mathewhe/aqua_rat huggingface dataset:
Question: (8^16)+(16^13)+(4^23) = ?
(A) (4)*(2^29+1)
(B) (6)*(2^48)
(C) (9)*(2^49)
(D) (28)*(2^53)
(E) 2^148
Rationale: I think you are assuming that (X^Y) + (X^Z) is = (X^Y+Z) which is not true, as it only applies to multiplication. Rather it would have to be (X^Y)(X^Z) = (X^YZ)
So when you simplify down to 2^48 + 2^52 + 2^48 you cannot just add exponents.
Here's how my brain works with this one,
Step 1: Recognize a common base.
(8^16) + (16^13) + (4^24) = ((2^2)^16) + ((2^4)^13) + ((2^2)^24) = (2^48) + (2^52) + (2^48)
Step 2: Recognize the factor and pull out of the equation.
= (2^48)(1 + (2^4) + 1)
= (2^48)(1 + 16 + 1)
= (2^48)(18)
Step 3: Recognize this is not an answer and adapt.
(2^48)(18) = (2^48)(2)(9) = (6)*(2^48)
Answer is B.
Answer: (B) (6)*(2^48)
Question: What approximate value should come in place of question mark (?) in the following equation?
33 1⁄3% of 768.9 + 25% of 161.2 – 66.12 = ?
(A) 230
(B) 225
(C) 232
(D) 220
(E) 240
Rationale: ? = 33 1⁄3% of 768.9 + 25% of 161.2 – 66.12
= 1⁄3 of 768.9 + 1⁄4 of 161.2 – 66.12
= 256.3 + 40.3 – 66.12 ≈ 232
Answer C
Answer: (C) 232
Question: Find the greatest number that will divide 28, 128 and 147 leaving 10, 2 and 3 as remainders respectively
(A) 19
(B) 17
(C) 13
(D) 9
(E) 18
Rationale: Explanation:
Answer will be HCF of (28-10, 128-2, 147-3)
HCF of (18, 126, 144) = 18
Option E
Answer: (E) 18
Question: Machine A can process 6000 envelopes in 3 hours. Machines B and C working together but independently can process the same number of envelopes in 2.5 hours. If Machines A and C working together but independently process 3000 envelopes in 1 hour, then how many hours would it take Machine B to process 5600 envelopes.
(A) 2
(B) 3
(C) 4
(D) 6
(E) 60/7
Rationale: You can either take the amount of work done as the same as Karishma has done or take the work done by each in the same time. I will do the latter
1. Work done in 1 hr by A is 2000 envelopes
2. Work done in 1 hr by A and C is 3000 envelopes
3. So work done in 1 hr by C is 1000 envelopes
4. Work done in 1 hr by B and C is 2400 envelopes
5. So work done in 1 hr by B is 1400 envelopes
6. So to process 5600 envelopes B will take 5600/1400 hrs = 4 hrs
So the answer is choice C
Answer: (C) 4
Question: 8 / 4 / 2 = ?
(A) 0
(B) 2
(C) 5
(D) 4
(E) 1
Rationale: 8 / 4 / 2 = (8 / 4) / 2 = 2/2 = 1
Answer is E.
Answer: (E) 1
Question: When the no.7y86038 is exactly divisible by 11, then the smallest whole no.in place of y?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 6
Rationale: The given number =7y86038
Sum of the odd places =8+0+8+7=23
Sum of the even places = 3+6+y
(Sum of the odd places)- (Sum of even places) = Number (exactly divisible by 11)
23-(9+y) = divisible by 11
14 � y = divisible by 11.
Y must be 3, to make given number divisible by 11.
C
Answer: (C) 3
Question: If the price of gasoline increases by 25% and a driver intends to spend only 5% more on gasoline, by how much percent should the driver reduce the quantity of gasoline that he buys?
(A) 20%
(B) 16%
(C) 15%
(D) 12%
(E) 10%
Rationale: Let x be the amount of gasoline the driver buys originally.
Let y be the new amount of gasoline the driver should buy.
Let P be the original price per liter.
