mathewhe/aqua_rat huggingface dataset:
Question: A rectangular garden is to be twice as long as it is wide. If 300 yards of fencing, including the gate, will completely enclose the garden, what will be the length of the garden, in yards?
(A) 40
(B) 50
(C) 60
(D) 70
(E) 100
Rationale: ALTERNATE APPROACH
Backsolving ( Using answer options to reach the correct answer ) can work wonders here if one is fast in calculations.
Given Perimeter is 300
So, 2 ( L + B ) = 300
Or, L + B = 150
Now use the answer options ( Given Length ; Breath will be half the length)
(A) 40
L = 40 ; B = 20
L + b = 60
(B) 50
L = 50 ; B = 25
L + b = 75
(C) 60
L = 60; B = 30
L + b = 90
(D) 70
L = 70; B = 35
L + b = 105
(E) 100
L = 100; B = 50
L + b = 150
Thus you see no, need of any calculations, U can reach the correct option only by checking options ; correct answer will be (E)
Answer: (E) 100
Question: The average weight of A, B and C is 30 kg. If the average weight of A and B be 25 kg and that of B and C be 28 kg, then the weight of B is:
(A) 14 kg
(B) 15 kg
(C) 18 kg
(D) 19 kg
(E) 16 kg
Rationale: EXPLANATION
Let A, B, C represent their respective weights. Then, we have:
A + B + C = (30 x 3) = 90 â€¦. (i)
A + B = (25 x 2) = 50 â€¦. (ii)
B + C = (28 x 2) = 56 â€¦.(iii)
Adding (ii) and (iii), we get: A + 2B + C = 106 â€¦. (iv)
Subtracting (i) from (iv), we get : B = 16.
Bâ€™s weight = 16 kg.
Answer E
Answer: (E) 16 kg
Question: A group of 55 adults and 70 children go for trekking. If there is meal for either 70 adults or 90 children and if 14 adults have their meal, find the total number of children that can be catered with the remaining food.
(A) 33
(B) 54
(C) 18
(D) 17
(E) 72
Rationale: Explanation:
As there is meal for 70 adults and 14 have their meal, the meal left can be catered to 56 adults.
Now, 70 adults = 90 children
7 adults = 9 children
Therefore, 56 adults = 72 children
Hence, the meal can be catered to 72 children.
ANSWER: E
Answer: (E) 72
Question: The average age of students of a class is 15.8 years. The average age of boys in the class is 16.4 years and that of the girls is 15.4 years, The ratio of the number of boys to the number of girls in the class is :
(A) 2:9
(B) 2:3
(C) 2:1
(D) 2:2
(E) 2:6
Rationale: Explanation:
Let the ratio be k : 1. Then,
k * 16.4 + 1 * 15.4 = (k + 1) * 15.8
<=> (16.4 - 15.8) k = (15.8 - 15.4) <=> k = 0.4/0.6 = 2/3.
Required ratio = 2/3 : 1 = 2 : 3.
Answer: B
Answer: (B) 2:3
Question: When the positive integer r is divided by 9, the remainder is 5. What is the remainder when 3r is divided by 9?
(A) 0
(B) 1
(C) 3
(D) 4
(E) 6
Rationale: Lets take the number as r
when r is divided by 9 the remainder is 5 hence r can be written as
r=9k +5
Multiplying by 3 will give
3r = 27k + 15
we can also write
3r = 27k + 9 + 6
Now 27k and 9 are divisible by 9 leaving the remainder as 6 hence E is the answer.
Answer: (E) 6
Question: David gets on the elevator at the 11th floor of a building and rides up at the rate of 57 floors per minute. At the same time, Albert gets on an elevator at the 51st floor of the same building and rides down at the rate of 63 floors per minute. If they continue travelling at these rates, then at which floor will their paths cross ?
(A) 30
(B) 20
(C) 10
(D) 50
(E) 40
Rationale: Suppose their paths cross after x minutes.
Then, 11 + 57x = 51 - 63x = 120x = 40
x = 1/3
Number of floors covered by David in (1/3) min. = (1/3 x 57)= 19.
