mathewhe/aqua_rat huggingface dataset:
Question: Peter has six times as many dimes as quarters in her piggy bank. She has 21 coins in her piggy bank totaling $2.55
How many of each type of coin does she have?
(A) 16
(B) 17
(C) 18
(D) 19
(E) 20
Rationale: Solution
Let x be the number of quarters. Let 6x be the number of dimes
Since one quarter equals 25 cents, x quarters equals x × 25 cents or 25x cents
Since one dime equals 10 cents, 6x dimes equals 6x × 10 cents or 60x cents
Since one 1 dollar equals 100 cents, 2.55 dollars equals 2.55 × 100 = 255 cents
Putting it all together, 25x cents + 60x cents = 255 cents
85x cents = 255 cents
85x cents / 85 cents = 255 cents / 85 cents
x = 3
6x = 6 × 3 = 18
Therefore Peter has 3 quarters and 18 dimes
Answer C
Answer: (C) 18
Question: For what value of x, is |x – 5| + |x + 5| + |x| = 27?
(A)  0
(B)  3
(C)  -3
(D)  9
(E)  -9
Rationale: For what value of x, is |x – 5| + |x + 5| + |x| = 27?
It's easiest just to plug in answer choices:
(D): 9
|x – 5| + |x + 5| + |x| = 27?
|9 - 5| + |9 + 5| + |9| = 27?
|4| + |14| + |9| = 27
(D)
Answer: (D)  9
Question: If a - b = 4 and a2 + b2 = 30, find the value of ab.
(A) A)7
(B) B)12
(C) C)15
(D) D)18
(E) E)20
Rationale: Explanation:
2ab = (a2 + b2) - (a - b)2
= 30 - 16 = 14
ab = 7
Answer: A
Answer: (A) A)7
Question: If n is an even integer, then which of the following must be an odd integer?
(A) 2n
(B) 3n
(C) 3n + n^2 + 2
(D) n^2 + 1
(E) 2n + n^2
Rationale: Answer: D
A: 2n = even
B: 3n = even
C: 3n + n^2 + 2 = even
D: n^2 + 1 = odd
E: 2n + n^2 = even
Answer: D
Answer: (D) n^2 + 1
Question: x, y, and z are three positive integers whose average is 10. If x≤y≤z and z-x=3, which of the following could be the median E of x, y, and z?
I. 9
II. 10
III. 11
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only
Rationale: Average gives us an idea that 3 nos. are close to 10.
so 10, 10, 10 is an unacceptable option because (z-x =3), but it helps in getting other combinations.
Let us see options.
If 9 has to be median E.
1st term has to less than 9 or equal to 9. (also maintain z-x = 3)
9 9 12 --> satisfies all conditions so 9 can be a median value.
If 11 has to be a median
3rd term has to be 11 or more than 11. (also maintain z-x = 3)
8 11 11 -->satisfies all conditions so 9 can be a median value.
Now for 10 to be median.
z+ x = 20 and z-x = 3, we wont have integer values of z.
10 cannot be a median
E is the answer.
Answer: (E) I and III only
Question: Three years ago the average age of a family of 4 members was 19 years. A boy have been born, the average age of the family is the same today. What is the age of the boy?
(A) A)7
(B) B)6
(C) C)5
(D) D)4
(E) E)3
Rationale: 4 * 22 = 88
5 * 19 = 95
--------------
7
Answer: A
Answer: (A) A)7
Question: A car was driving at 50 Km/h for 30 minutes, and then at 90 Km/h for another 40 minutes. What was its average speed?
(A) 102
(B) 80
(C) 75
(D) 70
(E) 65
Rationale: driving at 50 Km/h for 30 minutes ,distance covered = 50*1/2=25 km
driving at 90 km/h for 40 minutes ,distance covered = 90*2/3=60 km
average speed = total distance/total time = 85/5/6 = 102 km/h
Answer: A
Answer: (A) 102
Question: A big cube is formed by rearranging the 160 coloured and 56 non-coloured similar cubes in such a way that the exposure of the coloured cubes to the outside is minimum. The percentage of exposed area to the coloured is :
(A) 25.9%
(B) 44.44%
(C) 35%
(D) 61%
(E) None of these
Rationale: Well the big cube which has the side built with 6 little cubes (6^3) will haveinsidethe cube which has the side built with 4 little cubes (6-2 edges), so 4^3... Similarly, the cube which has the side built with 4 little cubes (4^3) will haveinsidethe cube which has the side built with 2 little cubes, (4-2 edges), so 2^3... answer is B
Answer: (B) 44.44%
Question: if 40% of (x-y) = 30% of (x+y) then what percent of x is y?
