
Answer: (C) (q-1)/2
Question: There are 8 executives, including the CEO and CFO, that are asked to form a small team of 5 members. However, the CEO and CFO may not both be assigned to the team. Given this constraint, how many ways are there to form the team?
(A) 34
(B) 35
(C) 36
(D) 37
(E) 38
Rationale: The total number of ways to form a team of 5 is 8C5=56.
We need to subtract the number of teams that have both the CEO and the CFO.
The number of teams with both the CEO and CFO is 6C3=20.
The number of ways to form an acceptable team is 56-20=36.
The answer is C.
Answer: (C) 36
Question: A car covers a distance of 720 km in 6 ½ hours. Find its speed?
(A) 104 kmph
(B) 187 kmph
(C) 120 kmph
(D) 175 kmph
(E) 106 kmph
Rationale: 720/6
= 120 kmph
Answer: C
Answer: (C) 120 kmph
Question: The parameter of a square is equal to the perimeter of a rectangle of length 8 cm and breadth 6 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square.
(A) 23.56
(B) 23.59
(C) 23.55
(D) 23.53
(E) 11.0
Rationale: Let the side of the square be a cm.
Parameter of the rectangle = 2(8 + 6) = 28 cm Parameter of the square = 28 cm
i.e. 4a = 28
A = 7
Diameter of the semicircle = 7 cm
Circimference of the semicircle
= 1/2(âˆ)7
= 1/2(22/7)(7) = 11 cm
Answer:E
Answer: (E) 11.0
Question: A man can swim in still water at 6 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
(A) 2
(B) 1.4
(C) 1.1
(D) 1.5
(E) 1.9
Rationale: M = 6
S = x
6 + x = (4.5 - x)2
6 + x = 12 -2x
3x = 6
x = 2
Answer:A
Answer: (A) 2
Question: A sprinter starts running on a circular path of radius r metres. Her average speed (in metres/minute) is πr during the first 30 seconds, πr/2 during next one minute, πr/4 during next 2 minutes, πr/8 during next 4 minutes, and so on. What is the ratio of the time taken for the nth round to that for the previous round?
(A) 4
(B) 8
(C) 16
(D) 32
(E) 36
Rationale: Explanation :
There is more than 1 way to approach the solution; however, I will detail the easiest way to go about it here.
We want to find the ratio of time taken for nth round : time taken for (n-1)th round
It will be same as finding the ratio of time taken for 2nd round : Time taken for 1st round.
1 round = Circumference of the circle = 2πr
1st round :
Speed = πr for 30 seconds. So, total distance travelled = πr/2.
Speed = πr/2 for 1 minute. So, total distance travelled = πr/2.
Speed = πr/4 for 2 minutes. So, total distance travelled = πr/2.
Speed = πr/8 for 4 minutes. So, total distance travelled = πr/2.
So, for a distance of 2πr, time taken is 7.5 minutes.
2nd round:
Speed = πr/16 for 8 minutes. So, total distance travelled = πr/2.
Speed = πr/32 for 16 minutes. So, total distance travelled = πr/2.
Speed = πr/64 for 32 minutes. So, total distance travelled = πr/2.
Speed = πr/128 for 64 minutes. So, total distance travelled = πr/2.
So, for a distance of 2πr, time taken is 120 minutes.
Ratio is 120:7.5 = 16:1.
Answer : C
Answer: (C) 16
Question: Anand and Deepak started a business investing Rs. 4,500 and Rs. 6,000 respectively. Out of a total profit of Rs. 420. Deepak's share is?
(A) s. 280
(B) s. 310
(C) s. 240
(D) s. 840
(E) s. 400
Rationale: Ratio of their shares = 4500 : 6000 = 3 : 4
Deepak's share = Rs. (420 * 4/7) = Rs. 240 ANSWER "C
Answer: (C) s. 240
Question: Evaluate : (2.39)(power 2) - (1.61) (power 2) / 2.39 - 1.61
(A) 4
(B) 6
(C) 8
(D) 2
(E) 10
Rationale: Given Expression = a(power 2) - b(power 2) / a-b
= (a + b)(a - b) / (a-b)
= (a + b) = (2.39 + 1.61) = 4.
Answer is A.
Answer: (A) 4
Question: The average of first 16 even numbers is?
