mathewhe/aqua_rat huggingface dataset:
Question: Rohit was 4 times as old as his son 8 years ago. After 8 years, Rohit will be twice as old as his son. What are their present ages?
(A) 16 and 40 years
(B) 13 and 37 years
(C) 10 and 34 years
(D) 11 and 35 years
(E) 20 and 44 years
Rationale: Let son's age 8 years ago be x years.
Then, Rohit's age 8 years ago = 4x years.
Son's age after 8 years = (x + 8) + 8 = (x + 16) years.
Rohit's age after 8 years = (4x + 8) + 8 = (4x+ 16) years.
2 (x + 16) = 4x + 16
2x = 16
x = 8.
Hence, son's 'present age = (x + 8) = 16 years.
Rohit's present age = (4x + 8) = 40 years.
Answer is A.
Answer: (A) 16 and 40 years
Question: Two friends P & Q started a business investing amounts in the ratio of 5 : 6. R joined them after six months investing an amount equal to that of Qâ€™s amount. At the end of the year 10% profit was earned which was equal to 98,000. What was the amount invested by R?
(A) 2,10,000
(B) 1,05,000
(C) 1,75,000
(D) 2,00,000
(E) None of these
Rationale: Ratio for amount invested by P, Q & R
= 5x Ã— 12 : 6x Ã— 12 : 6x Ã— 6
= 60x : 72x : 36x
= 5x : 6x : 3x
Profit = 98000 = 10% of T
where, T = Total amount
T = 980000
Amount received by
R = 3x /3x+6x+5x(980000)
= 210000
Answer A
Answer: (A) 2,10,000
Question: A box has 210 coins of denominations one-rupee and fifty paise only. The ratio of their respective values is 13:11. The number of one-rupee coin is
(A) 65
(B) 66
(C) 77
(D) 78
(E) NOne
Rationale: Solution: Respective ratio of the number of coins;
= 13:11*2 = 13:22
Hence, Number of 1 rupee coins;
= 13*210/(13+22) = 78.
Answer: Option D
Answer: (D) 78
Question: Mike took a taxi to the airport and paid $2.50 to start plus $0.25 per mile. Annie took a different route to the airport and paid $2.50 plus $5.00 in bridge toll fees plus $0.25 per mile. If each was charged exactly the same amount, and Annie's ride was 18 miles, how many miles was Mike's ride?
(A) 30
(B) 34
(C) 38
(D) 42
(E) 48
Rationale: The cost of Annie's ride was 2.5+5+(0.25*18) = $12
Let x be the distance of Mike's ride.
The cost of Mike's ride is 2.5+(0.25*x) = 12
0.25*x = 9.5
x = 38 miles
The answer is C.
Answer: (C) 38
Question: How many polynomials are there of the form x3rd - 8x2round + cx + d such
that c and d are real numbers and the three roots of the polynomial are
distinct positive integers?
(A) 0
(B) 1
(C) 1
(D) 2
(E) 5
Rationale: The sum of the roots of the polynomial is 8. Since the roots are distinct
positive integers, then they are either 1, 2, 5 or 1, 3, 4. Thus, the polynomial is either
(x − 1)(x − 2)(x − 5) or (x − 1)(x − 3)(x − 4).
correct answer C
Answer: (C) 1
Question: A woman invested $1,000, part at 5% and the rest at 6%. Her total investment with interest at the end of the year was $1,051. How much did she invest at 5%?
(A) $500
(B) $600
(C) $700
(D) $900
(E) $950
Rationale: et x be the portion invested at 5% and
Let (1-x) be the rest which is invested at 6%
The question states that the return after 1 year is (1051/1000)-1 = 0.051 = 5.1%
We want to find the dollar amount invested in X
Using our defined variables, put together the equation and solve for x (the percentage of 1000 invested at 5%)
0.05x+0.06(1-x)= 0.051
(0.05)x +0.06 - (0.06)x = 0.051
-0.01x = -0.009
x= -0.009/-0.01 = 9/10 = 90%
So X = 90% of the 1000 which is 900
ANSWER:D
Answer: (D) $900
Question: 2, 1, (1/2), (1/4), ?
