mathewhe/aqua_rat huggingface dataset:
Question: The length of the room is 5.5m and width is 3.75m. Find the cost of paving the floor by slabs at the rate of Rs.800 per sq meter
(A) 16500
(B) 16538
(C) 27778
(D) 27788
(E) 27781
Rationale: Explanation:
l=5.5m w=3.75m
area of the floor = 5.5 x 3.75 = 20.625 sq m
cost of paving = 800 x 20.625 = Rs. 16500
Answer: A) Rs.16500
Answer: (A) 16500
Question: In a class composed of x girls and y boys what part of the class is composed of girls
(A) y/(x + y)
(B) x/xy
(C) x/(x + y)
(D) y/xy
(E) 1/xy
Rationale: total no. of boys and girls=x+y
no. of girls=x
therefore,, x/(x+y)
ANSWER:C
Answer: (C) x/(x + y)
Question: If 4 persons can do 4 times of a particular work in 4 days, then, 7 persons can do 7 times of that work in?
(A) 2 days
(B) 3 days
(C) 5 days
(D) 4 days
(E) 9 days
Rationale: That is, 1 person can do one time of the work in 4 days.
Therefore, 7 persons can do 7 times work in the same 4 days itself.
D)
Answer: (D) 4 days
Question: A man walking at a rate of 10km/hr crosses a bridge in 10 minutes. The length of the bridge is?
(A) 1521
(B) 1492
(C) 1667
(D) 1254
(E) 1112
Rationale: Speed = 10*5/18 = 50/18 m/sec
Distance covered in 10minutes = 50/18 *10 *60 = 1667m
Answer is C
Answer: (C) 1667
Question: 3^13 is equal to which of the following?
(A) 1,595,423
(B) 1,595,401
(C) 1,595,477
(D) 1,595,432
(E) 1,595,409
Rationale: Given that the answers have different last digits, there are several ways to solve this, but the most straight forward way is to check the algorithm. 3^n has a cycle of 4.
3^1 = 3
3^2 = 9
3^3 = 27
3^4 = 81
3^5 = 243
Observe that the last digit of the resultant of 3^1 and 3^5 is 3. If we continue 3^n, the last digit follows the pattern 3, 9, 7, 1, 3, 9, 7, 1, 3, .... So, all we need look for is the last digit in the pattern.
Cycle of 4, power of 13, last digit is 3.
Answer: A
Answer: (A) 1,595,423
Question: In a three digit number, the hundred digit is 2 more than the tens digit and the units digit is 2 less than the tens digit. If the sum of the digits is 33, find the number?
(A) 12119
(B) 13919
(C) 13119
(D) 13016
(E) 12015
Rationale: C
13119
Let the three digit numbers be 100a + 10b + c
a = b + 2
c = b - 2
a + b + c = 3b = 33 => b = 11
So a = 13 and b = 9
Hence the three digit number is: 13119
Answer: (C) 13119
Question: In the xy-plane, the point (-2, 1) is the center of a circle. The point (-2, -3) lies inside the circle and the point (4, 1) lies outside the circle. If the radius r of the circle is an integer, then r =
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: An easy way to solve this question will be just to mark the points on the coordinate plane.
You'll see that the distance between the center (-2, 1) and the point inside the circle (-2, -3) is 4 units
(both points are on x=-2 line so the distance will simply be 1-(-3)=4)
So the radius must be more than 4 units.
The distance between the center (-2,1) and the point outside the circle (4,1) is 6 units
(both points are on y=1 line so the distance will simply be 4-(-2)=6)
So the radius must be less than 6 units, which implies 4 < r < 6, thus as r is an integer then r=5.
Answer: D.
Answer: (D) 5
Question: If the simple interest on a sum of a money for 2 years at 5% per annum is $50 what is the compound interest on the sum of the same rate and same time
(A) $57.96
(B) $78.89
(C) $88.45
(D) $51.25
(E) $78.24
Rationale: sum= 50*100/10=500
amount=$(500(1+10/100)^2)
=500*21/20*21/20
=$551.25
C.I=$(551.25-50)=$51.25
Answer (D)
Answer: (D) $51.25
Question: Harold works at a resort from the beginning of March to the end of September. During the month of August this past year, he made 3 times the average (arithmetic mean) of his monthly totals in tips for the other months. His total tips for August were what fraction of his total tips for all of the months he worked?