(A) 10
(B) 11
(C) 17
(D) 13
(E) 14
Rationale: Sum of 16 even numbers = 16 * 17 = 272
Average = 272/16 = 17
ANSWER:C
Answer: (C) 17
Question: A basket contains 9 marbles. 4 are red and 5 are blue marbles If two marbles are drawn at random what is the probability that at least one ball is red.
(A) 19/18
(B) 17/18
(C) 11/18
(D) 13/18
(E) 15/18
Rationale: Total probability=9C2=36
4C2 +4C1*5C1=6+20=26
therefore the probability that at least one of the red ball will be selected= 26/36=13/18
answer is D
Answer: (D) 13/18
Question: The average age of 38 students in a group is 14 years. When teacherâ€™s age is included to it, the average increases by one. What is the teacherâ€™s age in years?
(A) 31
(B) 36
(C) 53
(D) 58
(E) None
Rationale: Sol.
Age of the teacher = ( 39 Ã— 15 â€“ 38 Ã— 14 ) years = 53 years.
Answer C
Answer: (C) 53
Question: In a rectangular coordinate system, what is the area of a rectangle whose vertices have the coordinates (-7, 1), (1, 1), (1, -6) and (-7, -6)?
(A) 112
(B) 64
(C) 42
(D) 24
(E) 56
Rationale: Length of side 1= 7+1=8
Length of side 2= 6+1= 7
Area of rectangle= 7*8= 56
E is the answer
Answer: (E) 56
Question: How many three digit numbers N are divisible by 78 or 91?
(A) 17
(B) 19
(C) 20
(D) 21
(E) 22
Rationale: The answer will be 19.
Explanation:
78= 2*3*13 now multiples of 78, 156 ....780, now 1000-780 = 220 only two more muktiples of 78 can exists. So total number of 3 digit Multiples of 78 are 9+2=11
91= 13*7--Total number of three digit multiples --9
No remember we have a common multiples as well N-- 13*7*6=91*6=546
So total number of multiples--11+9 -1 =19.
Hence Answer is 19.B
Answer: (B) 19
Question: In three annual examinations, of which the aggregate marks of each was 500, a student secured
average marks 45% and 55% in the first and the second yearly examinations respectively. To secure 50% average total marks, it is necessary for him in third yearly examination to secure marks :
(A) 300
(B) 250
(C) 400
(D) 450
(E) 500
Rationale: total marks:1500 for three exams
50% of 1500=750
first exam marks=45% of 500=225
second exam marks=55% of 500=275
let X be the third exam marks
225 + 275 + X =750
X=250
ANSWER:B
Answer: (B) 250
Question: When divided by 5, x has a remainder of 3 and y has a remainder of 2. Which of the following could be the remainder when x + y is divided by 10?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 0
Rationale: x = 5k+3 and y = 5j+2
x+y = 5(j+k) + 5
When divided by 10, the remainder is either 5 or 0.
The answer is E.
Answer: (E) 0
Question: The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %?
(A) 18%
(B) 16%
(C) 17%
(D) 78%
(E) 28%
Rationale: 1500 ---- 270
100 ---- ? => 18%
Answer:A
Answer: (A) 18%
Question: Two circular signs are to be painted. If the diameter of the larger sign is six times that of the smaller sign, how many times more paint is needed to paint the larger sign? (We can assume that a given amount of paint covers the same area on both signs.)
(A) 6
(B) 12
(C) 24
(D) 36
(E) 48
Rationale: Let R be the radius of the smaller sign.
Then the diameter of the smaller sign is 2R, the diameter of the larger sign is 12R, and the radius of the larger sign is 6R.
The area A of the smaller sign is A = piR^2.
The area of the larger sign is pi(6R)^2=36piR^2=36A.
Since the area is 36 times larger, we need 36 times more paint for the larger sign.
The answer is D.
Answer: (D) 36
Question: A cube of edge 5cm is immersed completely in a rectangular vessel containing water. If the dimensions of the base of vessel are 10cm * 5cm , find the rise in water level?
(A) 2.5cm
(B) 3.6cm
(C) 5cm
(D) 6.43cm
(E) 7.56cm
Rationale: Increase in volume = volume of the cube = 5*5*5 cm^3
Rise in water level = volume / area = 5*5*5/10*5 = 2.5cm
Answer is A
Answer: (A) 2.5cm
Question: A baker filled with a measuring cup with 1/4 cup water. He poured 1/2 of the water into the batter, and then spilled 1/8 of the water on the floor. How much water will the baker needed to add what is left in the cup to have 50% more than what he started with?
