RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: The average (arithmetic mean) of four different positive integers is 4. If the first of these integers in 3 times the second integer and the second integer is 6 less than the third integer, what is the least possible value of the fourth integer?
A.5
B.3
C.4
D.2
Answer: C.4
Explanation: Let the second integer be x and the fourth be a.
Then [3x + x + (x+2) + a]/4 = 9
=> 5x + 2 + a = 36
=> 5x + a = 34
=> a = 34 - 5x
From the above equation we can see that a is minimum when x is maximum, provided both are positive
The maximum value that x can take in the above equation while still keeping a positive is x=6
This gives us a= 34 - 30 = 4
Therefore the minimum value that the fourth integer can have is 4.
Answer:C
Question: A school currently maintains a fixed number of students per class. If the ratio of students per class were to be increased by 1, 10 fewer classes would be run for a total of 120 students. What is the current ratio of students per class?
A.3
B.4
C.6
D.8
Answer: A.3
Explanation: Number of classes now : 120/x, where x is the number of students per class.
When it is increased by 1, Number of classes will be 120/(x+1).
We are told, 120/x - 120/(x+1) = 10 => Solving x = 3.
ANSWER:A
Question: 6^5 + 6^5 + 6^5 + 6^5 =
A.6^6
B.7^6
C.4^8
D.4^9
Answer: A.6^6
Explanation: Hi shakticnb,
Certain Quant questions on the GMAT are just about 'organizing' the information in a specific way. If you find yourself getting confused by a prompt, think about how you might change the way that the information is presented to you.
Here, for example, we're asked for....
6^5 + 6^5 + 6^5 + 6^5 =
Now, the GMAT doesn't really expect us to calculate this sum (but we could if we had to), but we are expected to find a way to organize this information... If, instead of all of those exponents, we had...
X + X + X + X =
What would the sum be?
Clearly, it would be 4(X) = 4X.....since we're just combining 'like' terms. Take that same idea with this prompt and you have...
6^5 + 6^5 + 6^5 + 6^5 =
6(6^5)
This can be re-written as...
(6^1)(6^5)
...and now we can use exponent rules; since we're MULTIPLYING 'bases' that are the same, we ADD the exponents...
(6^1)(6^5) = 6^6
Final Answer:
A
Question: On the first day of her vacation, Louisa traveled 240 miles. On the second day, traveling at the same average speed, she traveled 420 miles. If the 240-mile trip took 3 hours less than the 420-mile trip, what was the average speed, in miles per hour?
A.65
B.50
C.55
D.60
Answer: D.60
Explanation: (time)*(rate) = (distance)-->(rate) = (distance)/(time)--> given:(rate) = 240/t = 420/(t+3)-->4/t = 7/(t+3)-->4t+12=7t ---->3t= 12 . t= 4 ---->(rate ) = 240/4 = 60
Answer: D
Question: One hour after Adrienne started walking the 60 miles from X to Y, John started walking from X to Y as well. Adrienne walks 3 miles per hour and John walks 1 mile per hour faster than Adrienne. How far from X will John be when he catches up to Adrienne?
A.12 miles
B.9 miles
C.10 miles
D.11 miles
Answer: A.12 miles
Explanation: First, determine how far Adrienne has walked in the one hour. She has walked three miles which means she is three miles ahead of John when he sets off. John walks at four miles/hour which means that every hour, John will get one mile closer to Adrienne. If he gets one mile closer every hour, it will take him three hours to catch up to her which means he travels 3hours * 4 miles/hour = 12 miles and she travels 4 hours * 3 miles/hour = 12 miles. He will be 12 miles from X when he catches up to her.
A slightly different way to solve...
We don't know how long they will walk before they catch up to one another but we do know that A walks for one hour more than J. J = T and A = T+1. We are looking for the distance at which they meet up which means the distance will be the same. D=r*t so,
r*t (John ) = r*t (adrienne)
r*(t) = r*(t+1)
4t = 3t+3
t=3
d=r*t
d=4*3
d=12
A) 12 miles
Question: 5358 x 55 = ?