(A) 1/3
(B) 2/5
(C) 3/7
(D) 1/2
(E) 4/7
Rationale: The time from beginning of March to the end of September is 7 months.
If x is the average monthly tip for all months other than August then his August month tip will be 3*x
His total tip for the 7 months = 6*(average tip for the months other than August) + 3x
=9x
August tips as a fraction of total tips = 3x/9x =1/3. So Answer is A
Answer: (A) 1/3
Question: A man buys an article for 15% less than its value and sells it for 15% more than its value. His gain or loss percent is:
(A) no profit, no loss
(B) 20% profit
(C) less than 35% profit
(D) more than 35% profit
(E) None
Rationale: Let the article be worth Rs. x.
C.P. 85% of Rs. x = Rs. 85x/100
S.P. = 115% of Rs. x = Rs. 115x/100
Gain = (115x/100 - 85x/100) = Rs. 3x/10
Gain % = 3x/10 * 100/85x * 100 = 35 5/17 % > 35%
ANSWER:D
Answer: (D) more than 35% profit
Question: A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12100 after a year?
(A) Rs.3630
(B) Rs.2840
(C) Rs.3200
(D) Rs.5600
(E) Rs.5700
Rationale: 6300:4200:10500
3:2:5
3/10 * 12100 = 3630
ANSWER:A
Answer: (A) Rs.3630
Question: 60% of a number is added to 120, the result is the same number. Find the number?
(A) 300
(B) 277
(C) 266
(D) 99
(E) 121
Rationale: :
(60/100) * X + 120 = X
2X = 600
X = 300
Answer: A
Answer: (A) 300
Question: A batch of widgets costs p + 1 dollars for a company to produce and each batch sells for p(5 – p) dollars. For which of the following values of p does the company make a profit?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: to make profit, selling price should be greater than cost price
p(5-p) - p-1 >0
=> p^2-4*p+1<0
hence p=3
A
Answer: (A) 3
Question: If 40% of a certain number is 160, then what is 20% of that number?
(A) 75
(B) 100
(C) 120
(D) 30
(E) 80
Rationale: Explanation:
40% = 40*4 = 160
20% = 20*4 = 80
Answer: Option E
Answer: (E) 80
Question: The value of “A” varies in inverse proportion as the square of “B”. If the value of “A” is equal to 40 when “B” is equal to 12. What would be the value of “A” when “B” is equal to 24 ?
(A) 10
(B) 15
(C) 20
(D) 22
(E) None of these
Rationale: Explanation:
We have, A α 1/B2
A * B2 = K (constant)
When B = 12, A = 40 …..Given
K = 40 * (12)2 = 5760
Now, B = 24. Hence, A = 5760 / 576 = 10
ANSWER: A
Answer: (A) 10
Question: A man spends 2/5 of his salary on house rent, 3/10 of his salary on food and 1/8 of his salary on Conveyance. If he has $1400 left with him,find his expenditure on food and Conveyance.
(A) $8600
(B) $2400
(C) $1000
(D) $3000
(E) $3400
Rationale: Remaining Part of salary left=1-(2/5+3/10+1/8) =1 - (33/40) = 7/40
Let the monthly salary be $X
Then, 7/40 of X=$1400
X=(1400*40/7)
=$8600
Expenditure on food=$(3/10*800)=$2400
Expenditure on Conveyance=$(1/8*8000)=$1000
$2400 + $1000 = $3400
so the answer is option E) $3400
Answer: (E) $3400
Question: Find the simple interest on Rs. 78000 at 15(2/5) % per annum for 9 months.
(A) Rs. 9009
(B) Rs. 9008
(C) Rs. 9002
(D) Rs. 9202
(E) Rs. 9001
Rationale: Explanation:
P = Rs. 78000, R = 77/5 % p.a and T = 9/12 years = ¾ years
Therefore,
S.I = (P*R*T)/100
= (78000* 77/5 * ¾ * 1/100)
= Rs. 9009
ANSWER: A
Answer: (A) Rs. 9009
Question: The y intercept of a line L is 2. If the slope of L is negative, which of the following could be the x intercept of L.