So, their paths cross at (11 +19) i.e., 30th floor.
Answer is A.
Answer: (A) 30
Question: the numbers 272738 and 232342,when divided by n, a 2 digit number leave a remainder 13 and 17 respectively.Find the sum of digits of n?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: We have to find the h.c.f of both
1.272738-13
2.232325-17
H.c.f is 25
Ans is 7
ANSWER:D
Answer: (D) 7
Question: Calculate the sum of first 60 natural numbers.
(A) 1839
(B) 2830
(C) 1830
(D) 1831
(E) 1835
Rationale: Solution
We know that(1+2+3+.....+60)	= n(n+1)/2
Therefore (1+2+3+....+60)	=(60×61 / 2)
= 1830.
Answer C
Answer: (C) 1830
Question: 1.14 expressed as a per cent of 1.9 is:
(A) 6%
(B) 10%
(C) 60%
(D) 90%
(E) None
Rationale: Solution: Required percentage = (1.14*100)/1.9 = 60%.
Answer: Option C
Answer: (C) 60%
Question: Jane biked 21 2/3 miles in 3 hours and 20 minutes. What was her average rate of speed in miles per hour?
(A) 6 1/2
(B) 7
(C) 7 1/2
(D) 7 3/4
(E) 8
Rationale: D = 21(2/3) = 65/3
T = 3(1/3) = 10/3
S = D/T = 6 1/2
Answer = A
Answer: (A) 6 1/2
Question: At 15:00 there were 20 students in the computer lab. At 15:03 and every three minutes after that, 3 students entered the lab. If at 15:10 and every ten minutes after that 7 students left the lab, how many students were in the computer lab at 15:44 ?
(A) 7
(B) 14
(C) 25
(D) 27
(E) 30
Rationale: Initial no of students + 3 * (1 + No of possible 3 minute intervals between 15:03 and 15:44) -
8 *(1 + No of possible 10 minute intervals between 15:10 and 15:44)
20 + 3*14 -8 * 4 = 25
C
Answer: (C) 25
Question: Out of 10 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them?
(A) 5/8
(B) 5/2
(C) 5/1
(D) 5/6
(E) 5/5
Rationale: P(at least one graduate) = 1 - P(no graduates)
= 1 - 6C3/10C3 = 1 - (6 * 5 * 4)/(10 * 9 * 8)
= 5/6
Answer: D
Answer: (D) 5/6
Question: A 250 m long train is running at a speed of 55 Km/hr. It crossed a platform of length 300 m in ?
(A) 41.1 sec
(B) 20.2 sec
(C) 36 sec
(D) 50.4 sec
(E) none of the above
Rationale: Speed = 55 Km/hr
(to convert km/hr in to M/s)
= 55 x 5/18 M/s
Distance = 250 m + 300 m ( If questions is about train crossing a post you need to consider only the length of Train, )
= 550 m
Time = Distance / Speed
= 550 x 18 / (5 x 55)
= 36 sec
Ans is :C
Answer: (C) 36 sec
Question: The difference between a two-digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ?
(A) 4
(B) 8
(C) 16
(D) 20
(E) None of these
Rationale: Since the number is greater than the number obtained on reversing the digits, so the ten's digit is greater than the unit's digit.
Let ten's and unit's digits be 2x and x respectively.
Then, (10 x 2x + x) - (10x + 2x) = 36
9x = 36
x = 4.
Required difference = (2x + x) - (2x - x) = 2x = 8.
Answer:B
Answer: (B) 8
Question: If a sum of money borrowed at 5 percent/annum SI amounts to Rs.1020 in 4 yrs, then the sum of money borrowed is?
(A) Rs. 850
(B) Rs. 900
(C) Rs. 910
(D) Rs. 1000
(E) Rs. 1050
Rationale: Sol We have, A : Rs.1U2D
Let the pr xnpal be R5 x
Then mterest u — 12 : wzo — x
Therefore, by u xglurmula.