(A) 2.5%
(B) 10%
(C) 5%
(D) 14%
(E) 25%
Rationale: 40% of (x-y)=30% of(x+y)
(40/100)(x-y)=(30/100)(x+y)
4(x-y)=3(x+y)
x=7y
x=7y
therefore required percentage
=((y/x) X 100)% = ((y/7y) X 100) =14%
Answer is D.
Answer: (D) 14%
Question: If the area of circle O is 16π, what is the length of an arc on the circle formed by a central angle measuring 10 degrees?
(A) π
(B) 2π/9
(C) 2π
(D) 5π/2
(E) 8π
Rationale: Area = 16π
Radius = 4
Circumference = 2 x 4 x π = 8π
Angle forming the arc = 10 degrees. 10/360 = 1/36.
Therefore length of arc = 1/36 * 8π = 2π/9 - Answer choice B.
Answer: (B) 2π/9
Question: In what ratio must a grocer mix two varieties of pulses costing Rs. 15 and Rs. 20 per kg respectively so as to get a mixture worth Rs. 16.50 kg?
(A) 3 : 7
(B) 5 : 7
(C) 7 : 3
(D) 7 : 5
(E) 7 : 4
Rationale: Explanation:
By the rule of alligation:
Cost of 1 kg pulses of 1st kindCost of 1 kg pulses of 2nd kind
Required rate = 3.50 : 1.50 = 7 : 3.
ANSWER IS C
Answer: (C) 7 : 3
Question: Solve the equation for x : 6x - 27 + 3x = 4 + 9 - x
(A) 4
(B) 5
(C) 6
(D) 1
(E) 7
Rationale: Explanation:
9 x + x = 13 + 27
10 x = 40 => x = 4
Answer: A
Answer: (A) 4
Question: The value of 0.1 x 0.1 x 0.1 + 0.02 x 0.02 x 0.02/ 0.2 x 0.2 x 0.2 + 0.04 x 0.04 x 0.04	is:
(A) 0.215
(B) 0.512
(C) 0.521
(D) 0.125
(E) 0.152
Rationale: Given expression
=(0.1)(power 3) + (0.02)(power 3) /2(power 3) [(0.1)(power 3) + (0.02)(power 3)]
=1/8
= 0.125
Answer is D.
Answer: (D) 0.125
Question: A is older than B by 5years. Seven years hence, thrice A's age shall be equal to four times that of B. Find their present ages.
(A) 14, 7
(B) 10, 5
(C) 13, 8
(D) 12, 8
(E) 8, 12
Rationale: Explanation:
Let the present ages of A and B be 'a' and 'b' respectively.
3(a + 7)= 4( (b +7 ) --- (1) =>3a-4b=7 -------(1)
a-b = 5 -------(2) Solving (1) and (2) we get b=8
Substituting b = 8 in second equation, we get a= 13. Answer : C
=> 2a = 32 => a = 16.
Answer: C
Answer: (C) 13, 8
Question: 365:90::623:?
(A) 36
(B) 45
(C) 123
(D) 63
(E) none of these
Rationale: 365---3*6*5....90
623---6*2*3....36
answer A
Answer: (A) 36
Question: Each person in Room A is a student, and 1/6 of the students in Room A are seniors. Each person in Room B is a student, and 5/7 of the students in Room B are seniors. If 1 student is chosen at random from Room A and 1 student is chosen at random from Room B, what is the probability that exactly 1 of the students chosen is a senior?
(A) 5/42
(B) 37/84
(C) 9/14
(D) 16/21
(E) 37/42
Rationale: Probability of choosing senior from Room A=1/6, Non senior=5/6
Probability of choosing senior from Room B=5/7, Non senior=2/7
Reqd probability= (1/6*2/7)+(5/7*5/6)=27/42=9/14
Answer C
Answer: (C) 9/14
Question: if 1/8 of a pencil is black ½ of the remaining is white and the remaining 3 ½ is blue find the total length of the pencil?