I. -1
II. 0
III. 6
(A) I only
(B) II only
(C) III only
(D) I and II
(E) I and III
Rationale: C) III only
The y-intercept is 2. Therefore we have y=mx+2
It is given that the slope is negative. Therefore the line must go from top left to bottom right.
i.e: the x-intercept has to be positive. That itself rules out III.
If you choose to go with the options directly, here's an approach.
y=mx+2. For the x-intercept, y=0.
i.e. mx+2=0.
We know that the slope m is negative. Therefore, if x=-1 or x=0, the equation mx+2 =0 would never be satisfied.
If x=6, we have 6m+2=0. A value of m=-1/3 would satisfy this equation. (ANSWER C)
Answer: (C) III only
Question: Find the next term in series - 25, 37, 49, 61, ?
(A) 71
(B) 72
(C) 73
(D) 74
(E) 75
Rationale: Series is Increased by 12.
25 +12 =37
37 +12 =49
49 +12 =61
61 +12 =73
ANSWER:C
Answer: (C) 73
Question: If 1st October is Sunday, then 1st November will be
(A) sunday
(B) monday
(C) thursday
(D) friday
(E) Wednesday
Rationale: Given that 1st October is Sunday
Number of days in October = 31
31 days = 3 odd days
(As we can reduce multiples of 7 from odd days which will not change anything)
Hence 1st November = (Sunday + 3 odd days) = Wednesday
Answer:E) Wednesday
Answer: (E) Wednesday
Question: In what time a sum of money double itself at 3% per annum simple interest?
(A) 33 1/9%
(B) 33 1/3%
(C) 332 1/3%
(D) 33 9/3%
(E) 13 1/3%
Rationale: P = (P*3*R)/100
R = 33 1/3%
Answer:B
Answer: (B) 33 1/3%
Question: In honor of the year 2015, a donor has purchased 2016 books to be distributed evenly among the elementary schools in a certain school district. If each school must receive the same number of books, and there are to be no books remaining, which of the following is NOT a number of books that each school could receive?
(A) 18
(B) 36
(C) 42
(D) 56
(E) 58
Rationale: All options other than 'E' are factors of 2015. Hence, 'E' is the answer
Answer: (E) 58
Question: Dravid has x dollars more than Gayle has, and together they have a total of y dollars. Which of the following represents the number of dollars that Gayle has?
(A) (y – x)/2x
(B) (y – x)/2y
(C) (y – x)/2
(D) 3(y – x)/2
(E) 5(y – x)/2
Rationale: To solve, we will set up two equations. Let's start by defining two variables.
A = number of dollars Gayle has
B= number of dollars Dravid has
We are given that Dravid has x dollars more than Gayle. We set up an equation:
B= x + A
We are next given that together they have a total of y dollars. We can set up our second equation:
A + B = y
Since we know that B = x + A, we can substitute x + A for B into the second equation A+ B = y.
Notice that, after the substitution, we will only have variables of A, x, and y. Thus, we have:
A + x + A = y
2A + x = y
2A = y – x
A = (y – x)/2
Answer : C
Answer: (C) (y – x)/2
Question: The y intercept of a line L is 1. If the slope of L is negative, which of the following could be the x intercept of L.
I. -1
II. 0
III. 6
(A) I only
(B) II only
(C) III only
(D) I and II
(E) I and III
Rationale: C) III only
The y-intercept is 1. Therefore we have y=mx+1
It is given that the slope is negative. Therefore the line must go from top left to bottom right.
i.e: the x-intercept has to be positive. That itself rules out III.
If you choose to go with the options directly, here's an approach.
y=mx+1. For the x-intercept, y=0.
i.e. mx+1=0.
We know that the slope m is negative. Therefore, if x=-1 or x=0, the equation mx+1 =0 would never be satisfied.