(A) (1/3)
(B) (1/8)
(C) (2/8)
(D) (1/16)
(E) (3/16)
Rationale: This is a simple division series; each number is one-half of the previous number.
Answer : B.
Answer: (B) (1/8)
Question: If x = (y)(y + 1) and y is a prime number less than 6, which of the following could not be the product of 2 consecutive integers?
(A) a) 5x
(B) b) 11x
(C) c) 13x
(D) d) 30x
(E) e) 58x
Rationale: Given y is a prime number less than 6
possible values of y are 2 3 5
given, x=y*(y+1)
if y = 2 x=2*3=6
if y = 3 x=3*4=12
if y = 5 x=5*6=30
so possible values of x are 6,12,30
So from options
A. 5x can be (5*6)
B. 11x can be (11*12)
C. 13x can be (13*12)
D. 30x can be (30*31)
E. 58x cannot be
So answer option E
Answer: (E) e) 58x
Question: Find for what value(s) of k would there be an unique solution for the given set of questions.
2x - 3y = 1 and kx + 5y = 7
(A) -10/3
(B) -10/9
(C) -10/0
(D) -10/1
(E) -10/2
Rationale: : If two equations ax + by = M and cx + dy = N have a unique solution, then ac≠bdac≠bd
So in the above problem, k ≠−10/3
Answer:A
Answer: (A) -10/3
Question: 9 men and 12 boys finish a job in 12 days, 12 men and 12 boys finish it in 10 days. 10 men and 10 boys shall finish it in how many days?
(A) 18
(B) 17
(C) 12
(D) 19
(E) 12
Rationale: 9M + 12B ----- 12 days
12M + 12B ------- 10 days
10M + 10B -------?
108M + 144B = 120M +120B
24B = 12M => 1M = 2B
18B + 12B = 30B ---- 12 days
20B + 10B = 30B -----? => 12 days
Answer: C
Answer: (C) 12
Question: A family consists of two grandparents, two parents, and four grandchildren. The average age of the grandparents is 66 years, the average age of the parents is 40 years, and the average age of the grandchildren is 11 years. What is the average age (in years) of the family?
(A) 26
(B) 28
(C) 30
(D) 32
(E) 34
Rationale: Total age of the grandparents = 66 Ã— 2 = 132
Total age of the parents = 40 Ã— 2 = 80
Total age of the grandchildren = 11 Ã— 4 = 44
Average age of the family = (132+80+44)/8 = 256/8 = 32 years
The answer is D.
Answer: (D) 32
Question: Shanmukham buys good worth Rs. 6650. He gets a rebate of 6% on it. After getting the rebate, he pays sales tax @ 10%. Find the amount he will have to pay for the goods
(A) 6999.2
(B) 6876.1
(C) 6654
(D) 7000
(E) None of these
Rationale: Explanation :
Rebate = 6% of Rs. 6650 = Rs. 6/100 x 6650 = Rs. 399.
Sales tax = 10% of Rs. (6650 399) = Rs. 10/100 x 6251 = Rs. 625.10
Final amount = Rs. (6251 + 625.10) = Rs. 6876.10
Answer : B
Answer: (B) 6876.1
Question: A car owner buys petrol at Rs.7.50, Rs. 8 and Rs. 8.50 per litre for three successive years. What approximately is the average cost per litre of petrol if he spends Rs. 4000 each year?
(A) Rs. 7.98
(B) Rs. 8
(C) Rs. 8.50
(D) Rs. 9
(E) Rs. 9.50
Rationale: petrol used in 1st yr = 4000/7.5 = 533.33 ltr
petrol used in 2nd yr = 4000/8 = 500 ltr
petrol used in 3 rd year = 4000/8.5= 470.59 ltr
Total petrol used for Rs.12000(4000/- for each yaer) in 3rd yrs = 1503.92 ltr
Average cost per litre = 12000/1503.92 = Rs 7.98
ANSWER:A
Answer: (A) Rs. 7.98
Question: Sum of the squares of three numbers is 129 and the sum of their products taken two at a time is 250. Find the sum?