(A) 1/8 cup
(B) 3/8 cup
(C) 1/4 cup
(D) 1/2 cup
(E) 7/8 cup
Rationale: B
1/4 is the original water in cup .half in batter.So left is 1/8 out which 1/8 is spilled out.So again left with 0.
so 50% more than what he started was = 1/4+1/2*(1/4)=3/8
Amount of water needed to add = 3/8 - 0=3/8
B
Answer: (B) 3/8 cup
Question: If two positive numbers are in the ratio 1/8 : 1/5, then by what percent is the second number more than the first?
(A) 67%.
(B) 70%.
(C) 60%.
(D) 68%.
(E) 80%.
Rationale: Given ratio = 1/8 : 1/5 = 5 : 8
Let first number be 5x and the second number be 8x.
The second number is more than first number by 3x.
Required percentage = 3x/5x * 100 = 60%.
Answer: C
Answer: (C) 60%.
Question: A shopkeeper sold 8articles at the cost price of 10 articles. Then find the profit% or lost%
(A) 10%
(B) 25%
(C) 20%
(D) 30%
(E) 50%
Rationale: here 8 articles selling price = 10 articles cost price
so the difference = 10-8 = 2
% of profit = 2*100/8 = 25%
correct option is B
Answer: (B) 25%
Question: Compound interest earned on a sum for the second and the third years are Rs.1200 and Rs.1440 respectively. Find the rate of interest?
(A) 65% p.a
(B) 88% p.a
(C) 20% p.a
(D) 66% p.a
(E) 44% p.a
Rationale: Rs.1440 - 1200 = Rs.240 is the interest on Rs.1200 for one year.
Rate of interest = (100 * 240) / (100 * 1) = 20% p.a
Answer: C
Answer: (C) 20% p.a
Question: A certain rectangular window is (1/3) times as long as it is wide. If its perimeter is 28 feet, what are its dimensions in terms of length by width?
(A) 12 by 2
(B) 11 by 3
(C) 10.5 by 3.5
(D) 10 by 4
(E) 9 by 3
Rationale: 2x+2y=28
x+y=14
x+(1/3)x=14
4x=14*3
x=10.5
Answer C
Answer: (C) 10.5 by 3.5
Question: In how many years Rs 100 will produce the same interest at 5% as Rs. 200 produce in 2 years at 10%
(A) 8
(B) 10
(C) 9
(D) 12
(E) 11
Rationale: Explanation:
Clue:
Firstly we need to calculate the SI with prinical 200,Time 2 years and Rate 10%, it will be Rs. 40
Then we can get the Time as
Time = (100*40)/(100*5) = 8
Option A
Answer: (A) 8
Question: 5400 ÷ 9 ÷ 3 = ?
(A) 1800
(B) 900
(C) 450
(D) 300
(E) None of these
Rationale: 5400 ÷ 9 ÷ 3 = ?
or, ? = 5400 × 19×3=200
Answer E
Answer: (E) None of these
Question: A committee of three students has to be formed. There are seven candidates: Jane, Joan, Paul, Stuart, and Jessica. If Paul and Stuart refuse to be in the committee together and Jane refuses to be in the committee without Paul, how many committees are possible?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 8
Rationale: Let's try a different problem with your approach. There are five people: A, B, C, D, E. Need to chose 3 for a committee. A and B cannot be chosen together. B and C cannot be chosen together. How many options?
Your approach: total 10 options, 5c3.
Now, assume the wrong scenario where A and B are chosen together. There are three such scenarios. (A and B are chosen, just need one more person.) So we have to subtract the three wrong options. Similarly, there are three wrong scenarios where B and C are chosen together.
This gives us 10-3-3=4 as the answer.
Yet this answer is wrong. There are five possibilities: ACD, ACE, ADE, BDE, CDE.
E
Answer: (E) 8
Question: A library has an average of 600 visitors on Sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is:
(A) 250
(B) 260
(C) 300
(D) 285
(E) None
Rationale: Since the month begins with sunday,to there will be five sundays in the month
Average required = (600x5 + 240x25) /30) = 300
Answer: Option C
Answer: (C) 300
Question: What is the length of the longest pole which can be kept in a room 12 m long, 4 m broad and 3 m high?