(1.25*P)y = 1.05(P*x)
y = (1.05/1.25)x = 0.84x which is a reduction of 16%.
The answer is B.
Answer: (B) 16%
Question: Find the average of first 75 natural numbers?
(A) 35
(B) 38
(C) 32
(D) 36
(E) 39
Rationale: Sum of first 100 natural numbers = 75*76/2 = 2850Required average = 2850/75 = 38Answer is B
Answer: (B) 38
Question: If the circus were to sell all of its 220 tickets for this month's performance at their usual price, the revenue from sales would be 10% greater than that collected last month. However, the circus raised the ticket price by 5% and sold only 200 tickets as a result. What percent less was last month's revenue than that of this month?
(A) 2
(B) 5
(C) 100/21
(D) 110/20
(E) 9/4
Rationale: 220p = 1.1RL (220 tickets at regular P price = 1.1 (or 10% more) than revenue last month (RL)
to find RL just multiply each side by 10/11 (1.1*10 = 11/11 = 1)
220(10/11)p = 1.1(10/11)R:
200p = RL (so the revenue last month was = to 200p)
Now what does our revenue look like at the new ticket price this month:
200(1.05)P = 210p
so...if the revenue this month will be 210p, what percentage less was last months revenue at 200p than that of this month?
(210p-200p)/210p = 10p/210p = 1/21
we're looking for percentage though, so multiply this by 100
1/21(100) = 100/21
Answer C
Answer: (C) 100/21
Question: Working together, printer A and printer B would finish the task in 20 minutes. Printer A alone would finish the task in 60 minutes. How many pages does the task contain if printer B prints 4 pages a minute more than printer A ?
(A) 120
(B) 180
(C) 240
(D) 280
(E) 340
Rationale: 20*A + 20*B = x pages
in 20 mins printer A will print = 20/60 * x pages = 1/3*x pages
thus in 20 mins printer printer B will print x - 1/3*x = 2/3*x pages
Also it is given that printer B prints 4 more pages per min that printer A. In 20 mins printer B will print 80 more pages than printer A
thus 2/3*x - 1/3*x = 80 => x = 240 pages
Answer: C
Answer: (C) 240
Question: The height of the wall is 6 times its width and length of the wall is 7 times its height .if the volume of the wall be 129024 cu.m.its width is
(A) 4m
(B) 5m
(C) 6m
(D) 7m
(E) 8m
Rationale: Explanation:
Let width = x
Then, height=6x and length=42x
42x Ã— 6x Ã— x = 129024
x = 8
Answer: E
Answer: (E) 8m
Question: The average age of the district level hockey team of eleven is 35 years.The average age gets increased by 1 year when the coach age is also included.what is the age of the coach ?
(A) 43 yrs.
(B) 44 yrs.
(C) 45 yrs.
(D) 47 yrs.
(E) 46 yrs.
Rationale: Explanation:
Total age of players in team = 35 x 11 = 385
When coach is included, total members = 12, Avg age increases by one becomes 23
Total age when coach is included = 36x12 = 432
Age of coach = 432-385 = 47 yrs.
Answer:D
Answer: (D) 47 yrs.
Question: P is four times as fast as Q and working together, they can complete a work in 20 days. In how many days can Q alone complete the work?
(A) 35 days
(B) 15 days
(C) 16 days
(D) 25 days
(E) 18 days
Rationale: P = 4Q
P + Q = 4Q + Q = 5Q
These 5Q people can do the work in 20 days, which means Q can do the work in 100 days.
Hence, P can do the work in 25 days.
ANSWER:D
Answer: (D) 25 days
Question: The number of bacteria in a petri dish increased by 50 percent every 2 hours. If there were 108 million bacteria in the dish at 4: 00 p.m., at what time were there 32 million bacteria in the dish?
(A) 6: 00 p.m.
(B) 8: 00 p.m.
(C) 10: 00 a.m.
(D) 8: 00 a.m.
(E) 11: 00 a.m.