(A) 20
(B) 23
(C) 25
(D) 26
(E) 29
Rationale: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 129 + 2* 250
a + b + c = √529 = 23
B
Answer: (B) 23
Question: Nitin borrowed 8000 at the rate of 6% p.a. for the first three years, 8% p.a.for the next five years and 12% p.a.for the period beyond eight years. At the end of eleven years how much money did he give as interest?
(A) 8000
(B) 10,000
(C) 5,000
(D) 7,520
(E) None of these
Rationale: Let the interest be i Then,
(8000×3×6/100)+(8000×5×8/100)+(8000×3×12/100)=i
⇒ 1440 + 3200 + 2880 = i
⇒ i = 7520
Answer D
Answer: (D) 7,520
Question: In a group of 90 students, 36 are taking History, and 30 are taking Statistics. If 59 students are taking History or Statistics or both, then how many students are taking History but not Statistics?
(A) 9
(B) 19
(C) 23
(D) 27
(E) 29
Rationale: Number of students taking history =H=36
Number of students taking statistics =S= 30
Total number of students =T= 90
Number of students taking History or Statistics or both =B= 59
Number of students taking neither history nor statistics =N= 90-59=31
LetXbe the number of students taking both history and statistics.
Then
T = H + S + N - X
or 90 = 36 + 30 +31 - X
or X = 7
Now,
Number of students taking only history will be
H-X
or 36-7 = 29
Answer:- E
Answer: (E) 29
Question: If k and y are integers, and 10k + y is odd , which of the following must be true?
(A) k is odd
(B) k is even
(C) y is odd integer
(D) y is even
(E) both k and y are odd
Rationale: 10k will be always even as 10 has 2 as one of its factors
if 10k+y is odd, then the only possible explanation is that y is odd
correct answer C
Answer: (C) y is odd integer
Question: Which of the following is equal to (y+1)!/y!?
(A) y-1
(B) 1+(1/y)
(C) 1
(D) y+1
(E) y
Rationale: (y + 1)! = (y + 1) * x!
(y + 1)!/y! = y + 1
Answer: D
Answer: (D) y+1
Question: A tiger is 50 of its own leaps behind a deer. The tiger takes 5 leaps per minutes to deer’s 4. If the tiger and the deer cover 8 m and 5 m per leap respectively, what distance will the tiger have to run before it catches the deer ?
(A) 600m
(B) 700m
(C) 800m
(D) 1000m
(E) 1200m
Rationale: Tiger takes 5 leaps /m and Deer takes 4 leaps/ m
Thus, tiger runs at the speed of 5 x 8 = 40 m/min
and deer runs at the speed of 4 x 5 = 20 m/min
Tiger is 50 leaps behind,which is 50 x 8 = 400 m
Relative speed of tiger and deer is = 20 m/min
Thus, 400/20 = 20 m
Thus,the tiger will catch deer = 20 x 40 =800 m
ANSWER:C
Answer: (C) 800m
Question: A number is doubled and 9 is added. If resultant is trebled, it becomes 75. What is that number
(A) 8
(B) 10
(C) 12
(D) 14
(E) 15
Rationale: Explanation:
=> 3(2x+9) = 75
=> 2x+9 = 25
=> x = 8
Answer: Option A
Answer: (A) 8
Question: An event manager has ten patterns of chairs and eight patterns of tables.In how many ways can he make a pair of table and chair?
(A) 70
(B) 60
(C) 100
(D) 80
(E) 90
Rationale: He has 10 patterns of chairs and 8 patterns of tables.
Hence,A chair can be arranged in 10 ways
A table can be arranged in 8 ways
Hence one chair and one table can be arranged=(10*8)ways
=80 ways
Answer is option D
Answer: (D) 80
Question: If there are 4 pairs of twins, and a committee will be formed with 3 members. In how many ways this committee formed in a way that no siblings in a group?
(A) 32
(B) 24
(C) 56
(D) 44
(E) 40
Rationale: The first member can be anybody, so 8 possibilities.
The second member cannot be the sibling of the previous member, therefore 6 possibilities (anybody from the remaining 3 pairs).