(A) 7
(B) 9
(C) 11
(D) 13
(E) None
Rationale: Explanation:
d2 = 122 + 42 + 32 = 13
D)
Answer: (D) 13
Question: At the faculty of Aerospace Engineering, 312 students study Random-processing methods, 222 students study Scramjet rocket engines and 112 students study them both. If every student in the faculty has to study one of the two subjects, how many students are there in the faculty of Aerospace Engineering?
(A) 404
(B) 452
(C) 444
(D) 468
(E) 422
Rationale: 312 + 222 - 112 (since 112 is counted twice )= 422
E is the answer
Answer: (E) 422
Question: A shopkeeper buys two articles for Rs.1000 each and then sells them, making 15% profit on the first article and 15% loss on second article. Find the net profit or loss percent?
(A) 200
(B) 768
(C) 150
(D) 280
(E) 279
Rationale: Profit on first article = 150% of 1000 = 150.
This is equal to the loss he makes on the second article. That, is he makes neither profit nor loss.
Answer: C
Answer: (C) 150
Question: Find the invalid no.from the following series 2,3,12,37,86,166,288
(A) 2
(B) 3
(C) 166
(D) 12
(E) 288
Rationale: 3-2=1
12-3=9
37-12=25
86-37=49
166-86=80(this must be 81=167-86=81)
so wrong number in the sequence is 166
difference between two sucessive numbers sequence would be
1,9,25,49,81,121(square of 1,3,5,7,9,11)
C
Answer: (C) 166
Question: The volumes of two cones are in the ratio 1 : 12 and the radii of the cones are in the ratio of 1 : 3. What is the ratio of their heights?
(A) A)3:4
(B) B)2:7
(C) C)2:2
(D) D)2:1
(E) E)2:9
Rationale: The volume of the cone = (1/3)πr2h
Only radius (r) and height (h) are varying.
Hence, (1/3)π may be ignored.
V1/V2 = r12h1/r22h2 => 1/12 = (1)2h1/(3)2h2
=> h1/h2 = 3/4
i.e. h1 : h2 = 3: 4
Answer: A
Answer: (A) A)3:4
Question: In a room there are 8 people. Each person shook hands with every other person. How many hand shakes were there?
(A) 26
(B) 28
(C) 30
(D) 32
(E) 34
Rationale: 8C2 = 28
The answer is B.
Answer: (B) 28
Question: The average (arithmetic man) of three integers a, b, and c is exactly four times the median. If a < b < c and a = 0, what is the value of c/b?
(A) 2
(B) 3
(C) 4
(D) 11
(E) Cannot be determined from the information given.
Rationale: The average of three integers a, b, and c is exactly twice the median --> (a+b+c)/3=4b --> since a=0, then (0+b+c)/3=4b --> c=11b --> c/b=11.
Answer: D.
Answer: (D) 11
Question: If f(x)= 5x^2- 2x+6 and g(y)= 3y-4, then g(f(x))
(A) 82x^2-9x+38
(B) 15x^2-6x+14
(C) 58x^2-4x+58
(D) 87x^2-5x+96
(E) 98x^2-7x+94
Rationale: g(f(x))=3(5x^2-2x+6)-4
=15x^2-6x+18-4
=15x^2-6x+14
the answer is B
Answer: (B) 15x^2-6x+14
Question: In a village there are 150 men and 90 women in present time.if in next year population will be P=(a^2 +b^2)^1/2 , and in every year men are reduces 8%.what is population of after 2 year.
(A) 140
(B) 141
(C) 142
(D) 143
(E) 144
Rationale: next year total population=[150^2+90^2]^.5=174.92=175
man decreased by 8% so total man =150*.92=138
women will be= 175-138=37
so population after two years= [135^2+37^2]^.5=142.87=143
so population after two year= 143
ANSWER:D
Answer: (D) 143
Question: Ramesh spends 50% of his monthly salary on food, and saves 90% of the remaining amount. If his monthly salary is Rs.10,000, how much money does he save every month ?
(A) Rs.2500
(B) Rs. 4500
(C) Rs.8000
(D) Rs.3000
(E) Rs.1000
Rationale: Explanation:
Ramesh's monthly income = Rs.10,000
He spends 50% on food.
The total money spent on food = 50/100 * 10000 = Rs. 5000
Now, his monthly remaining income = Rs.10000 – Rs.500 = Rs. 5000
Out of Rs. 5000, he saves 90%.
Amount saved = 90/100 * 5000 = Rs. 4500
ANSWER:B
Answer: (B) Rs. 4500