Rationale: Given:
he number of bacteria in a petri dish increased by 50 percent every 2 hours
There were 108 million bacteria in the dish at 4: 00 p.m
Since the bacteria is increasing by 50% every 2 hours, this means that the number is multiplied by 1.5 every 2 hours.
Required: At what time were there 32 million bacteria in the dish?
Assume that there were n intervals of 2 hours between 32 million and 108 million.
32 * (1.5)^n = 108
(3/2)^n = 108/32 = 27/8 = (3/2)^3
Hence n = 3 intervals.
Each interval was of 2 hours. Therefore, the number of hours = 6
Subtracting 6 hours from 4 PM, we get 10 AM as the answer.
Option C
Answer: (C) 10: 00 a.m.
Question: 20% of a 6 litre solution and 60% of 4 litre solution are mixed. What percentage of the mixture of solution
(A) 36%
(B) 35%
(C) 34%
(D) 33%
(E) 32%
Rationale: 20% of 6 litre is (6*20/100)=1.2 litre
60% of 4 litre is (60*4/100)=2.4 litre
the mixture is 3.6 litre
so the percentage is(3.6*100/10)=36%
ANSWER:A
Answer: (A) 36%
Question: Suresh can complete a job in 15 hours. Ashutosh alone can complete the same job in 25 hours. Suresh works for 9 hours and then the remaining job is completed by Ashutosh. How many hours will it take Ashutosh to complete the remaining job alone?
(A) 4
(B) 5
(C) 6
(D) 10
(E) None of these
Rationale: The part of job that Suresh completes in 9 hours
= 9â„15 = 3â„5
Remaining job = 1 - 3â„5 = 2â„5
Remaining job can be done by Ashutosh in 2â„5 Ã— 25 = 10 hours
Answer D
Answer: (D) 10
Question: Which of the following lists the no. of points at which a circle can intersect a square ?
(A) 2 & 8 only
(B) 2, 4 & 8 only
(C) 2, 4, 6 & 8 only
(D) 1, 2, 3, 4, 6 & 8 only
(E) 1, 2, 3, 4, 5, 6, 7 & 8 only
Rationale: Soln:
Tangent intersects the circle at exactly one point ,All the points are possible.
1, 2, 3, 4, 5, 6, 7 & 8 only
ANSWER:E
Answer: (E) 1, 2, 3, 4, 5, 6, 7 & 8 only
Question: Out of 12 employs of a bank, one employ retires and his place, a new employ of age 24 years joins as a result average age of employs reduces by 4 years. The age of the retired employ is:
(A) 72
(B) 74
(C) 78
(D) 79
(E) 60
Rationale: 72
Option 'A'
Answer: (A) 72
Question: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
(A) 40 sec
(B) 42 sec
(C) 45 sec
(D) 48 sec
(E) 60 sec
Rationale: Formula for converting from km/hr to m/s: X km/hr =[ X *( 5/18) ]m/s.
Therefore, Speed =[ 45 x( 5/18) m/sec=( 25/2 )m/sec.
Total distance to be covered = (360 + 140) m = 500 m.
Formula for finding Time =( Distance/Speed )
Required time = [ (500 x 2)/25 ] sec = 40 sec.
Answer:A
Answer: (A) 40 sec
Question: A fort had provision of food for 150 men for 45 days. After 10 days, 25 men left the fort. Find out the number of days for which the remaining food will last.
(A) 44
(B) 42
(C) 40
(D) 38
(E) 36
Rationale: Explanation:
Given that fort had provision of food for 150 men for 45 days
Hence, after 10 days, the remaining food is sufficient for 150 men for 35 days
Remaining men after 10 days = 150 - 25 = 125
Assume that after 10 days, the remaining food is sufficient for 125 men for x days
More men, Less days (Indirect Proportion)
(men) 150 : 125 :: x : 35
⇒150×35=125x
⇒6×35=5x
⇒x=6×7=42
i.e., the remaining food is sufficient for 125 men for 42 days
Answer: Option B
Answer: (B) 42
Question: 20,180,9120,40880,501370 which number is wrong in series
(A) 20
(B) 9120
(C) 501370
(D) 180
(E) 40880
Rationale: 501370...........
all are multiples of 20 expect 501370
ANSWER:C
Answer: (C) 501370
Question: A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m3) is:
(A) 4830
(B) 5120
(C) 6420
(D) 7500
(E) 8960
Rationale: l = (48 - 16)m = 32 m,
b = (36 -16)m = 20 m,
h = 8 m.