(A) 8
(B) 5
(C) 7
(D) 6
(E) 4
Rationale: Let the total length be xm
Then black part =x/8cm
The remaining part=(x-x/8)cm=7x/8cm
White part=(1/2 *7x/8)=7x/16 cm
Remaining part=(7x/8-7x/16)=7x/16cm
7x/16=7/2
x=8cm
Answer is A.
Answer: (A) 8
Question: Cars P and Q are approaching each other on the same highway. Car P is moving at 47 mph northbound and Car Q is moving at 53 mph southbound. At 2:00 pm, they are approaching each other and 190 miles apart. Eventually they pass each other. At what clock time are they moving away from each other and 35 miles apart?
(A)  3:30 pm
(B)  3:45 pm
(C)  4:00 pm
(D)  4:15 pm
(E)  4:30 pm
Rationale: Total distance, which should be covered by both cars is 190+35=225 miles.
Let t be the time so the equation will be 47t+53t=225 thus,
t=2.25 hours
Answer: D
Answer: (D)  4:15 pm
Question: Jimâ€™s Taxi Service charges an initial fee of $2.0 at the beginning of a trip and an additional charge of $0.35 for each 2/5 of a mile traveled. What is the total charge for a trip of 3.6 miles?
(A) $5.15
(B) $4.45
(C) $4.80
(D) $5.05
(E) $5.40
Rationale: Let the fixed charge of Jimâ€™s Taxi Service = 2 $
and charge per 2/5 mile(.4 mile) = .35$
Total charge for a trip of 3.6 miles = 2 + (3.6/.4) * .35
= 2 + 9*.35
= 5.15 $
Answer A
Answer: (A) $5.15
Question: The graphs of the two linear equations ax + by = c and bx - ay = c, where a, b and c are all not equal to zero,
(A) are parallel
(B) intersect at one point but not perpendicular
(C) intersect at two points
(D) perpendicular
(E) none of the above
Rationale: find the slopes of the two lines
a x + b y = c , slope m1 = - a / b
b x - a y = c , slope m2 = b / a
m1*m2 = (- a / b)(b / a) = - 1
The two lines are perpendicular
ANSWER : D
Answer: (D) perpendicular
Question: In a class, there are 20 boys whose average age is decreased by 2 months, when one boy aged 16 years replaced by a new boy. The age of the new boy is?
(A) 12 years 8 months
(B) 15 years
(C) 16 years 4 months
(D) 17 years 10 months
(E) 17 years
Rationale: Total decrease = (20 x 2) months
= 3 years 4 months
Age of the new boy
= 16 years - 3 years 4 months.
= 12 years 8 months.
ANSWER:A
Answer: (A) 12 years 8 months
Question: Sally bought a dozen items at 120.00 per dozen. What will Sally have to sell each item for to generate a 15% profit?
(A) 10.15
(B) 11.5
(C) 15.0
(D) 21.5
(E) 150.0
Rationale: C.P. is 120/12=10
Desired profit=15%
The calculation for markup is (C.P.*desired profit/100)=10*15/100=1.5
The calculation for final sale price=C.P.+markup=10+1.5=11.5
ANSWER:B
Answer: (B) 11.5
Question: In an examination a pupil's average marks were 63 per paper. If he had obtained 22 more marks for his Geography paper and 2 more marks for his History paper, his average per paper would have been 65. How many papers were there in the examination?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
Rationale: Let the number of papers be x. Then,
63x + 22 + 2 = 65x
= 2x = 24
= x = 12.
ANSWER:E
Answer: (E) 12
Question: log3 N+log15 N what is 3 digit number N that will be whole number
(A) 3375
(B) 7292
(C) 8291
(D) 3929
(E) 2727
Rationale: No of values N can take is 1
15^3=3375
ANSWER:A
Answer: (A) 3375
Question: The largest 4 digit number exactly divisible by 88 is?
(A) A)9944
(B) B)9954
(C) C)9967
(D) D)9969
(E) E)9970
Rationale: Largest 4-digit number = 9999
88) 9999 (113
88
----
119
88
----
319
264
---
55
---
Required number = (9999 - 55)
= 9944.