If x=6, we have 6m+1=0. A value of m=-1/6 would satisfy this equation. (ANSWER C)
Answer: (C) III only
Question: The length of the rectangular field is double its width. Inside the field there is square shaped pond 8m long. If the area of the pond is 1/8 of the area of the field. What is the length of the field?
(A) 54
(B) 32
(C) 75
(D) 28
(E) 11
Rationale: A/8 = 8 * 8 => A = 8 * 8 * 8
x * 2x = 8 * 8 * 8
x = 16 => 2x = 32
Answer:B
Answer: (B) 32
Question: If t is an odd integer, which of the following must also be odd?
(A) 2t + 8
(B) t + t
(C) 3t + 3
(D) 2t + t
(E) t^2 + 1
Rationale: Things to keep in mind:
Odd + odd = even
Odd + even = odd
Odd*odd = odd
Odd*even = even
On checking each option
A. 2t + 8
2t = even, 2t + 8 = even + even = even.
B. t + t
Odd + odd = even. This will be even
C. 3t + 3
3t = odd, 3t + 3 = odd + odd = even
D. 2t + t
2t = even, 2t + t = even + odd = odd
E. t^2 + 1
t^2 = odd, t^2 + 1 = odd + odd = even
Correct option: D
Answer: (D) 2t + t
Question: For a certain exam,a score of 42 was 5 standard deviations below mean and a score of 67 was 2.5 standard deviations above mean.What was the mean score for the exam?
(A) 74
(B) 76
(C) 78
(D) 58.67
(E) 82.2
Rationale: Mean-5SD=42
Mean+2.5SD=67
By solving above equations we get,
SD (absolute value)=3.33
Mean=58.67
ANS. D
Answer: (D) 58.67
Question: If M equals the sum of the odd integers from 1 to 111, inclusive, and T equals the sum of the even integers from 2 to 50, inclusive, what is the value of M + T?
(A) 400
(B) 5550
(C) 6922
(D) 3786
(E) 5553
Rationale: Use following formulae for such problems:
Sum of evenly spaced integers = (# of integers)*(mean of integers)
# of integers = [(last - first)/2] + 1
Mean of integers = (last + first)/2
In above problem:
# of integers = [(111 - 1)/2] + 1= 56 and [(50-2)/2]+ 1 = 25
Mean of integers = (111 + 1)/2 = 56 and (50 + 2)/2 = 26
Sum of integers = (56*56) = 3136 and (25*26) = 650
Thus their sum (M + T) = 3786
ANSWER:D
Answer: (D) 3786
Question: The sum of three consecutive numbers is 87. The greatest among these three numbers is:
(A) 26
(B) 28
(C) 29
(D) 30
(E) 31
Rationale: Let the numbers be x, x+1 and x+2
X+x+1+x+2=87
3x=84
X=28
Greatest number is =30
ANSWER D 30
Answer: (D) 30
Question: One fourth of a solution that was 10% sugar by weight was replaced by a second solution resulting in a solution that was 18percent sugar by weight. The second solution was what percent sugar by weight?
(A) 34%
(B) 24%
(C) 42%
(D) 18%
(E) 8.5%
Rationale: Instead of using complex calculations and remembering formulae, why dont u directly get to weighted average.
3 parts of 10% + 1 part of x (unknown) % = 4 parts of 18%
=> x% = 72%-30% = 42%
ans C it is.
Answer: (C) 42%
Question: Evaluate: |9 - 8(3 - 12)| - |5 - 11| = ?
(A) 75
(B) 50
(C) 60
(D) 70
(E) 80
Rationale: According to order of operations, inner brackets first. Hence
|9 - 8(3 - 12)| - |5 - 11| = |9 - 8*(-9)| - |5 - 11|
According to order of operations, multiplication within absolute value signs (which may be considered as brackets when it comes to order of operations) next. Hence
= |9 + 72| - |5 - 11|
= |81| - |-6|
= 81 - 6 = 75
correct answer A)75
Answer: (A) 75
Question: A can do a piece of work in 10 days and B can do it in 15 days and C can do it 20 days. They started the work together and A leaves after 5 days and B leaves after 3 days from the beginning. How long will work lost?