A.272258
B.272358
C.294690
D.274258
Answer: C.294690
Explanation: 5358 x 51	= 5358 x (50 + 5)
= 5358 x 50 + 5358 x 5
= 267900 + 26790
= 294690.
C)
Question: A student gets 50% in one subject, 60% in the other. To get an overall of 60% how much should get in third subject.
A.75%
B.70%
C.45%
D.55%
Answer: B.70%
Explanation: Let the 3rd subject % = x
50+60+x = 3*60
110+x =180
x = 180-110 =70
Answer :B
Question: Dhoni has x dollars more than Rahul has, and together they have a total of y dollars. Which of the following represents the number of dollars that Rahul has?
A.(y – x)/3
B.(y – x)/2
C.(y – x)/4
D.(2y – x)/2
Answer: B.(y – x)/2
Explanation: To solve, we will set up two equations. Let's start by defining two variables.
R = number of dollars Rahul has
D= number of dollars Dhoni has
We are given that Dhoni has x dollars more than Rahul. We set up an equation:
D= x + R
We are next given that together they have a total of y dollars. We can set up our second equation:
R + D = y
Since we know that D = x + R, we can substitute x + R for D into the second equation R+ D = y.
Notice that, after the substitution, we will only have variables of R, x, and y. Thus, we have:
R + x + R = y
2R + x = y
2R = y – x
R = (y – x)/2
Answer : B
Question: If the 9th day of a month is two days earlier than Monday, What day will it be on the nineteenth day of the month?
A.Saturday
B.Tuesday
C.Sunday
D.Wednesday
Answer: B.Tuesday
Explanation: Explanation:
Given that 9th day of a month is two days earlier than Monday
=> 9th day is Saturday
=> 16th is Saturday
=> 19th is Tuesday
Answer: Option B
Question: If s and t are positive integers such that s/t = 64.24, which of the following could be the remainder when s is divided by t?
A.15
B.20
C.25
D.30
Answer: D.30
Explanation: 0.24 = 24/100 = 6/25
The remainder must be divisible by 6.
The answer is D.
Question: Set A: 3, q, 8, 10
Set B: 4, y, 9, 11
The terms of each set above are given in ascending order. If the median of Set A is equal to the median of Set B, what is the value of y – q?
A.-2
B.-1
C.0
D.1
Answer: B.-1
Explanation: So we have even no. of elements in the Set
So median is the average of Middle two numbers
(q+8)/2= (y+9)/2
y - q= -1
Answer B
Question: Two trains of equal length, running with the speeds of 60 and 40 kmph, take 36 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions?
A.10 sec
B.16 sec
C.19 sec
D.7.2 sec
Answer: D.7.2 sec
Explanation: RS = 60 -40 = 20 * 5/18 = 100/18
T = 36
D = 36 * 100/18 = 200
RS = 60 + 40 = 100 * 5/18
T = 200 * 18/500 = 7.2 sec
Answer: D
Question: $500 will become $1000 in 5 years find the rate of interest?
A.10%
B.20%
C.25%
D.30%
Answer: B.20%
Explanation: SI = simple interest = A-P = 1000-500 = $500
R = 100SI/PT = 100*500/500*5 =20%
Answer is B
Question: The average of 11 numbers is 10.9. If the average of first six is 10.5 and that of the last six is 11.4 the sixth number is?
A.11.9
B.11.6
C.11.4
D.11.5
Answer: D.11.5
Explanation: 1 to 11 = 11 * 10.9 = 119.9
1 to 6 = 6 * 10.5 = 63
6 to 11 = 6 * 11.4 = 68.4
63 + 68.4 = 131.4 – 119.9 = 11.5
6th number = 11.5
Answer:D
Question: 9 men went to a restaurant for taking their snacks. Eight of them spent Rs.15 each on their snacks and the ninth spent Rs.8 more than the average expenditure of all the nine. What was the total money spent by them.