A)
Answer: (A) A)9944
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
(A) 277 m
(B) 268 m
(C) 276 m
(D) 150 m
(E) 125 m
Rationale: Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train
= (Speed x Time) = (50/3 * 9) m
= 150 m.
Answer:D
Answer: (D) 150 m
Question: Find 10th term in the series 1, 3, 5, 7, ...
(A) 19
(B) 20
(C) 21
(D) 22
(E) 23
Rationale: SOLUTION:
a = 1
d = 3 – 1 = 2
10th term, t10 = a + (n-1)d = 1 + (10 – 1)2 = 1 + 18 = 19
ANSWER IS A
Answer: (A) 19
Question: The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 3 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each?
(A) s.2718
(B) s.4586
(C) s.4597
(D) s.4530
(E) s.4528
Rationale: Area of the four walls = 2h(l + b)
Since there are doors and windows, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft.
Total cost = 906 * 3
=Rs.2718
Answer: A
Answer: (A) s.2718
Question: A sum was put at simple interest at a certain rate for 3 years Had it been put at 3% higher rate, it would have fetched 81 more. Find the sum.
(A) 500
(B) 600
(C) 700
(D) 800
(E) 900
Rationale: Difference in S.I. = P×T/100(R1−R2)
⇒ 81 = P×3x3/100(∵ R1 - R2 = 2)
⇒ P = 81×100/3x3=900
Answer E
Answer: (E) 900
Question: A car travels the first 1/3 of certain distance with a speed of 12km/hr the next 1/3 distance with a speed of 20 km/hr, and the last 1/3 distance with a speed of 60 km/hr. the average speed of the car for the whole journey is?
(A) 12km/hr
(B) 20km/hr
(C) 89km/hr
(D) 52km/hr
(E) 79km/hr
Rationale: Let the whole distance travelled be x km
and the average speed of the car for he whole journey be y km/hr
then (x/3)/12+(x/3)/20+(x/3)/60=x/y
x/36+x/60+x/180=x/y
1/20y=1
y=20km/hr
Answer(B)
Answer: (B) 20km/hr
Question: If a sum of money doubles itself in 8 years at simple interest, the ratepercent per annum is
(A) 12
(B) 12.5
(C) 13
(D) 13.5
(E) 14
Rationale: Explanation:
Let sum = x then Simple Interest = x
Rate = (100 * x) / (x * 8) = 12.5
Option B
Answer: (B) 12.5
Question: Find the least number which when divided by 5,6,7, and 8 leaves a remainder 3, but when divided by 9 leaves no remainder.
(A) 1683
(B) 1753
(C) 1523
(D) 1433
(E) None of them
Rationale: L.C.M. of 5,6,7,8 = 840.
Therefore, Required number is of the form 840k + 3
Least value of k for which (840k + 3) is divisible by 9 is k = 2.
Therefore, Required number = (840 X 2 + 3)=1683
Answer is A.
Answer: (A) 1683
Question: 26 buses are running between two places P and Q. In how many ways can a person go from P to Q and return by a different bus?
(A) 625
(B) 650
(C) 576
(D) 600
(E) 700
Rationale: we can go in any bus out of the 26 buses.
Hence He can go in 26 ways.
Since we can not come back in the same bus that he used for travelling,
we can return in 25 ways.
Total number of ways = 26 x 25 = 650
ANSWER:B
Answer: (B) 650
Question: A sum was put at simple interest at a certain rate for 10 years . Had it been put at 5% higher rate , it would have fetched Rs.600 more. What was the Sum?
(A) Rs.1200
(B) Rs.1300
(C) Rs.1400
(D) Rs.1500
(E) Rs.1600
Rationale: At 5% more rate, the increase in S.I for 10 years = Rs.600 (given)
So, at 5% more rate, the increase in SI for 1 year = 600/10 = Rs.60/-
i.e. Rs.60 is 5% of the invested sum
So, 1% of the invested sum = 60/5
Therefore, the invested sum = 60 × 100/5 = Rs.1200 Answer: A
Answer: (A) Rs.1200
Question: Positive integer x has p factors; 3x has 3 factors; Which of the following values can p take?