Volume of the box = (32 x 20 x 8) m3 = 5120 m3.
Answer: Option B
Answer: (B) 5120
Question: Three people (1 couple and 1 single) are seated at random in a row of 6 chairs. What is the probability that the couple does not sit together?
(A) 2/3
(B) 4/5
(C) 2/7
(D) 3/5
(E) 5/12
Rationale: The total number of arrangements of 3 people is 6*5*4 = 120
Let's think of the couple as a single unit.
The number of arrangements when the couple sits together is 5*4*2 = 40.
Note that we multiply by 2 because the couple can switch places with each other.
The number of ways the couple won't sit together is 120 - 40 = 80
P(couple won't sit together) = 80/120 = 2/3
The answer is A.
Answer: (A) 2/3
Question: A leak in the bottom of a tank can empty the full tank in 8 hours. An inlet pipe fills water at the rate of 6 litres a minute. When the tank is full, the inlet is opened and due to the leak, the tank is empty in 12 hours. How many litres does the cistern hold?
(A) 7580
(B) 7960
(C) 8290
(D) 8640
(E) none
Rationale: Sol.
Work done by the inlet in 1 hour = (1/8 - 1/12) = 1/24.
Work done by the inlet in 1 hour = (1/24 x 1/60) = 1/1440.
∴ Volume of 1/1440 part = 6 litres.
∴ Volume of whole = (1440 x 6) litres = 8640 litres.
Answer D
Answer: (D) 8640
Question: Ratio of the earnings of A and B is 4:7. If the earnings of A increases by 50% and those of B decreased by 25%, the new ratio of their earnings becomes 8:7. What are A's earnings?
(A) 8:5
(B) 8:8
(C) 8:3
(D) 8:7
(E) 8:1
Rationale: Let the original earnings of A and B be Rs. 4x and Rs. 7x.
New earnings of A = 150% 0f Rs. 4x = (150/100 * 4x) = Rs. 6x
New earnings of B = 75% of Rs. 7x = (75/100 * 7x) = Rs. 21x/4
6x:21x/4 = 8:7
This does not give x. So, the given data is inadequate.
Answer:D
Answer: (D) 8:7
Question: A and B together invested Rs. 9,000 in a business. At the end of the year, out of total profit is Rs. 3,000 B's share was Rs. 1500. A's investment was
(A) s. 4,500
(B) s. 8,250
(C) s. 10,500
(D) s. 11,250
(E) s. 12,250
Rationale: A+B=9000
total profit=3000
3000-1500=1500
1500;1500=1:1
then 1*9000/2=4500
ANSWER:A
Answer: (A) s. 4,500
Question: The average salary of a person for the months of January, February, March and April is Rs.8000 and that for the months February, March, April and May is Rs.8500. If his salary for the month of May is Rs.6500, find his salary for the month of January?
(A) Rs.4500
(B) Rs.4557
(C) Rs.4509
(D) Rs.4526
(E) Rs.4513
Rationale: Sum of the salaries of the person for the months of January, February, March and April = 4 * 8000 = 32000 ----(1)
Sum of the salaries of the person for the months of February, March, April and May = 4 * 8500 = 34000 ----(2)
(2)-(1) i.e. May - Jan = 2000
Salary of May is Rs.6500
Salary of January = Rs.4500
Answer:A
Answer: (A) Rs.4500
Question: n^(n/2)=6 is true when n=6 in the same way what is the value of n if n^(n/2) =9?
(A) 16
(B) 14
(C) 18
(D) 6
(E) 9
Rationale: n^(n/2)=9Apply logN/2logn=log9nlogn=2log9=log9^2=log81Logn=log81Now apply antilogn=81/nNow n=9.ANSWER:E
Answer: (E) 9
Question: An inspector rejects 0.000008% of the meters as defective. How many will be examine to project ?