A.Rs 115
B.Rs116
C.Rs 144
D.Rs 178
Answer: C.Rs 144
Explanation: Explanation :
Let the average expenditure of all the nine be RS.x
Then, 15 8 + (x + 8) = 9x
Therefore x = 16
Total money spent = 9x = RS.(9 16) = Rs.144
Answer : C
Question: The sum of present age of Abe and the age before 7 years is 27. Find the present age of Abe. What will be his age after 7 years?
A.25
B.24
C.27
D.28
Answer: B.24
Explanation: Present age = x
Before 7yrs, y=x-7
After 7yrs, z=x+7
By the qn,
x+(x-7)=27
2x-7=27
2x=27+7
x=34/2
x=17
z=x+7
=17+7
=24
ANSWER:B
Question: If 42.18 = k(14 + m/50), where k and m are positive integers and m < 50, then what is the value of k + m ?
A.6
B.7
C.8
D.9
Answer: A.6
Explanation: 42.18 = 14K + Km/50...we can rewrite the number as follows:
42+ 0.18= 14K + Km/50........Since K is integer, then 42=14K..........K=3
0.18=Km/50......18/100=3m/50......m=3
k+m=3+3=6
Answer: A
Question: How many 5 digit number can be formed out of digits 0,2,4,6,8 that is divisible by 8.
A.26
B.30
C.38
D.98
Answer: B.30
Explanation: For a number to be divisible by 8, its last three digits must divisible by 8.
So, last three digits can be from the following group
(024), (048), (064), (208), (240), (248), (264), (280), (408), (480), (608), (624), (640), (648), (680), (824), (840), (864),
There are 18 such groups.
Consider these 12 groups in which zero is there
(024), (048), (064), (208), (240), (280), (408), (480), (608), (640), (680), (840)
With each of these 12 groups, first digit can be any of the remaining 2 digits and second digit can be the remaining one digit
Therefore, 12×2 = 24 such numbers
Consider the 6 groups in which zero does not come
(248), (264), (624), (648), (824), (864),
With each of these 6 groups, first digit can be the one remaining digit(because zero cannot be the first digit)
Second digit can be zero
Therefore, 6×1 = 6 such numbers
Therefore, total count of 5 digit numbers = 24 + 6 = 30
So, Ans is 30
ANSWER:B
Question: The length, breadth and height of a room are in the ratio 9 : 4 : 2. If the breadth and height are halved while the length is doubled, then the total area of the four walls of the room will
A.(a) remain the same
B.(b) decrease by 13.64%
C.(c) decrease by 15%
D.(d) decrease by 23.08%
Answer: D.(d) decrease by 23.08%
Explanation: Length (L) = 9
Breadth (B) = 4
Height (H) = 2
Total Area of Walls = 2(BH + LH) = 2*(4*2 + 9*2) = 2*(8+18) = 52
Then, Finally
Length (L) = 2*9 = 18
Breadth (B) = 4/2 = 2
Height (H) = 2/2 = 1
Total Area of Walls = 2(BH + LH) = 2*(2*1 + 18*1) = 2*(2+18) = 40
% change in Area of four walls = (Final Area-Initial Area)*100 /Initial Area
i.e. % change in Area of four walls = (40-52)*100 /52=- 23.08% (Decrease)
Answer: Option D
Question: A chair is bought for Rs.500/- and sold at a loss of 10% find its selling price
A.Rs.450/-
B.Rs.451/-
C.Rs.440/-
D.Rs.455/-
Answer: A.Rs.450/-
Explanation: Loss = 500*10/100 = 50
S.P = C.P - Loss
= 500- 50
=Rs.450/-
Answer : A
Question: A person purchased a TV set for Rs. 13000 and a DVD player for Rs. 6250. He sold both the items together for Rs. 31150. What percentage of profit did he make?