Finally, the third member, can be chosen from the remaining 2 pairs, so 4 possibilities.
This would give us 8*6*4 possibilities, but in this case we don't care about the order in which we choose them, we have to divide the product we obtained by 6(=3!), which is the number of possibilities we can chose the same three distinct members, say ABC (it can be BAC, CAB,...). You can count those possibilities for such a small number as 3, but why avoid permutations? Is it better to start listing the possibilities instead of just accepting the already proven result?
So, the correct answer is 8*4=32.
Answer A.
Answer: (A) 32
Question: Two trains of lengths 156.62 and 100 meters are running on parallel lines with respective speeds of 30 km/hr and 36 km/hr. The time of crossing each other, if they run in the opposite direction is
(A) 322 sec
(B) 14 sec
(C) 11sec
(D) 13 sec
(E) 34 sec
Rationale: Explanation:
Total distance to be covered = 156.62 + 100 = 256.62 m
Trains are running in opposite directions, hence
Relative speed = 30 + 36 = 66 km/hr = 18.33 m/sec
Time = Distance / Relative Speed
= 256.62 /18.33 sec
= 14 sec
Therefore, the time of crossing each other in the opposite direction is 14 seconds.
ANSWER: B
Answer: (B) 14 sec
Question: James can eat 25 marshmallows is 20 minutes. Dylan can eat 25 in one hour. In how much time will the two eat 150 marshmallows?
(A) 40 minutes.
(B) 1 hour and 30 minutes.
(C) 1 hour
(D) 1 hour and 40 minutes.
(E) 2 hours and 15 minutes
Rationale: Rate =Output/Time
James Rate=25/20=5/4
Dylan Rate=25/60=5/12
Combined rate = 5/4+5/12= 20/12
Combined Rate*Combined Time= Combined Output
20/12*t=150
t=90 mins => 1 hr 30 min
ANSWER:B
Answer: (B) 1 hour and 30 minutes.
Question: The mean proportional between 234 and 104 is
(A) 12
(B) 39
(C) 54
(D) 156
(E) None
Rationale: Sol.
Required mean proportional = √234 x 104
= √13x9x2x13x8 = (13x3x4) = 156.
Answer D
Answer: (D) 156
Question: How many positive integers will divide evenly into 560?
(A) 8
(B) 12
(C) 16
(D) 18
(E) 20
Rationale: 520 = 10*13*4 = 8*5*13 = 2^3*5*13
We need to positive integers will divide evenly into 520 or simply the factors of 520
If a number is of the form 2^a*3^b*5^c,
Total factors = (a+1)(b+1)(c+1)
Therefore, number of factors of 520 = (3+1)*(1+1)*(1+1) = 4*2*2 = 20
Option E
Answer: (E) 20
Question: George takes 30 days to do a piece of work and Mark takes 45 days for the same work. For the first 15 days only George works. Then Mark also joins him. Find the time taken to complete the entire work.
(A) 24 days
(B) 25 days
(C) 26 days
(D) 27 days
(E) 28 days
Rationale: George 1 day work= 1/30
Mark 1 day work= 1/45
George 15 day work= 15*1/30 =1/2
Work remaining= 1-1/2 =1/2
George + Mark 1 day work= 1/30 + 1/45 =1/18
Number of day required to complete 1/2 work= (1/2)/(1/18)= 9 days
So total days required to complete the work is 15+9= 24 days.
ANSWER:A
Answer: (A) 24 days
Question: What is the probability of rolling a total of 5 with a single roll of two fair six-sided dice, each with the distinct numbers 1 through 6 on each side?
(A) 1/12
(B) 1/6
(C) 2/7
(D) 1/3
(E) 1/9
Rationale: Totalsample spacefrom two fair six-sided dice is 36.
There are six possible ways to be 5 i.e. (1+4), (2+3), (3+2), (4+1)
So, total probability is 4/36 or 1/9.
Answer is E.
Answer: (E) 1/9
Question: The number of meters in WB is equal to the square root of the number of centimeters in WB. What is the length of WB (1 meter=100 centimeters)?