(A) 2000
(B) 2300
(C) 2700
(D) 25000000
(E) 250
Rationale: Let the number of meters to be examined be x.
Then, 0.000008% of x =2
[(8/1000000)*(1/100)*x] = 2
x = [(2*1000000*100)/8] = 25000000
Answer is D.
Answer: (D) 25000000
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are drawn what is the probability that one is yellow and two are red?
(A) P(E)=12/455
(B) 12/458
(C) 12/487
(D) 12/456
(E) 12/4512
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
When three marbles are drawn , the probability that one is yellow and two are red
= (2 * 4 * 3 * 3 * 2)/(1 * 2 * 15 * 14 * 13)
= 12/455
Answer:A
Answer: (A) P(E)=12/455
Question: The speed of light is approximately 93 * 10^4 miles per second. This approximate speed is how many miles per hour?
(A)  1,11 * 10^7
(B)  3,35 * 10^6
(C)  1,11 * 10^8
(D)  1,86 * 10^8
(E)  3,35 * 10^7
Rationale: The easiest way to answer this question is by POE, it does not require any calculation (answered in 30seconds). In one hour there are 3600 seconds, therefore speed in miles/hour will be.
(.93*10^4)*3600 = (.93*10^4)*(3.6*10^3) = some number*10^7...
The key is realizing that thesome numberhas to be bigger thatn .93(because .93*3.6), and the only answer that fits that is E.
Answer: (E)  3,35 * 10^7
Question: In a certain town, there are four times as many people who were born in the town’s state as there are people who were born in another state or country. The ratio of those residents born in the town’s state to the town’s total population is
(A) 1 to 4
(B) 1 to 3
(C) 1 to 2
(D) 3 to 4
(E) . 4 to 5
Rationale: Town state: 4 times the whole town or country
then ratio will be 4(times)/5 total(times)
So the answer is 4/5.
ANSWER:E
Answer: (E) . 4 to 5
Question: The average age of 8 men increases by 2 years when two women are included in place of two men of ages 20 and 24 years. Find the average age of the women?
(A) 29
(B) 78
(C) 30
(D) 28
(E) 12
Rationale: 20 + 24 + 8 * 2 = 60/2 = 30
Answer: C
Answer: (C) 30
Question: Set A = {1, 2, 3, 4, 5, 6, w}
Which of the following possible values for w would cause Set A to have the smallest standard deviation?
(A)  1
(B)  2.5
(C)  3
(D)  3.5
(E)  7
Rationale: I agree. The mean of the set w=1,2,3,4,5,6 is 3.5 . Now if we add one extra number to the set, in order for the standard deviation to be minimum, that number must be as close as possible to the original set (1,2,3,4,5,6). Therefore we have to choose the number closest to 3,5 from the options we have, leaving D as the best choice.
Answer D.
Answer: (D)  3.5
Question: In how many ways can the letters of the word REPEAT be arranged?
(A) 2580
(B) 360
(C) 2000
(D) 2520
(E) 3420
Rationale: REPEAT has 6 words, but E is repeated two times. Thus ways = 6! / 2! = 360ways
B
Answer: (B) 360
Question: If 3 : 7 :: x : 21, then find the value of x
(A) 7
(B) 8
(C) 11
(D) 6
(E) 9
Rationale: Explanation:Treat 3:7 as 3/7 and x:21 as x/21, treat :: as = So we get 3/7 = x/21=> 7x = 63=> x = 9 Option E
Answer: (E) 9
Question: A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length?
(A) 11 seconds
(B) 38 seconds
(C) 40 seconds
(D) 88 seconds
(E) 19 seconds
Rationale: Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
= 500 * (2/25) = 40 seconds
Answer: C
Answer: (C) 40 seconds
Question: A 2-year certificate of deposit is purchased for A dollars. If the certificate earns interest at a n annual rate of 6 percent compound quarterly, which of the following represents the value, in dollars, of the certificate at the end of 2 years?