A.16.82%
B.87.82%
C.61.82%
D.17.82%
Answer: C.61.82%
Explanation: The total CP = Rs. 13000 + Rs. 6250 = Rs. 19250 and SP
= Rs. 31150
Profit(%) = (31150 - 19250)/19250 * 100
= 61.82%
Answer:C
Question: A cistern of capacity 40 litres has an inlet and an outlet pipe. When both the pipes are opened at once, it takes 8 minutes to fill the cistern. However, if the outflow rate is increased 1.5 times, the cistern never gets filled. Which of the following can be the outflow rate?
A.8 litres/minute
B.6 litres/minute
C.12 litres/minute
D.9 litres/minute
Answer: C.12 litres/minute
Explanation: DETAILED SOLUTION
Initially, net flow in the tank = 40 litres/ 8 minutes = 5 litres/minute
Now, the increase in outflow should be greater than 5 litres/min for the tank to fill up
Increase in outflow = 1.5x – x = 0.5x
Only in option c) 0.5 X 12 = 6 litres/min > 5 litres/min
CORRECT ANSWER C
Question: Of the 24 participants in a certain competition, half are male, and half of the males are younger than 18 years of age. If half of the female competitors are also younger than 18 years of age, into how many distinct groups of 4 competitors could the participants be divided if each group must contain two males under 18 years of age and 2 females over 18 years of age?
A.225
B.45
C.65
D.95
Answer: A.225
Explanation: M under 18 - 6
F above 18 - 6
How many distinct groups can be formed now: 6c2 * 6c2 = 225
Answer : A
Question: The speed of a boat in still water is 30kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
A.kmph
B.kmph
C.kmph
D.kmph
Answer: B.kmph
Explanation: Speed downstream = 30+ 20 = 50 kmph
Speed upstream = 30 - 20 = 10 kmph
Answer:B
Question: In how many different F ways can 4 ladies and 4 gentlemen be seated at a round table so that all ladies sit together?
A.70
B.288
C.576
D.10,080
Answer: C.576
Explanation: Treat the 4 ladies as one object, now you have 5 objects to arrange around a table (m1,m2,m3,m4,women). This can be done in (5-1)! ways
And there are 4! ways to arrange ladies among themselves
Answer F= (4!)^2 = 576 or C
Question: 16384, 8192, 2048, 256, 16, ?
A.0.5
B.1
C.1.5
D.2
Answer: A.0.5
Explanation: Terms are continuously divided by 2,4,8,16, and so on
16384
16384 ÷ 2 = 8192
8192 ÷ 4 = 2048
2048 ÷ 8 = 256
256 ÷ 16 = 16
16 ÷ 32 = 0.5
Answer is A.
Question: George went to a fruit market with certain amount of money. With this money he can buy either 50 oranges or 40 mangoes. He retains 5% of the money for taxi fare and buys 25 mangoes. How many oranges can he buy?
A.25
B.30
C.20
D.22.5
Answer: D.22.5
Explanation: Let the amount of money be 200
Let cost of 1 Orange be 4
Let cost of 1 mango be 5
He decides to retain 5% of 200 = 10 for taxi fare, so he is left with 190
He buys 20 mangoes ( @ 5) so he spends 100
Money left is 90 (190 - 100)
No of oranges he can buy = 90/4 =>22,5
So, George can buy 20 Oranges.
D
Question: A manufacturer sells a pair of glasses to a wholesale dealer at a profit of 18%. The wholesaler sells the same to retailer at a profit of 20%. The retailer in turn sells them to a customer for Rs. 30.09, there by earning a profit of 25%. The cost price for the manufacturer is?
A.33
B.29
C.17
D.10
Answer: C.17
Explanation: Explanation:
Let the cost price for the manufacturer be Rs. x. Then, 125% of 120% of 118% of x = 30.09.
125/100 * 120/100 * 118/100 * x = 3009/100
177/100 x = 3009/100 => x = 17
Answer:C
Question: A, B, C enter into a partnership investing Rs. 35,000, Rs. 45,000 and Rs. 55,000 respectively. The respective shares of A, B, C in annual profit of Rs. 40,500 are?