(A) 100 meters
(B) 10 meters
(C) 100 centimeters
(D) 10 centimeter
(E) 1 centimeter
Rationale: I'd plug in the options for this question.
Check option A: if the number of meters in WB is 100, then the number of centimeters is 100*100. The square root of 100*100 is 100: 100 = 100.
Answer: A.
Answer: (A) 100 meters
Question: (17)3.75 x (17)? = 178
(A) 2.29
(B) 2.75
(C) 4.25
(D) 4.5
(E) None of these
Rationale: Solution
let (17)3.75 * (17)x = 178. then, (17)3.5 + x = (17)8.
∴ 3.75 + x = 8 ⇔ x = (8 - 3.75) ⇔ x = 4.25
Answer C
Answer: (C) 4.25
Question: There are 10 teams in a certain league and each team plays each of the other teams exactly twice. If each game is played by 2 teams, what is the total number of games played?
(A) 15
(B) 16
(C) 28
(D) 56
(E) 90
Rationale: Every team plays with 9 teams...so total no of matches = 10 x 9 = 90.
Now, each match is played twice => 90 x 2
But 2 teams play a match => 90 x 2 /2 = 90.
Answer: E
Answer: (E) 90
Question: Four of the following five are alike in a certain way and hence form a group. Which one does not belong to the group?
(A) 70
(B) 80
(C) 52
(D) 48
(E) 68
Rationale: A
All the numbers are multiple of 4, except 70.
Answer: (A) 70
Question: A father said to his son, "I was as old as you are at present at the time of your birth." If the father's age is 26 years now, the son's age five years back was?
(A) 8 years
(B) 14 years
(C) 18 years
(D) 19 years
(E) 15 years
Rationale: Let the son's present age be x years.
Then, (26 - x) = x
2x = 26 => x = 13
Son's age 5 years back = (13 - 5)
= 8 years.
Answer: A
Answer: (A) 8 years
Question: a certain no. of men can finish a piece f work in 10 days.If however there were 10 men less it will take 10 days more for the work to be finished.How many men were there originally
(A) 100
(B) 110
(C) 120
(D) 130
(E) none of these
Rationale: 20 men will do work in 10 day
but 10 i.e. (20-10) will complete work in 20i.e. (10+10) days.
ANSWER:E
Answer: (E) none of these
Question: Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is ?
(A) 5/11
(B) 5/12
(C) 5/16
(D) 5/10
(E) 5/13
Rationale: Explanation:
Using question number 11 and 12, we get the probability as
1 - (1/36 + 5/9) = 5/12
Answer:B
Answer: (B) 5/12
Question: I bought two books; for Rs.480. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss?
(A) 299
(B) 280
(C) 288
(D) 271
(E) 212
Rationale: x*(85/100) = (480 - x)119/100
x = 280
Answer: B
Answer: (B) 280
Question: Cost is expressed by the formula tb^4. If b is doubled, the new cost E is what percent of the original cost?
(A) E=200
(B) E=600
(C) E=800
(D) E=1600
(E) 50
Rationale: Original Cost E, C1=t1*b1^4
New Cost C2= t2*b2^4....only b is doubled so t2=t1 and b2=2b1
C2=t2*(2b1)^4
=16(t1*b1^4)
=16C1
16 times C1=>1600% of C1
Ans D=1600
Answer: (D) E=1600
Question: Let the number which when multiplied by 16 is increased by 375.
(A) 14
(B) 20
(C) 26
(D) 25
(E) 30
Rationale: Solution
Let the number be x .
Then, 16x - x = 375
‹=›15x = 375
x ‹=› 25.
Answer D
Answer: (D) 25
Question: How many two-element subsets of <1, 2,3,4,5,6,7> are there that do not contain the pair of elements 2 and 4?
(A) 11
(B) 12
(C) 14
(D) 15
(E) 20
Rationale: 7C2 - 1 = 20 Answer is E
Answer: (E) 20
Question: If E=x^4 + y^4 = 100, then the greatest possible value of x is between
(A) 0 and 3
(B) 3 and 6
(C) 6 and 9
(D) 9 and 12
(E) 12 and 15
Rationale: My attempt:
If E=x^4+y^4=100, then the greatest possible value of x would be when y is minimum.