I. 1
II. 2
III. 3
(A) II or III
(B) I or III
(C) I or II
(D) only I
(E) only II
Rationale: Squares have odd number of factors.The square which is a multiple of 3 is 9.
3 has factors 1,3 .
Therefore 2 factors
Answer E
Answer: (E) only II
Question: Jeff has 252 ounces of peanut butter in 16, 28. and 40 ounce jars. He has an equal number of each sized jar. How many jars of peanut butter does Jeff have?
(A) 9
(B) 8
(C) 7
(D) 10
(E) 11
Rationale: Let p equal the number of each sized jarThen 16p + 28p + 40p = 25284p = 252p = 3Therefore, the total number of jars of peanut butter Jeff has = 3p = 9Answer: A
Answer: (A) 9
Question: Bricks are sold in packages of eight or thirteen only. If Timmy, a builder, bought 144 bricks exactly, what could be the number of large packs Timmy bought?
(A) 12
(B) 5
(C) 6
(D) 8
(E) 7
Rationale: Let number of packs of eight = e
let number of packs of thirteen = t
8e + 13t = 144
Now , we need to test for values of t .
Since sum 144 is even and 8s will always be even , t can't be odd .
Now , we can test for values e = 12 , 8 and 6
8*5 + 13*8 = 40 + 104 = 144
Answer D
Answer: (D) 8
Question: Lagaan is levied on the 60 percent of the cultivated land. The revenue department collected total Rs. 3,84,000 through the lagaan from the village of Mettur. Mettur, a very rich farmer , paid only Rs.480 as lagaan. The percentage of total land of Mettur over the total taxable land of the village is:
(A) 0.20833
(B) 1.23455
(C) 2.45466
(D) 5.54353
(E) 6.45343
Rationale: Total land of Sukhiya = \inline \frac{480x}{0.6} = 800x
\therefore Cultivated land of village = 384000x
\therefore Required percentage = \inline \frac{800x}{384000}\times 100 = 0.20833
A
Answer: (A) 0.20833
Question: Two circular frames are kept one above the other. Frame X has a diameter of 16 cm and Frame Y has a diameter of 12 cm. What fraction of the surface of Frame X is not covered by Frame Y?
(A) 3/5
(B) 7/16
(C) 12/16
(D) 24/12
(E) 2/3
Rationale: The questions asks us to find the surface which is not covered by the Frame Y i.e., area of the surface not covered.
Where as circumference is the length along the edge of the circle,
2*pi*r implies the length of the curve
pi*r^2 implies area enclosed by that curve..hence Area of the circle is considered for this problem
Area of the Frame Y=pi* r^2, where r=6
=>pi*36
Area of the Frame X=pi*64
Surface not covered by the Frame Y=pi*64-pi*36=Pi*28
fraction of Frame X's surface is not covered by a Frame Y= Pi*28/total area of the Frame X
=28/64=7/16
Answer is B
Answer: (B) 7/16
Question: The product of two numbers is 192 and the sum of these two numbers is 28. What is the smaller of these two numbers?
(A) 10
(B) 12
(C) 14
(D) 15
(E) 16
Rationale: Solution
Let the number be x and (28 - x)	= Then,
x (28 - x) = 192
‹=›x2 - 28x + 192 = 0.
‹=›(x - 16) (x - 12) = 0
‹=›x = 16 or x = 12.
Answer B
Answer: (B) 12
Question: My grandson is about as many days as my son in weeks, and my grandson is as many months as I am in years. My grandson, my son and I together are 120 years. Can you tell me my age in years ?
(A) 70
(B) 69
(C) 82
(D) 89
(E) 72
Rationale: Let m be my age in years. If s is my son's age in years, then my son is 52s weeks old. If g is my grandson's age in years, then my grandson is 365g days old. Thus,
365g = 52s.
Since my grandson is 12g months old,
12g = m.
Since my grandson, my son and I together are 120 years,
g + s + m = 120.
The above system of 3 equations in 3 unknowns (g, s and m) can be solved as follows.
m / 12 + 365 m / (52 x 12) + m = 120 or
52 m + 365 m + 624 m = 624 x 120 or
m = 624 x 120 / 1041 = 72.