(A) 2
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: 5/10 + 3/15 + x/20 = 1
x = 18/3 = 6
Answer: D
Answer: (D) 6
Question: How many plants will be there in a circular bed whose outer edge measure 33 cms, allowing 4 cm2 for each plant ?
(A) 18
(B) 750
(C) 21
(D) 120
(E) None of these
Rationale: Circumference of circular bed = 33 cm
Area of circular bed = (33)2â„4Ï€
Space for each plant = 4 cm2
âˆ´ Required number of plants
= (33)2â„4Ï€ Ã· 4 = 21.65 = 21(approx)
Answer C
Answer: (C) 21
Question: Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how
many minutes does the bus stop per hour ?
(A) 8 minutes
(B) 10 mintues
(C) 12 minutes
(D) 14 minutes
(E) 15 minutes
Rationale: Explanation:
Due to stoppages, it covers 9 km less.
Time taken to cover 9 km = (9/54) hour
= (1/6)*60 minutes
= 10 minutes
Answer: B
Answer: (B) 10 mintues
Question: Vijay bought 160 shirts at the rate of Rs. 225 per shirt. The transport expenditure was Rs. 1400. He paid an octroi at the rate of Rs. 1.75 per shirt and labour charges were Rs. 320. What should be the selling price of one shirt, if he wants a profit of 30%?
(A) 282
(B) 229
(C) 277
(D) 308.75
(E) 2812
Rationale: Total CP per shirt = 225 + 1400/160 + 1.75 + 320/160 = Rs. 237.5
SP = CP[(100 + profit%)/100]
= 237.5 * [(100 + 30)/100] = Rs. 308.75.
Answer:D
Answer: (D) 308.75
Question: In the xy-coordinate system, if (m, n) and (m + 4, n + k) are two points on the line with the equation x = 2y + 5, then k =
(A) 1/2
(B) 1
(C) 2
(D) 5/2
(E) 4
Rationale: Since (m, n) and (m + 2, n + k) are two points on the line with the equation x = 2y + 5 they should satisfy m=2n +5 and m+4 =2 *(n+k)+5.
By 1st equation we have m-2n=5 and by 2nd equation m-2n = 2k+1 ---> 5=2k+1 --->k=2.
The answer is, therefore, (C).
Answer: (C) 2
Question: What is the decimal equivalent of (1/9)^2?
(A) 0.0123
(B) 0.0625
(C) 0.16
(D) 0.25
(E) 0.5
Rationale: (1/9)² = (1/9)(1/9)= 1/81
APPROACH #1: use long division to divide 81 into 1 to get 1/81 = 0.0123
A
Answer: (A) 0.0123
Question: Two numbers N and 16 have LCM = 48 and GCF = 8. Find N.
(A) 24
(B) 34
(C) 44
(D) 54
(E) 64
Rationale: The product of two integers is equal to the product of their LCM and GCF. Hence.
16 × N = 48 × 8
N = 48 × 8 / 16 = 24
correct answer A
Answer: (A) 24
Question: If a person buy radio worth Rs 2468 and pay 7% sales .how much price of radio should reduce to pay only Rs 2468.
(A) 162
(B) 158
(C) 159
(D) 130
(E) 160
Rationale: (x+.07x)=2468
1.07x=2468
x=2306
reduce=2468-2306=162
ANSWER:A
Answer: (A) 162
Question: A goods train runs at the speed of 72 km/hr and crosses a 250 m long platform in 26 sec. What is the length of the goods train?
(A) 250
(B) 260
(C) 270
(D) 280
(E) 290
Rationale: Speed = 72 * 5/18 = 20 m/sec.
Time = 26 sec.
Let the length of the train be x meters.
Then, (x + 250)/26 = 20
x = 270 m.
Answer: Option D
Answer: (D) 280
Question: An integer n between 1 and 99, inclusive, is to be chosen at random. What is the probability that n(n+1) will be divisible by 2 ?
(A) 1/9
(B) 1/3
(C) 1/2
(D) 2/3
(E) 5/6
Rationale: n(n+1) to be divisible by 2 either n or n+1 must be a multiples of 2.