Let y^4 be 0. Now x^4 = 100. x should be definitely greater than 3 but less than 4. The only option that fits this range is B
Hence answer is --
b) 3 and 6.
Answer: (B) 3 and 6
Question: What should come in place of the question mark (?) in the following number series?
3 7 19 55 163 ?
(A) 467
(B) 487
(C) 475
(D) 485
(E) None of these
Rationale: Explanation:
3
7=3+4
19=7+4*3
55=19+12*3
163=55+36*3
487=163+108*3
Answer: B
Answer: (B) 487
Question: If the number 517*324 is completely divisible by 9, then the smallest whole number in the place of * will be:
(A) 3
(B) 1
(C) 5
(D) 4
(E) 2
Rationale: Sum of digits = (5 + 1 + 7 + x + 3 + 2 + 4) = (22 + x), which must be divisible by 9.
x = 5.
C
Answer: (C) 5
Question: Rahul's Mathematics test had 70 problems, 10 arithmetic, 30 algebra, 35 geometry problems.
Although he answered 70% of arithmetic, 40% of arithmetic and 60% of geometry problems correctly,
still he got less than 60% problems right. How many more questions he would have to answer more to get
passed
(A) 5
(B) 6
(C) 2
(D) 8
(E) 9
Rationale: Explanation:
Number of questions attempted correctly = (70% of 10 + 40% of 30 + 60% of 35)
= 7 + 12 + 21 = 40.
Questions to be answered correctly for 60% = 60% of total quations
= 60 % of 70 = 45.
He would have to answer 42 - 40 = 2
Answer: Option C
Answer: (C) 2
Question: The manager of a theater noted that for every 10 admissions tickets sold, the theater sells 3 bags of popcorn at 2.25 $ each, 4 sodas at 1.70 $ each and 2 candy bars at 1.00$ each. To the nearest cent, what is the average (arithmetic mean) amount of these snacks sales per ticket sold?
(A) 1.48$
(B) 1.56$
(C) 1.60$
(D) 1.64$
(E) 1.70$
Rationale: For every 10 tickets amount of snacks sold is 3*2.25+4*1.7+2*1=$15.55, hence amount of the snacks sales per ticket is $15.55/10=~$1.56.
Answer: B.
Answer: (B) 1.56$
Question: If x+y=20, x-y=36, for integers of x and y, x=?
(A) 20
(B) 25
(C) 28
(D) 20
(E) 42
Rationale: x+y = 20
x-y = 36
2x =56
x = 28
Answer is C
Answer: (C) 28
Question: When the number 72y6139 is exactly divisible by 11, then the smallest whole number that can replace y is?
(A) 1
(B) 3
(C) 5
(D) 6
(E) 9
Rationale: The given number =72y6139
Sum of the odd places =9+1+y+7
Sum of the even places = 3+6+2=11
(Sum of the odd places)- (Sum of even places) = Number (exactly divisible by 11)
(16+y)-(11) = divisible by 11
y � 5 = divisible by 11.
Y must be 6, to make given number divisible by 11.
D
Answer: (D) 6
Question: List F consists of 12 consecutive integers. If -4 is the least integer in list F, what is the range of positive integers in list F?
(A) 5
(B) 6
(C) 7
(D) 11
(E) 12
Rationale: Since -4 is the least integer in list F, then 7 is the largest integer in that list. Thus the range of the positive integers in the list is 7-1=6.
Answer: B.
Answer: (B) 6
Question: A car covers a distance of 624 km in 8 hours. Find its speed?
(A) 78
(B) 277
(C) 298
(D) 269
(E) 213
Rationale: 624/8 = 78 kmph
Answer:A
Answer: (A) 78
Question: Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?