Answer: (E) 72
Question: Find the unit digit in
(544)102+(544)103
(A) 2
(B) 4
(C) 0
(D) 1
(E) 3
Rationale: Explanation:
Required digit is =
(4)102+(4)103
as
(4)2
gives unit digit 6 so
(4)102
unit digit is 6 and
(4)103
unit digit is, unit digit of
6×4
= 4, so answer will be unit digit of 6 + 4 = 0
Option C
Answer: (C) 0
Question: A customer pays 50 dollars for a coffee maker after a discount of 20 dollars
What is the original price of the coffe maker?
(A) 50
(B) 40
(C) 70
(D) 60
(E) 20
Rationale: Let x be the original price.
x - 20 = 50
x - 20 + 20 = 50 + 20
x + 0 = 70
x = 70
Answer: (C) 70
Question: For any non-zero a and b that satisfy |ab| = ab and |a| = a
|b - 4| + |ab - b| = ?
(A) ab-4
(B) 2b - ab - 4
(C) ab+4
(D) ab - 2b + 4
(E) 4-ab
Rationale: |ab| = ab and |a| = -a
=> b is also negative.
So
|b-4| + |ab -b|
= (b-4) + ab - b ( as ab is positive and -b is positive, so expression is totally positive)
=b-4+ab-b
=ab-4
Answer -A
Answer: (A) ab-4
Question: The value of x + x(xx) when x = 8
(A) A) 520
(B) B) 516
(C) C) 518
(D) D) 536
(E) E) 564
Rationale: x + x(xx)
Put the value of x = 8 in the above expression we get,
8 + 8(88)
= 8 + 8(8 Ã— 8)
= 8 + 8(64)
= 9 + 512
= 520 The answer is (A)
Answer: (A) A) 520
Question: A vessel contains 20 liters of a mixture of milk and water in the ratio 3:2. 10 liters of the mixture are removed and replaced with an equal quantity of pure milk. If the process is repeated once more, find the ratio of milk and water in the final mixture obtained?
(A) 9:1
(B) 4:2
(C) 5:2
(D) 9:2
(E) 9:0
Rationale: Milk = 3/5 * 20 = 12 liters, water = 8 liters
If 10 liters of mixture are removed, amount of milk removed = 6 liters and amount of water removed = 4 liters.
Remaining milk = 12 - 6 = 6 liters
Remaining water = 8 - 4 = 4 liters
10 liters of pure milk are added, therefore total milk = (6 + 10) = 16 liters.
The ratio of milk and water in the new mixture = 16:4 = 4:1
If the process is repeated one more time and 10 liters of the mixture are removed, then amount of milk removed = 4/5 * 10 = 8 liters.
Amount of water removed = 2 liters.
Remaining milk = (16 - 8) = 8 liters.
Remaining water = (4 -2) = 2 liters.
The required ratio of milk and water in the final mixture obtained = (8 + 10):2 = 18:2 = 9:1.
Answer:A
Answer: (A) 9:1
Question: Sally has to pick her son up at 2 p.m. It is now 12:30 p.m. She has to travel 53 miles to get her son from camp. What time should she leave to pick her on up with the closest time to 2 p.m, without being late, given the distance of 53 miles with a constant speed of 50 mph?
(A) She needs to leave at 12:53 pm
(B) She needs to leave at 12:57 p.m
(C) She needs to leave at 1:03 p.m
(D) She cannot get there in time.
(E) She needs to leave at 1:15 p.m
Rationale: B, she is traveling 50 miles per hour and needs to travel 53 miles. Given that 50/53= 1.03 so approximately 1 hour and 3 minutes. 2 p.m- 1 hour 3 minutes= 12:57 pm. While A gets her there on time it is not as close to 2pm.
Answer: (A) She needs to leave at 12:53 pm
Question: If A and B are digits and 5AB is a 3-digit number that is divisible by 10, which of the following is a possible product of A and C?
(A) 57
(B) 21
(C) 52
(D) 38
(E) 50
Rationale: Key to this question is to remember the fact that a number divisible by 10 must end with only 0 (i.e B).
If B had to be 0, product should also be 0 regardless of A.
Only one answer choice meets the requirement.
Ans E.