_umxx
’ Rx’: (
, _ma>< 1nzn—xv
\4Ve|\a\e,Jc— 5“
:> ~(:51DD—S*(or6x:51UU
or, J: : w 350
. The sum of money burrowed : Rs. 850
A)
Answer: (A) Rs. 850
Question: What was the day of the week on 15th August, 1947 ?
(A) Wednesday
(B) Tuesday
(C) Friday
(D) Thursday
(E) None of these
Rationale: 15th August, 1947 = (1946 years + Period from 1st Jan.,1947 to 15th Aug., 1947)
Counting of odd days :
1600 years have 0 odd day. 300 years have 1 odd day.
47 years = (11 leap years + 36 ordinary years)
= [(11 × 2) + (36 × 1)]odd days
= 58 odd days
⇒ 2 odd days.
= 227 days = (32 weeks + 3 days) = 3 odd days.
Total number of odd days = (0 + 1 + 2 + 3) odd days = 6 odd days.
Hence, the required day was ‘Friday’.
Answer C
Answer: (C) Friday
Question: A multiple choice test consists of 4 questions, and each question has 5 answer choices. In how many ways can the test be completed if every question is unanswered?
(A) 24
(B) 120
(C) 625
(D) 720
(E) 1024
Rationale: 5 choices for each of the 4 questions, thus total of 5*5*5*5 = 5^4 = 625 ways.
Answer: C.
Answer: (C) 625
Question: A shopping cart contains only apples, oranges, and pears. If there are twice as many oranges as apples, and twice as many pears as oranges, then the apples are equivalent to what fraction of the pears?
(A) 1/4
(B) 1/3
(C) 1/2
(D) 2/3
(E) 3/4
Rationale: O = 2A
P = 2O = 4A
A = P/4
The answer is A.
Answer: (A) 1/4
Question: Kelly and Jody packed boxes with books. If Jody packed 10% of the total number of boxes, what was the ratio of the number of boxes Kelly packed to the number that Jody packed?
(A) 1 to 6
(B) 1 to 4
(C) 2 to 5
(D) 9 to 1
(E) 2 to 3
Rationale: Explanation:
If Jody packed 10% of the boxes then Kelly packed 90%. The ratio of the number of boxes Kelly packed to the number Jody packed is thus 90%/10%=9/1
Answer: Option D
Answer: (D) 9 to 1
Question: A Certain car costs Rita $1500 afterwards she spent $50 over it. Now at what price must Rita sell this car in order to make a profit of 7% ?
(A) $1712
(B) $1715
(C) $1720
(D) $1725
(E) $1730
Rationale: Cost Price = $1500 + $50 = $1600
Profit % = 7
Selling Price = ?
Selling Price = (100 + Profit %) * Cost Price /100
= (100 + 7) * 1600 / 100
= 1712
Answer is A
Answer: (A) $1712
Question: A group of 7 students bought movie tickets in one row next to each other. If Bob and Lisa are in this group, what is the probability that Bob and Lisa will each sit next to only one of the six other students from the group?
(A) 5.76%
(B) 4.76%
(C) 15.75%
(D) 20.67%
(E) 25.15%
Rationale: The question basically asks about the probability that Bob and Lisa sit at the ends.
The total # of sitting arrangements is 7!.
Desired arrangement is either BVWXYZL or LVWXYZB. Now, VWXYZ can be arranged in 5! ways, therefore total # of favorable arrangements is 2*5!.
P=(favorable)/(total)=(2*5!)/7!=1/21.
Answer: B.
Answer: (B) 4.76%
Question: Pipe A can fill a tank in 5 hours, pipe B in 10 hours and pipe C in 30 hours. If all the pipes are open, in how many hours will the tank be filled?
(A) 2
(B) 2.5
(C) 3
(D) 3.5
(E) None
Rationale: Sol.
Part filled by (A + B + C) in 1 hour = (1/5 + 1/10 + 1/30) = 1/3.
∴ All the three pipes together will fill the tank in 3 hours.