(A) 217
(B) 444
(C) 728
(D) 278
(E) 268
Rationale: 1h ----- 5
? ------ 60
12 h
RS = 16 + 21 = 37
T = 12
D = 37 * 12 = 444
Answer: B
Answer: (B) 444
Question: A speed of 11 metres per second is the same as :
(A) 50.4 km/hr
(B) 55 km/hr
(C) 60 km/hr
(D) 68.5 km/hr
(E) 39.6 km/hr
Rationale: Sol.
11 m/sec = [11 * 18/5] km/hr = 39.6 km/hr.
Answer E
Answer: (E) 39.6 km/hr
Question: A, B and C have Rs.700 between them, A and C together have Rs.300 and B and C Rs.600. How much does C have?
(A) 200
(B) 250
(C) 300
(D) 350
(E) 400
Rationale: A+B+C = 700
A+C = 300
B+C =600
--------------
A+B+2C = 900
A+B+C = 700
----------------
C = 200
ANSWER:A
Answer: (A) 200
Question: If the average of e, b, c, 14 and 15 is 12. What is the average value of e, b, c and 29
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Rationale: e+b+c+14+15 = 12*5 = 60
=>e+b+c = 60-29 = 31
e+b+c+29 = 31+29= 60
Average = 60/4 = 15
Answer D
Answer: (D) 15
Question: The diagonals of a rhombus are 30 cm and 12 cm. Find its area?
(A) 176
(B) 190
(C) 180
(D) 278
(E) 292
Rationale: 1/2 * 30 * 12
= 180
Answer:C
Answer: (C) 180
Question: Three years ago the average age of a class of six members was 22 years. A boy have been added, the average age of the class is the same today. What is the age of the boy?
(A) A)1
(B) B)2
(C) C)3
(D) D)4
(E) E)5
Rationale: 6 * 25 = 150
7 * 22 = 154
`4
D
Answer: (D) D)4
Question: Consider a lady took a loan from a bank at the rate of 12% p.a. simple interest. After 3 years she had to pay Rs. 5400 interest only for the period. The principal amount borrowed by her was
(A) Rs. 2000
(B) Rs. 10000
(C) Rs. 15000
(D) Rs. 20000
(E) None of these
Rationale: Explanation :
Principal = Rs. (100×5400 / 12×3)
=> Rs. 15,000.
Answer : C
Answer: (C) Rs. 15000
Question: A, B and C enter into a partnership. They invest Rs. 1,20,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdraws Rs. 40,000, while at the end of the second year, C withdraws Rs. 80,000. In what ratio will the profit be shared at the end of 3 years ?
(A) 9 : 4 : 8
(B) 9 : 4 : 7
(C) 3 : 4 : 2
(D) 3 : 4 : 1
(E) 9 : 4 : 5
Rationale: A : B : C = (120000 x 36) : (80000 x 12 + 40000 x 24) : (120000 x 24 + 40000 x 12)
= 432 : 192 : 336
= 9 : 4 : 7.
Answer: B
Answer: (B) 9 : 4 : 7
Question: If w is the square of a positive integer, which of the following must be equal to the square of the next positive integer?
(A) √n + 1
(B) n + 1
(C) n^2 + 1
(D) w + 2√w + 1
(E) n^2 + 2n + 1
Rationale: If w is the square of a positive integer, which of the following must be equal to the square of the next positive integer?
w = (x)^2 where x is a positive integer
To calculate -
(x+1)^2 = x^2 + 2x + 1
root(w) = x
Ans - w + 2 root(w) + 1
This should beD
Answer: (D) w + 2√w + 1
Question: Apple costs X rupees per kilogram for first 30 kgs and Y rupees per kilogram for each additional kilogram. If the price of 40 kilograms is 420 and for 50 kgs of Apples is 540 then the cost of first 10 kgs of Apples is
(A) 100
(B) 3.66
(C) 3.6
(D) 3.62
(E) 3.61
Rationale: Ans: By framing equations we get
30X+10Y=420
30X+20Y=540
Eliminate Q by multiplying the first equation by 2 and subtracting second equation from the first
60x+20y = 840 -
30x+20y = 540
=> 30x = 300 => x = 10
Then we get X = 10
Cost of 10 kgs of apples = 10x 10 = 100
Answer:A
Answer: (A) 100