(A) A(1.06)^2
(B) A(1.06)^8
(C) A(1.015)^2
(D) A(1.015)^8
(E) k(1.03)^4
Rationale: Annual Rate of interest= 6%
Quaterly rate of interest= 6/4% = 1.5%
Now, periods of compounding in 2 years= 8 (8 quarters)
Thus A(1.015)^8
Answer: D
Answer: (D) A(1.015)^8
Question: At a meeting of the 8 Joint Chiefs of Staff, the Chief of Naval Operations does not want to sit next to the Chief of the National Guard Bureau. How many ways can the 8 Chiefs of Staff be seated around a circular table?
(A) 120
(B) 480
(C) 960
(D) 2520
(E) 5080
Rationale: Bunuel, I'm also a little confused with the number of arrangements of n distinct objects in a circle. Why is it given by (n-1)!. In theveritasanswer they say:answer E (5080), should be the number of ways to arrange all 7 without the seating restriction given. Is this incorrect?E
Answer: (E) 5080
Question: The amount of principal Rs.8000 at compound interest at the ratio of 5% p.a. for 6 years is
(A) s.9621
(B) s.6921
(C) s.10721
(D) s.6261
(E) s.6361
Rationale: c.i=p(1+r/100)^n
=8000(1+5/100)^6
=Rs10721
ANSWER:C
Answer: (C) s.10721
Question: A customer went to a shop and paid a total of $40, out of which 90 cents was for sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
(A) $22.70
(B) $23.20
(C) $24.10
(D) $25.50
(E) $26.90
Rationale: The total cost was $40.
The tax was $0.90
Let the original price of the taxable items = x
Given that tax rate = 6%
0.06x = 0.90
x = $15
The cost of the tax free items was $40 - $15 - $0.90 = $24.10
The answer is C.
Answer: (C) $24.10
Question: A cricketer has certain average for 10 innings. In the 11 inning he scored 108 runs, there by increasing his average by 6 runs. His new average is
(A) 30
(B) 50
(C) 42
(D) 62
(E) 80
Rationale: Let the average for 10 innings be x
Then, (10x+108)/11 = x+6
x = 42
Answer is C
Answer: (C) 42
Question: If n + 10 is a positive odd integer, which of the following must be true about the sum of the next four integers?
(A) It is a multiple of 3
(B) It is a multiple of 4
(C) It is a prime number
(D) It is a multiple of 5
(E) It is a multiple of 2
Rationale: n+10 is a positive odd integer. This means n will be an odd integer
The next 4 integers would be: n + 10, n + 11, n + 12, n + 13
Sum = 4n + 46
This sum will always be even.
Option E
Answer: (E) It is a multiple of 2
Question: Last week Vartan spent 20 percent of his wages on recreation. This week, his wages are 20 percent less than last weekʼs wages and he spent 40 percent of his wages on recreation. The amount he spends on recreation this week is what percent of the amount he spent on recreation last week?
(A) 150%
(B) 170%
(C) 175%
(D) 160%
(E) 180%
Rationale: Say Vartan's wages last week were $100, so he spent 0.20*100=$20 on recreation;
This week's wages is 0.8*100=$80, so he spends 0.4*80=$32 on recreation;
32/20=1.6, hence the amount he spends on recreation this week is 160% of the amount he spent on recreation last week: 20*1.6=32
Answer: D
Answer: (D) 160%
Question: A van takes 5 hours to cover a distance of 465 km. What speed in kph should the van maintain to cover the same distance in 3/2 of the previous time?
(A) 56
(B) 58
(C) 60
(D) 62
(E) 64
Rationale: (3/2)*5 = 7.5 hours
465 / 7.5 = 62 kph
The answer is D.
Answer: (D) 62
Question: The apartment on King-Williams street is an asset that its value is tramping about. From the year 1973 to 1983 it's value decreased by 16% and from 1983 to 1993 it's value increased by 16%. What is the value of the asset in 1993 if in 1973 it was worth $45,000?
(A) $43,848.