A.Rs. 10,500, Rs. 13,500, Rs. 16,500
B.Rs. 10,500, Rs. 13,500, Rs. 16,509
C.Rs. 10,500, Rs. 13,500, Rs. 16,506
D.Rs. 10,500, Rs. 13,500, Rs. 16,588
Answer: A.Rs. 10,500, Rs. 13,500, Rs. 16,500
Explanation: A:B:C = 35000 : 45000 : 55000 = 7:9:11
A's share = 40500 * 7/27 = Rs. 10500
B's share = 40500 * 9/27 = Rs. 13500
C's share = 40500 * 11/27 = Rs. 16500.Answer: a
Question: If by selling an article for Rs.60, a person loses 1/7 of money, what would he have gained or lost % by selling it for Rs.77?
A.5%
B.10%
C.23%
D.25%
Answer: B.10%
Explanation: Sol. CP - = EC7 = 70 1-7 6 77-70 % Profit = 100 = 10%
B
Question: In a class, if 50% of the boys were girls, then there would be 50% more girls than boys. What percentage of the overall class is girls?
A.25%
B.33.33%
C.40%
D.20%
Answer: D.20%
Explanation: DETAILED SOLUTION
For questions of this type, it is best to go from the final step. In the final state, the number of girls should be 1.5 * the number of boys.
When 50% of the boys are taken as girls, let the number of boys = x
Number of girls = 1.5x
total number of students = 2.5x
Original number of boys = 2x (50% of boys = x)
Original number of girls = 0.5x
Girls form 20% of the overall class.
CORRECT ANSWER D.
Question: A garrison of 400 men had a provision for 31 days. After 28 days 280 persons re-enforcement leave the garrison. Find the number of days for which the remaining ration will be sufficient?
A.65 days
B.45 days
C.10 days
D.16 days
Answer: C.10 days
Explanation: 400 --- 31
400 --- 3
120 --- ?
400*3 = 120*x => x =10 days.Answer: C
Question: Tanks X and Y contain 500 and 200 gallons of water respectively. If water is being pumped out of tank X at a rate of K gallons per minute and water is being added to tank Y at a rate of M gallons per minute, how many hours will elapse before the two tanks contain equal amounts of water?
A.5/M+K hours
B.6(M+K) hours
C.300/M+K hours
D.300/M−K hours
Answer: C.300/M+K hours
Explanation: Consider k=1,m=2
Then per the question,
500 - 1x = 200 + 2x
x=100
Check answer options for No. of hours (x)=100 for k=1 and m=2
ANSWER:C
Question: In how many different number of ways 4 boys and 3 girls can sit on a bench such that girls always sit together?
A.720
B.740
C.760
D.790
Answer: A.720
Explanation: Option 'A'
Question: The probability of a lottery ticket being a prized ticket is 0.2. When 4 tickets are purchased, the probability of winning a prize on atleast one ticket is?
A.0.5919
B.0.5904
C.0.5929
D.0.5928
Answer: B.0.5904
Explanation: P(winning prize atleast on one ticket)
= 1 - P("Losing on all tickets")
= 1 - (0.8)4 = (1 + (0.8)2)(1 - (0.8)2)
= (1.64)(0.36) = 0.5904
Answer: B
Question: Find the cost of fencing around a circular field of diameter 12 m at the rate of Rs.3.50 a meter?
A.131.95
B.132.9
C.140.33
D.123.4
Answer: A.131.95
Explanation: 2 * 22/7 * 6 = 37.7
37.7 * 3 1/2 = Rs.131.95
Answer: A
Question: A palindrome is a number that reads the same forward and backward, such as 242. How many even nine-digit numbers are palindromes?
A.40
B.40000
C.500
D.5,000
Answer: B.40000
Explanation: if the palindrome must be even, it must begin and end in 2,4 6 and 8 ( 4 ways) e.g 222212222,444414444.