Answer C
Answer: (C) 3
Question: In a secondary school the seats for Maths, physics and social studies are in the ratio 8 : 5 : 7. there is a proposal to increase these seats by 75%, 40% and 50% respectively. What will be the new ratio?
(A) 5 : 3 : 4
(B) 4 : 2 : 3
(C) 10 : 7 : 9
(D) 1 : 3 : 4
(E) None of these
Rationale: Explanation :
Solution: Originally, let the number of seats for Maths, physics and social studies be 8x, 5x and 7x respectively.
Number of increased seats are (175% of 8x), (140% of 5x) and (150% of 7x).
i.e. (175*7x/100), (140*5x/100) and(150*7x/100) i.e. 14x, 7x and 21x/2.
.'. Required ratio = 14x : 7x : 21x/2 = 28x : 14x : 21x = 4 : 2 : 3
Answer : B
Answer: (B) 4 : 2 : 3
Question: X is 3 times as fast as Y and is able to complete the work in 40 days less than Y. Find the time in which they can complete the work together?
(A) 15 days
(B) 16 days
(C) 17 days
(D) 18 days
(E) 19 days
Rationale: If X can complete work in x days and y can complete work in 3x days.
Then 2x = 40
x= 20 days.
so X can complete work in 20 days and y can complete work in 60 days.
they can complete the work together in 1/(1/20 + 1/60) = 1/ (4/60) = 15 days
ANSWER:A
Answer: (A) 15 days
Question: The C.P of 10 pencils is equal to the S.P of 12 pencils. Find his gain % or loss%?
(A) 18 2/3%
(B) 58 2/3%
(C) 16 2/3%
(D) 46 2/3%
(E) 6 2/3%
Rationale: Option C
Explanation:
10 CP = 12 SP
12 --- 2 CP loss
100 --- ? => 16 2/3%
Answer: (C) 16 2/3%
Question: Of the 100 athletes at a soccer club, 40 play defense and 66 play midfield. If at least 20 of the athletes play neither midfield nor defense, the number of athletes that play both midfield and defense could be any number between
(A) 10 to 20
(B) 10 to 40
(C) 26 to 40
(D) 30 to 70
(E) 40 to 70
Rationale: First of all notice that since only 40 athletes play defense, then the number of athletes that play both midfield and defense cannot possibly be greater than 40.Eliminate D and E.
{Total} = {defense} + {midfield} - {both} + {neither}
100 = 40 + 66 - {both} + {neither}
{both} = {neither} + 6.
Since the least value of {neither} is given to be 20, then the least value of {both} is 20+6=26.Eliminate A and B.
Answer: C.
Answer: (C) 26 to 40
Question: A and B started a business investing Rs. 21,000 and Rs. 28,000 respectively. Out of a total profit of Rs. 14,000, B’s share is :
(A) 7600
(B) 7700
(C) 7800
(D) 7900
(E) 8000
Rationale: Ratio of their shares = 21000 : 28000 = 3 : 4.
B’s share = Rs. 14000 * 4/7
= Rs. 8000
ANSWER:E
Answer: (E) 8000
Question: When positive integer N is divided by positive integer J, the remainder is 10. If N/J = 205.08, what is value of J?
(A) 125
(B) 100
(C) 75
(D) 150
(E) 50
Rationale: When a number is divided by another number, we can represent it as : Dividend = Quotient * Divisor + Remainder
So, Dividend/Divisor = Quotient + Remainder/Divisor
Given that N/J = 205.08
Here 205 is the quotient.
Given that Remainder = 10
So, 205.08 = 205 + 10/J
So, J = 125
Answer: A
Answer: (A) 125
Question: A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is:
(A) 18
(B) 24
(C) 42
(D) 81
(E) 90
Rationale: Explanation:
Let the ten's and unit's digit be x and 8/x respectively.
Then,
(10x + 8/x) + 18 = 10 * 8/x + x
9x2 + 18x - 72 = 0
x2 + 2x - 8 = 0
(x + 4)(x - 2) = 0
x = 2
So, ten's digit = 2 and unit's digit = 4.
Hence, required number = 24.