In each following group of numbers: {1, 2, 3}, {4, 5, 6}, {7, 8, 9}, ..., {97, 98, 99} there are EXACTLY 2 numbers out of 3 satisfying the above condition. For example in {1, 2, 3} n can be: 2, or 3. Thus, the overall probability is 2/3.
Answer: D.
Answer: (D) 2/3
Question: Jim drove 1096 miles of a 1200 miles journey. How many more miles does he need to drive to finish his journey?
(A) 104 miles
(B) 432 miles
(C) 456miles
(D) 887 miles
(E) 767 miles
Rationale: The number of miles to drive to finish his journey is given by
1200 - 1096= 104 miles
correct answer A
Answer: (A) 104 miles
Question: 385, 462, 572, 396, 423, 671, 264
(A) 385
(B) 423
(C) 671
(D) 264
(E) None of these
Rationale: Solution
In each number except 423,the middle digit is the sum of the other two. Answer B
Answer: (B) 423
Question: On rainy mornings, Mo drinks exactly N cups of hot chocolate (assume that N is an integer). On mornings that are not rainy, Mo drinks exactly 6 cups of tea. Last week Mo drank a total of 22 cups of tea and hot chocolate together. If during that week Mo drank 14 more tea cups than hot chocolate cups, then how many rainy days were there last week?
(A) 0
(B) 1
(C) 4
(D) 5
(E) 6
Rationale: T= the number of cups of tea
C= the number of cups of hot chocolate
T+C = 22 T-C=14 -> T= 18. C=2.
Mo drinks 6 cups of tea a day then number of days that are not rainy = 18/6 = 3
So number of rainy days = 7-3 = 4
C is the answer.
Answer: (C) 4
Question: Each week, Harry is paid x dollars per hour for the first 15 hours and 1.5x dollars for each additional hour worked that week. Each week, James is paid x dollars per per hour for the first 40 hours and 2x dollars for each additional hour worked that week. Last week James worked a total of 41 hours If Harry and James were paid the same amount last week, how many hours did Harry work last week ?
(A) 33
(B) 36
(C) 37
(D) 38
(E) 39
Rationale: 42x=15x+1.5x(H-15)
==> 42=15+1.5(H-15)
==> H-15 = 27/1.5=18 ==> H = 33
Answer is A
Answer: (A) 33
Question: The average runs of a cricket player of 5 innings was 20. How many runs must he make in his next innings so as to increase his average of runs by 3?
(A) 12
(B) 42
(C) 44
(D) 76
(E) 84
Rationale: Explanation:
Average after 6 innings = 23
Required number of runs = (24 * 6) – (20 * 5)
= 144 – 100 = 44
ANSWER C
Answer: (C) 44
Question: Raj invested an amount of Rs.17400 for two years. Find the rate of compound interest that will fetch him an amount of Rs.1783.50 at the end of two years?
(A) 1
(B) 2
(C) 6
(D) 5
(E) 7
Rationale: Explanation:
Let the rate of interest be R% p.a.
17400[1 + R/100]2 = 17400 + 1783.50
[1 + R/100]2 = (17400 + 1783.50)/17400
= 1 + 1025/10000 = 1 + 41/400
= 441/400 = [21/20]2
[1 + R/100] = 21/20
R/100 = 1/20
Therefore R = 5
Answer:D
Answer: (D) 5
Question: In a certain town, 80 percent of the registered voters are x and the rest are y. In a mayoral race, if 75 percent of the registered voters who are x and 20 percent of the registered voters who are y are expected to vote for Candidate A, what percent of the registered voters are expected to vote for Candidate A ?
(A)  64%
(B)  53%
(C)  54%
(D)  55%
(E)  57%
Rationale: Say there are total of 100 registered voters in that city. Thus 60 are Democrats and 40 are Republicans.
80*0.75=60 Democrats are expected to vote for Candidate A;
20*0.20=4 Republicans are expected to vote for Candidate A.
Thus total of 60+4=64 registered voters are expected to vote for Candidate A, which is 64% of the total number of registered voters.
Answer: A.