The middle number in the nine-digit could be 0-9 ( 10 ways), e.g 22522, 22822
The 2nd and fourth numbers
, the 3rd and 5th and 4th and 6th could must also be same i.e 0-9( 10 ways) e.g 242343242, 648565846
we thus have, 4 *10*10*10*10=40000 B
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.3
B.4
C.9
D.3
Answer: B.4
Explanation: Explanation:
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: Option B
Question: A 270 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train?
A.230
B.200
C.250
D.300
Answer: A.230
Explanation: Answer: Option A
Explanation:
Relative speed = 120 + 80 = 200 km/hr.
= 200 * 5/18 = 500/9 m/sec.
Let the length of the other train be x m.
Then, (x + 270)/9 = 500/9 => x = 230.
ANSWER A
Question: In shop there are 10 bulbs, a total of 4 are defective. If a customer buys 4 bulbs selected at random from the box, what is the probability that neither bulbs will be defective?
A.2/19
B.3/29
C.4/15
D.1/15
Answer: D.1/15
Explanation: First, there are 6C4 ways you can select 6 good bulbs from 4 good ones.
Second, there are 10C4 ways you select 4 bulbs from 10 ones in the box.
Then, the probability that neither bulb will be defective is: 6C4/10C4=15/210 = 1/15
Answer is D
Question: A salesman's income consists of a commission and a base salary of $350 per week. Over the past 5 weeks, his weekly income totals have been $556, $413, $420, $436 and $395. What must his average (arithmetic mean) commission be per week over the next two weeks so that his average weekly income is $500 over the 7-week period?
A.$150
B.$290
C.$365
D.$715
Answer: B.$290
Explanation: Total weekly income over 5 weeks=$556+$413+$420+$436+$395=$2220
For avg weekly income to be $500 over 7 weeks, we need total weekly income over 7 weeks=$3500
Now, $3500-$2220=$1280
From this, we subtract base salary for 2 weeks i.e $350*2=$700
Therefore, commission=$1280-$700=$580 for 2 weeks
Avg weekly commission=$290
Answer B
Question: The population of a town is 216400. If it increase at the rate of 4% per annum. What will be its population for 3years hence?
A.200000
B.243420
C.194582
D.194481
Answer: B.243420
Explanation: population after 3years = 216400*(1+ 4/100)^3 = 243420
Answer is B
Question: If u and v are positive integers, and 3 is not a factor of v, then v may be which of the following?
A.(u−1)·u·(u+1)
B.(u−3)·(u−1)·(u+1)
C.(u−2)·u·(u+2)
D.(u−1)·u·(u+2)
Answer: D.(u−1)·u·(u+2)
Explanation: Plugged in values :
let u=5
A. (u−1)·u·(u+1) --> divisible by 3
B. (u−3)·(u−1)·(u+1) --> divisible by 3
C. (u−2)·u·(u+2) --> divisible by 3
D. (u−1)·u·(u+2) --> not divisible. Hence the answer.
Question: In how many different ways can 2 identical blue balls and 2 identical red balls be shared among 4 children such that each child receives a ball?
A.10
B.24
C.34
D.20
Answer: B.24
Explanation: GGG RRR
Therefore total number of ways is
4! but there are two groups of 2 identical things.
Therefore total number of "different" ways is
4!/ (2!) (2!) = 24 ANS:B
Question: If x^2 + y^2 = 20 and xy = 3, then (x − y)^2 =
A.8
B.11
C.14
D.17
Answer: C.14
Explanation: but you cannot take xy+ 3 to mean xy=-3..
only if xy+3=0, it will mean xy=-3..
rest your solution is perfect and you will get your correct answer as 20-2*3=14..
Answer C
Question: If k, l, and m are distinct positive prime numbers, then (k^3)(l)(m) has how many different positive factors greater than 1?
A.a. 8
B.b. 9
C.c. 12
D.d. 10
Answer: D.d. 10
Explanation: Let Number is (k^3)(l)(m) = (1^3)(4)(20) = 80
We can write 80 as product of two numbers in following ways
1*80
2*40
4*20
5*16
8*10
5 cases = 5*2 i.e. 10 factors (including 1)
Factors greater than 1 = 9
Answer: Option D
Question: A man can row a boat at 18 kmph in still water. If the speed of the stream is 12 kmph, what is the time taken to row a distance of 90 km downstream?