ANSWER IS B
Answer: (B) 24
Question: For any integer k greater than 1, the symbol k* denotes the product of all the fractions of the form 1/t, where t is an integer between 1 and k, inclusive. What is the value of 1*/4* ?
(A) 5
(B) 5/4
(C) 4/5
(D) 1/4
(E) 1/5
Rationale: When dealing with 'Symbolism' questions, it often helps to 'play with' the Symbol for a few moments before you attempt to answer the question that's asked. By understanding how the Symbol 'works', you should be able to do the latter calculations faster.
Here, we're told that K* is the PRODUCT of all the fractions of the form 1/T, where T is an integer between 1 and K, inclusive.
Based on this definition....
IF....
K = 2
K* = (1/1)(1/2) = 1/2
IF....
K = 3
K* = (1/1)(1/2)(1/3) = 1/6
We're asked to find the value of 5*/4*
Now that we know how the Symbol 'works', solving this problem shouldn't be too difficult. You can actually choose to do the math in a couple of different ways....
5* = (1/1)(1/2)(1/3)(1/4)(1/5)
Don't calculate this just yet though....since we're dividing by 4*, many of those fractions will 'cancel out.'
4* = (1/1)(1/2)(1/3)(1/4)
We're looking for the value of:
(1/1)(1/2)(1/3)(1/4)(1/5) / (1/1)(1/2)(1/3)(1/4)
Since the first four fraction in the numerator and denominator cancel out, we're left with just one fraction:
4/5
A
Answer: (A) 5
Question: Amber works 28 days a month at d dollars per day for m months out of the year. Which of the following represents her monthly pay?
(A) m/(20d)
(B) 20d
(C) 10md/6
(D) 28d
(E) 20md
Rationale: ANSWER: D The passage states that she works 28 days a month at d dollars per day, so 28 d is her monthly pay
Answer: (D) 28d
Question: A certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 11 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?
(A) 42
(B) 70
(C) 140
(D) 165
(E) 385
Rationale: Ans: 385
7C1 * 11C2
Answer E)
Answer: (E) 385
Question: At a florist shop on a certain day, all corsages sold for either $20 or $30. If 8 of the corsages that sold for $30 had instead sold for $20, then the store's revenue from corsages that day would have been reduced by 10 percent. What was the store's actual revenue from corsages that day?
(A) $200
(B) $400
(C) $600
(D) $800
(E) $1000
Rationale: Let, No. of corsages @ $20 = x, no. of corsages @ $30 = y and revenue= r
so, 20x+30y=r.........(1)
Now,
Given the situation, 20(x+8) + 30(y-8)= r-.1r
=> 20x+160+30y-240 = .9r
=> 20x+30y = .9r+80............(2)
so, r = .9r+80
=> r = 800
The answer is D.
Answer: (D) $800
Question: After getting 2 successive discounts, a shirt with a list price of Rs 150 is available at Rs 105. If the second discount is 12.55,find the first discount.
(A) 22%
(B) 18%
(C) 24%
(D) 17%
(E) 20%
Rationale: Let the first discount be x%
Then,87.5% of (100-x)% of 150= 105
=	87.5/100*(100-x)/100*450=150=>105=>100-x=(105*100*100)/(150*87.5)=80
x=(100-80)=20
first discount = 20%
Answer is E.
Answer: (E) 20%
Question: How many times digit 6 is used while writing numbers from 100 to 1100?
(A) 648
(B) 320
(C) 252
(D) 225
(E) 26
Rationale: There are 100 numbers which begin with 600
Next, In every 10 numbers such as 100 to 110, 110 to 120, 120 to 130 6 comes at least once. Number of such intervals = End limit - First no. / interval. Our range of numbers is 100 - 1000
1000 - 100 = 900/10 = 90
Number of 10s interval in this is 90. So 90 '6s'
So far we have calculated 190.
The total now comes to 280. The nearest to which is 320. Hence B.