(B) $40,000.
(C) $38,976.
(D) $39,679.
(E) $36,796.
Rationale: 45,000 *1.16*.84= 43,848
Answer A
Answer: (A) $43,848.
Question: The first doughnut is priced at $1 and then if you purchase additional doughnuts as dozens then the price is $6/dozen. What is the total number of doughnuts purchased if you paid $20?
(A) 30
(B) 32
(C) 34
(D) 36
(E) 38
Rationale: $20 = 3 * $6 + $2
The number of doughnuts is 3*12 + 2 = 38
The answer is E.
Answer: (E) 38
Question: P, Q and R have Rs.5000 among themselves. R has two-thirds of the total amount with P and Q. Find the amount with R?
(A) Rs.3000
(B) Rs.3600
(C) Rs.2000
(D) Rs.4000
(E) None of these
Rationale: Let the amount with R be Rs.r
r = 2/3 (total amount with P and Q)
r = 2/3(5000 - r) => 3r = 10000 - 2r
=> 5r = 10000 => r = 2000.
ANSWER:C
Answer: (C) Rs.2000
Question: If 4w^4 − 41w^2 + 100 = 0, then what is the sum of the two greatest possible values of w ?
(A) 4
(B) 9/2
(C) 7
(D) 41/4
(E) 25
Rationale: just forget about the value of w^4 for the moment and let w^2= X. (its better to work with power of 2 than 4)
now we have equation as 4x^2 -41x +100 =0, factoring them gives us 4X^2 -16x -25x +100 =0. which can be solved as (4x-25)(x-4) , so x= 4 and 25/4.
so w^2 = 4 and 25/4
so w= +2 and minus 2 and +5/2 and minus 5/2
The two greatest values are +2 and +5/2. so their sum 2+5/2 =9/2 = B
Answer: (B) 9/2
Question: 15 men can complete a piece of work in 30 days. In how many days can 10 men complete that piece of work?
(A) 45
(B) 50
(C) 34
(D) 27
(E) 11
Rationale: 15 * 30 = 10 * x => x = 45 days
Answer:A
Answer: (A) 45
Question: If A,B,C are three integers and AB+C is even ; which of the following must be true?
A)C is even
B)B is even
C)AB is even
(A) I only
(B) II only
(C) III only
(D) II,III only
(E) None of the above
Rationale: If AB is Odd then C will not even. O+E = O
If B is even AB is even always. But If C is Odd E+O = O
None of the above are true
Answer: (E) None of the above
Question: If the price of petrol increases by 25% and Benson intends to spend only an additional 15% on petrol, by how much % will he reduce the quantity of petrol purchased?
(A) 8%
(B) 7%
(C) 10%
(D) 6%
(E) 9%
Rationale: Explanation:
Assume that the initial price of 1 Litre petrol = Rs.100 ,Benson spends Rs.100 for petrol,
such that Benson buys 1 litre of petrol
After the increase by 25%, price of 1 Litre petrol = 100 × (100+25)/100 = Rs.125
Since Benson spends additional 15% on petrol,
amount spent by Benson = 100× (100+15)/100 = Rs.115
Hence Quantity of petrol that he can purchase = 115/125 Litre
Quantity of petrol reduced = (1−115/125) Litre
Percentage Quantity of reduction = (1−115125)/1 × 100 = 10/125 × 100 = 105 × 4 = 2 × 4 = 8%
Answer: Option A
Answer: (A) 8%
Question: The L.C.M of two numbers is 2310 and their H.C.F is 30. If one number is 770 the Other is
(A) 330
(B) 90
(C) 270
(D) 250
(E) 350
Rationale: The other number
= L.C.M * H.C.F/given number
= 2310*30/770= 90
Answer is B.
Answer: (B) 90
Question: The cost price of a radio is Rs.1500 and it was sold for Rs.1110, find the loss %?
(A) 18
(B) 16
(C) 26
(D) 17
(E) 11
Rationale: Explanation:
1500 ---- 390
100 ---- ? => 26%
Answer:C
Answer: (C) 26