Answer: (A)  64%
Question: Zn = 2Zn-1 + 4 and Qn = 4Qn-1 + 8 for all n > 1. If Z5 = Q4 and Z7 = 316, what is the first value of n for which Qn is an integer?
(A)  1
(B)  2
(C)  3
(D)  4
(E)  5
Rationale: Assuming I have understood the symbols used correctly answer is C- 3
Z7 = 2S6 +4 = 316
Z6 = 312/2 = 156 = 2Z5 + 4
Z5 = 152/2 = 76 = Q4
Q4 = 4Q3 + 8 = 76
Q3 = 68/4 = 17
Q3 = 4Q2 + 8 = 17
Q2 = 9/4 = 2.25
Q2 = 4Q1 + 8
Q1 will not be integer
Answer: (C)  3
Question: If a and b are different positive integers and a + b+2 = a(a + b), then which of the following must be true?
I. a = 1
II. b = 1
III. a < b
(A) I only
(B) II only
(C) III only
(D) I and II
(E) I and III
Rationale: Number picking might not be the best way to solve MUST BE TRUE questions.
The question asks which of the followingMUSTbe true, or which of the following isALWAYStrue no matter what set of numbers you choose. For such kind of questionsif you can prove that a statement is NOT truefor one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer.
So the set you chose just proves that II is not always true and hence it's not a part of a correct choice. As for I and III: they might be true for this particular set of numbers but not true for another set, so you can not say that I and III are always true just based on one set of numbers (it just happens to be that I and III are always true).
As forCOULD BE TRUEquestions:
The questions asking which of the followingCOULDbe true are different:if you can prove that a statement is truefor one particular set of numbers, it will mean that this statement could be true and hence is a correct answer.
B
Answer: (B) II only
Question: An order was placed for the supply of a carper whose length and breadth were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and breadth were in the ratio 7 : 3 but were was no change in its parameter. Find the ratio of the areas of the carpets in both the cases.
(A) 8 : 2
(B) 8 : 7
(C) 8 : 3
(D) 8 : 5
(E) 8 : 76
Rationale: Let the length and breadth of the carpet in the first case be 3x units and 2x units respectively.
Let the dimensions of the carpet in the second case be 7y, 3y units respectively.
From the data,.
2(3x + 2x) = 2(7y + 3y)
=> 5x = 10y
=> x = 2y
Required ratio of the areas of the carpet in both the cases
= 3x * 2x : 7y : 3y
= 6x2 : 21y2
= 6 * (2y)2 : 21y2
= 6 * 4y2 : 21y2
= 8 : 7
Answer: Option B
Answer: (B) 8 : 7
Question: A shopkeeper sold an article offering a discount of 4% and earned a profit of 26%. What would have been the percentage of profit earned if no discount was offered?
(A) 24
(B) 28
(C) 31
(D) 32
(E) 34
Rationale: Let C.P. be Rs. 100.
Then, S.P. = Rs. 126
Let marked price be Rs. x. Then, 96/100 x = 126
x = 12600/96 = Rs. 131.25
Now, S.P. = Rs. 131.25, C.P. = Rs. 100
Profit % = 31%.
ANSWER:C
Answer: (C) 31
Question: Car A is 24 miles behind car B, which is traveling in the same direction along the same route as Car A.Car A is traveling at a constant speed of 58 miles per hour and Car Bis traveling at a constant speed of 50miles per hour.How many hours will it take for Car A to overtake and drive 8 miles ahead of Car B?
(A) 1.5
(B) 2.0
(C) 2.5
(D) 3.0
(E) 4.0
Rationale: Relative speed of car A is 58-50=8 miles per hour, to catch up 24 miles and drive 8 miles ahead so to drive 32 miles it'll need 32/8=4 hours.
Answer: E.
Answer: (E) 4.0
Question: The speed of a boat in still water is 40kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
(A) 80,70 kmph
(B) 80,40 kmph
(C) 10,40 kmph
(D) 80,80 kmph
(E) 60,20 kmph
Rationale: Speed downstream = 40 + 20
= 60 kmph
Speed upstream = 40 - 20
= 20 kmph
Answer: E
Answer: (E) 60,20 kmph