Answer: (B) 320
Question: Find large number from below question The difference of two numbers is 1355. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder
(A) 1234
(B) 1265
(C) 1350
(D) 1467
(E) 1623
Rationale: Let the smaller number be x. Then larger number = (x + 1355).
x + 1355 = 6x + 15
5x = 1340
x = 268
Large number = 268+1355 = 1623
E
Answer: (E) 1623
Question: In the accounting branch of a commercial institute, the percentage of male and female workers is 48% and 52% respectively. In this branch, 40% of males and 20% of females are age 25 or older. If one of the workers is selected at random, what is the probability that the worker is under 25 years old?
(A) 0.3
(B) 0.25
(C) 0.45
(D) 0.7
(E) 0.9
Rationale: Percentage of male worker = 48
Percentage of female worker = 52
Let total number of workers = 1000
number of male workers= 480
number of female workers = 520
Number of male age 25 or older = (4/10)*480 = 192
Number of female age 25 or older =(2/10)*520 = 104
Total number of workers 25 or older = 192+104 = 296
Total number of workers under 25 = 1000 - 296 = 704
Probability that a worker randomly selected is under 25 years old = 704/1000 = .704
Alternatively , since the answer options are not close , we can use estimation here .
Percentage of male worker 25 or older = (4/10)*48 = 20 % approx
Percentage of female worker 25 or older = (2/10)*52 = 10 % approx
Percentage of total worker 25 or older = 30 %
Percentage of total worker under 25 = 70 %
Probability that a worker randomly selected is under 25 years old = .7
Answer D
Answer: (D) 0.7
Question: For a certain set of numbers, if x is in the set, then x - 3 is also in the set. If the number 2 is in the set , which of the following must also be in the set ?
a) 4
b) -4
c) -5
(A) a only,
(B) b only,
(C) c only,
(D) a and b only
(E) b and c only
Rationale: Notice that the question asks which of the following MUST be in the set, not COULD be in the set.
Since 2 is in the set, then so must be 2-3=-1. Similarly, since -1 is in the set, then so must be -1-3=-4. Could 4 and -1 be in the set? Certainly, but we don't know that for sure.
Answer: B.
Regarding your question: we don't know which is the source integer in the set, if it's 1, then 4 won't be in the set but if the source integer is say 7, then 4 will be in the set. So, 4 may or may not be in the set.
Answer: (B) b only,
Question: The area of Circle O is added to its diameter. If the circumference of Circle O is then subtracted from this total, the result is 4. What is the area of Circle O?
(A) 2/π
(B) 2
(C) 8
(D) 4
(E) 4π
Rationale: area+diameter-circumference=4
pi*r^2+2r=4+2pi*r
isolate r and get r(pi*r+2)=4+2pi*r
r=(4+2pi*r)/(pi*r+2) =>2(2+pi*r)/(pi*r+2)
r=2
Area = pi * r^2 => pi * 4
E
Answer: (E) 4π
Question: Suppose that AB = AC = CD and
AD = BD. What is the measure of
6 ADC in degrees?
(A) 24
(B) 28
(C) 32
(D) 36
(E) 40
Rationale: Let be the measure of \ADC. Then since ADC is isosceles, we obtain that
the measures of \CAD and \DCA are and 180 􀀀 2, respectively. It follows that
\ACB has measure 2. Since ACB is isosceles, we obtain that the measures of \CBA
and \BAC are 2 and 180 􀀀 4, respectively. Since ADB is isosceles, we deduce that
the measures of \CBA and \BAD are the same. This gives that 2 = (180 􀀀 4) +
which implies 5 = 180. Therefore, = 36.
correct answer D
Answer: (D) 36
Question: In the coordinate plane, Line A has a slope of -1 and an x-intercept of 2. Line B has a slope of 5 and a y-intercept of -10. If the two lines intersect at the point (a,b), what is the sum a+b?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: The equation of Line A is y = -x + 2
The equation of Line B is y = 5x - 10
5x - 10 = -x + 2
x = 2
y = 0
The point of intersection is (2,0) and then a+b = 2.
The answer is C.