A.6 hours
B.4 hours
C.3 hours
D.5 hours
Answer: C.3 hours
Explanation: Speed downstream = 18 +12 = 30 kmph.
Time required to cover 90 km downstream = d/s = 90/30 = 3 hours.Answer:C
Question: Ayisha's age is 1/6th of her father's age. Ayisha's father's age will be twice Shankar's age after 10 years. If Shankar's eight birthdays was celebrated two years before, then what is Ayisha's present age.
A.5
B.10
C.7
D.9
Answer: A.5
Explanation: Shankar's present age =8+2=10
Ayisha's father's age after 10 years =2(10+10)=40
Ayisha's father's present age =40−10=30
Ayisha's present age =16×30=5
Answer is A.
Question: 3 years ago, the average age of P and Q was 20years. With R joining them, theiraverage age becomes 23years. What is the age of R?
A.18 years
B.20 years
C.21years
D.23 years
Answer: D.23 years
Explanation: Three years ago, the average age of P and Q was 20 years.
Three years ago, their sum of the ages was 2x20= 40 years
Present age of P+Q+R = 3 X23 =69
Present age of P+Q=40+( 2 x 3)= 46
Present age of R = ( P+Q+R)- (P+Q)= 69-46 =23 years
D
Question: For all integers x>1. <x>=2x+(2x-1)+(2x-2)+......2+1. What is the value of <2>*<3>?
A. 210
B. 116
C. 212
D. 263
Answer: A. 210
Explanation: Since <x>=2x+(2x-1)+(2x-2)+......2+1=1+2+..+(2x-2)+(2x-1)+2x then<x> is basically the sum of all integers from 1 to 2x, inclusive.
Hence <3> is the sum of all integers from 1 to 2*3=6 and <2> is the sum of all integers from 1 to 2*2=4 --> <3>=21 and <2>=10 --> <3>*<2>=21*10=210.
Answer: A
Question: Tea worth Rs.126 per kg are mixed with a third variety in the ratio 1: 1 : 2. If the mixture is worth Rs.173 per kg, the price of the third variety per kg will be
A.Rs.169.50
B.Rs.1700
C.Rs. 195.50
D.Rs. 180
Answer: C.Rs. 195.50
Explanation: Solution
Since first second varieties are mixed in equal proportions, so their average price = Rs.(126+135/2) = Rs.130.50
So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x.
x-173/22.50 = 1 =â€º x - 173 = 22.50 =â€º x=195.50.
Hence, price of the third variety = Rs.195.50 per kg.
Answer C
Question: If f(x) = k(x - k) and k is a constant, what is the value of f(6) - f(2), in terms of k?
A. 1
B. 4k
C. 7k - 1
D. k^2 + k
Answer: B. 4k
Explanation: First, distribute f(x). k(x - k) = kx - k^2. Now evaluate f(6) and f(2):
f(6) = k(6) - k^2 = 6k - k^2
f(2) = 2k - k^2
Answer B
Question: Insert the missing number.
2, 6, 12, 20, 30, 42, 56, (....)
A.22
B.38
C.72
D.66
Answer: C.72
Explanation: Explanation:
The pattern is 1 x 2, 2 x 3, 3 x 4, 4 x 5, 5 x 6, 6 x 7, 7 x 8.
So, the next number is 8 x 9 = 72.
Answer: C) 72
Question: In the junior basketball league there are 15 teams, 2/3 of them are bad and ½ are rich. What can't be the number of teams that are rich and bad?
A.4.
B.6.
C.7.
D.9.
Answer: D.9.
Explanation: total teams =16
bad teams=(2/3)*15=10
rich teams=8
so maximum value that the both rich and bad can take will be 8. so E= 9 can not be that value.
ans D.