Answer: (E) 50
Question: A pipe can fill a cistern in 20 minutes whereas the cistern when fill can be emptied by a leak in 28 minutes. When both pipes are opened, find when the cistern will be full?
(A) 65 minutes
(B) 76 minutes
(C) 70 minutes
(D) 62 minutes
(E) 52 minutes
Rationale: 1/20 - 1/28
= 1/70
70 minutes
Answer:C
Answer: (C) 70 minutes
Question: If the tens digit x and the units digit y of a positive integer n are reversed, the resulting integer is 27 less than n. What is y in terms of x ?
(A)  10 - x
(B)  9 - x
(C)  x + 3
(D)  x - 3
(E)  x - 9
Rationale: Original Digits=xy i.e. Number=10x+y
After reversing the digits:
Digits=yx i.e. Number=10y+x
10y+x is 27 less than 10x+y
10x+y-27=10y+x
10x-x-27=10y-y
9x-27=9y
x-3=y
OR
y=x-3
Ans:D
Answer: (D)  x - 3
Question: A polling company surveyed a certain country, and it found that 35% of that country’s registered voters had an unfavorable impression of both of that state’s major political parties and that 20% had a favorable impression only of Party Q. If one registered voter has a favorable impression of both parties for every two registered voters who have a favorable impression only of Party B, then what percentage of the country’s registered voters have a favorable impression of both parties (assuming that respondents to the poll were given a choice between favorable and unfavorable impressions only)?
(A) 15
(B) 20
(C) 30
(D) 35
(E) 45
Rationale: S=100
not( Q and B ) =35
only Q=20
(Q and B)/B=1/2
let ( Q and B ) =x
only B =2x
so now, 20+35+x+2x=100
x= 15
A ans
Answer: (A) 15
Question: 2 + 2^2 + 2^3 + ... + 2^8 = ?
(A) 510
(B) 310
(C) 210
(D) 410
(E) None of them
Rationale: Given series is a G.P. with a = 2, r = 2 and n = 8.
sum = a(r^n-1)/(r-1) = 2 x (2^8 –1)/(2-1)= (2 x 255) =510
Answer is A.
Answer: (A) 510
Question: A textile manufacturing firm employees 50 looms. It makes fabrics for a branded company. The aggregate sales value of the output of the 50 looms is Rs 5,00,000 and the monthly manufacturing expenses is Rs 1,50,000. Assume that each loom contributes equally to the sales and manufacturing expenses are evenly spread over the number of looms. Monthly establishment charges are Rs 75000. If one loom breaks down and remains idle for one month, the decrease in profit is:
(A) 13000
(B) 7000
(C) 10000
(D) 5000
(E) None of these
Rationale: Explanation :
Profit = 5,00,000−(1,50,000+75,000) =Rs. 2,75,000.
Since, such loom contributes equally to sales and manufacturing expenses.
But the monthly charges are fixed at Rs 75,000.
If one loan breaks down sales and expenses will decrease.
New profit :-
=>500000×(49/50)−150000×(49/50)−75000.
=>Rs 2,68,000.
Decrease in profit
=>2,75,000−2,68,000
=>Rs. 7,000.
Answer : B
Answer: (B) 7000
Question: A no. when divided by the sum of 555 and 445 gives 2times their difference as quotient & 70 as remainder. Find the no. is?
(A) 145646
(B) 236578
(C) 645353
(D) 456546
(E) 220070
Rationale: (555 + 445) * 2 * 110 + 70 = 220000 + 70 = 220070
E
Answer: (E) 220070
Question: For any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum of all the even integers between 99 and 151?
(A) 2050
(B) 2350
(C) 2650
(D) 2950
(E) 3250
Rationale: 100 + 102 + ... + 150 =
100*26 + (2+4+...+50) =
100*26 + 2*(1+2+...+25) =
100*26 + 2(25)(26)/2 =
100*26 + 25*26 = 125(26) = 3250
The answer is E.
Answer: (E) 3250
Question: A can do a job in 10 days and B can do it in 30 days. A and B working together will finish twice the amount of work in ------- days?
(A) 14 days
(B) 15 days
(C) 22 days
(D) 11 days
(E) 19 days
Rationale: B
1/10 + 1/30 = 2/15
15/2 *2 = 15 days
Answer: (B) 15 days