Answer: (C) 2
Question: If the circus were to sell all of its 220 tickets for this month's performance at its usual price, the revenue from sales would be 10% greater than that collected last month. If the circus raised the ticket price by 5% and sold only 200 tickets as a result, what percent less would last month's revenue be compared to this month's revenue?
(A) 2
(B) 5
(C) 100/21
(D) 110/20
(E) 9/4
Rationale: Last months revenue can be calculated as 220x / 1.10 = 200x
Now consider the next statement - > if the price of ticket is hiked by 5% the new price is 1.05 x.
So the new revenue when only 200 tickets are sold = 200 * 1.05x = 210x.
We need to find the percentage difference ; so we have (new-old/new*100) 210x-200x/210x*100 = 100/21
Answer: C
Answer: (C) 100/21
Question: The ratio of 2 numbers is 1:2 and their H.C.F. and L.C.M are 10 and 20. Find the numbers.
(A) 20, 10
(B) 10, 20
(C) 20, 30
(D) 30, 20
(E) 10, 10
Rationale: Let the numbers be x and 2x
Their H.C.F. = 10
L.C.M = 20
ie) 2x^2 = 200
x^2 = 100, x = 10 t The numbers are x and 2x , ie)10, 20 respectively.
Answer is B
Answer: (B) 10, 20
Question: By how much is two-fifth of 500 greater than five - seventh of 210 ?
(A) 50
(B) 75
(C) 120
(D) None of these
(E) Cannot be determined
Rationale: Solution
2/5of 500 - 5/7 of 210 = 50.
Answer A
Answer: (A) 50
Question: The present average age of a family of five members is 26 years. If the present age of the youngest member in the family is ten years, then what was the average age of the family at the time of the birth of the youngest member ? (Assume no death occurred in the family since the birth of the youngest?
(A) 80 years
(B) 70 years.
(C) 20 years.
(D) 30 years.
(E) 20 years.
Rationale: Present total age of the members = 26(5) = 130 years.
Present age of the youngest member = 10 years
Present total age of the remaining four members = 130 -10 = 120 years
Their average age at the time of the birth of the youngest member = [120 - (4 * 10)] / 4 = 30 - 10 = 20 years.
Answer: C
Answer: (C) 20 years.
Question: If m and n are positive integers, and m=2n and k=2m, then -
(A) 2m is a factor of k.
(B) m/2 is a factor of k.
(C) 3m is a factor of k/2.
(D) k is a factor of m.
(E) k is a factor of m/2.
Rationale: m=2n --> m is even.
k=2m --> m is factor of k, thus m/2 = integer must also be a factor of k.
Answer: B.
Answer: (B) m/2 is a factor of k.
Question: A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.630 find the share of A?
(A) 240
(B) 288
(C) 266
(D) 216
(E) 123
Rationale: (3*8 + 2*4):(4*8 + 5*4)
8:13
8/21 * 630 = 240
Answer: A
Answer: (A) 240
Question: If |x^2 − 12| = x, which of the following could be the value of x?
(A) -4
(B) -3
(C) 1
(D) 2
(E) 3
Rationale: |x2−12|=x|x2−12|=x
|x2−12||x2−12|cannot be negative; anything that comes out of mod is always positive
so |x2−12|>0|x2−12|>0
Out of our options A= -4 B= -3 cannot be the right answer because none of them are greater than 0
Now only Option C=1 or D=2 or E=3 are contenders for right answers.
A quick Cursory crude calculation will tell you that E is the right choice
|−32−12|=3|−32−12|=3
|9−12|=3|9−12|=3
|−3|=3|−3|=3
3=33=3
ANSWER IS E
Answer: (E) 3
Question: If log 27 = 1.437, then the value of log 9 is:
(A) 0.934
(B) 0.945
(C) 0.954
(D) 0.958
(E) 0.998
Rationale: log 27 = 1.437
log (3cube ) = 1.437
3 log 3 = 1.437
log 3 = 0.479
log 9 = log(3square ) = 2 log 3 = (2 x 0.479) = 0.958.
Answer: Option D
Answer: (D) 0.958