mathewhe/aqua_rat huggingface dataset:
Question: How many integers from 0 to 50 inclusive have a remainder of 3 when divided by 6?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: The numbers should be of the form 6c+3.
The minimum is 3 when c=0.
The maximum is 45 when c=7.
There are 8 such numbers.
The answer is D.
Answer: (D) 8
Question: If w is divisible by 15 and 9, w must be a multiple of which of the following?
(A) 12
(B) 18
(C) 25
(D) 36
(E) 45
Rationale: If w is divisible by 3*5 and 3*3, then w is divisible by 3*3*5 = 45.
The answer is E.
Answer: (E) 45
Question: A department of nine people - four men and five women - needs to send a team of five to a conference. If they want to make sure that there are no more than three members of the team from any one gender, how many distinct groups are possible to send?
(A) 100
(B) 120
(C) 150
(D) 180
(E) 200
Rationale: They can make a team of 3 men and 2 women.
The number of ways to do this is 4C3*5C2=4*10 = 40
They can make a team of 2 men and 3 women.
The number of ways to do this is 4C2*5C3=6*10 = 60
The total number of distinct groups is 100.
The answer is A.
Answer: (A) 100
Question: If m, n and r are positive integers greater than 1, and p and q are factors of r, which of the following must be the factor of r^(mn)?
I. m+n
II. n^m
III. m^2 * n^2
(A) I only
(B) II only
(C) III only
(D) I and II
(E) II and III
Rationale: given that m and n are factors of r.
so we can picture it this way r=m*n*n (n-some another factor of r)
so, r^mn= (m*n*n)^mn
I. m+n .since the question is MUST BE TRUE, we eleminate this option
II. (m*n*n)^mn / n^m= integer YES!
III.(m*n*n)^mn/ m^2 * n^2 YEs, since we are said that integer m>1 and integer n>1
Answer: (E) II and III
Question: A number when successively divided by 5, 3, 2 gives remainder 0, 2, 1 respectively in that order. What will be the remainder when the same number is divided successively by 2, 3, 5 in that order
(A) 22
(B) 87
(C) 26
(D) 25
(E) 08
Rationale: use this simple technique.[ (1 x 3) + 2] = 5
[(5 x 5) + 0] = 25
Answer:D
Answer: (D) 25
Question: How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length?
(A) 13.9 sec
(B) 12.1 sec
(C) 17.9 sec
(D) 61.9 sec
(E) 47.98 sec
Rationale: Speed = 72 * 5/18 = 20 m/sec
Total distance covered = 110 + 132 = 242 m.
Required time = 242/20 = 12.1 sec.
Answer:B
Answer: (B) 12.1 sec
Question: The cost price of 13 articles is equal to the selling price of 11 articles. Find the profit percent?
(A) 18 2/19%
(B) 18 2/11%
(C) 18 2/41%
(D) 18 4/11%
(E) 48 2/11%
Rationale: 13 CP = 11 SP
11 --- 2 CP
100 --- ? =>18 2/11%
Answer: B
Answer: (B) 18 2/11%
Question: If a hostal has eleven romos and two of those romos has view to the lake and others has view to the camp. What is the probability that you get a room with view to the lake?
(A) 2/8
(B) 2/11
(C) 1
(D) none
(E) 12
Rationale: the total number of rooms is 11
and the number of romos with view to the lake is 2
then, in one chance the probability to pick a room with view to the lake is
2/11
Answer B
Answer: (B) 2/11
Question: There were r red balls and y yellow balls in a bag. Three red balls and four yellow ones were added to the bag. What is the probability that a yellow ball and then a red ball will be selected if Jerry pulls out two balls at random, and puts the first ball back before pulling the second ball?
(A) (y+4)/(y+r+7)*(r+3)/(y+r+7)
(B) (y+3)/(y+r+7) + (r+4)/(y+r+6)
(C) (y+3)/(y+r+7)*(r+4)/(y+r+6)
(D) (y+3)/(y+r+7)*(r+3)/(y+r+7)
(E) (y+3)/(y+r+7) + (r+3)/(y+r+6)
Rationale: Currently we have r red and y yellow balls.
After adding new balls, we have
red = r + 3
Yellow = y + 4.
Total = r + y + 7
Now question says we are taking one ball first putting it back and then taking another ball. So, it means both the times, the number of ways of selecting one ball will be Total C 1 or (r+y+7)C1
So, Probability of selecting 1st as yellow and then 2nd as red = [(y+4)C1 / (r+y+7)C1] * [(r +3)C1 / (r+y+7)C1]
Answer : option A.
Answer: (A) (y+4)/(y+r+7)*(r+3)/(y+r+7)
Question: The area of a triangle is with base 4.5m and height 6m?
(A) 11 m2
(B) 10 m2
(C) 13.5 m2
(D) 19 m2
(E) 12.5 m2
Rationale: 1/2 * 4.5 * 6
= 13.5 m2
Answer: C
Answer: (C) 13.5 m2
Question: If y ¤ w = y^(2w) for all positive integers, then (3 ¤ 4) ¤ 2 =
(A) 3^8
(B) 3^12
(C) 3^16
(D) 3^24
(E) 3^32
Rationale: y ¤ w = y^(2w)
3 ¤ 4 = 3^(8)
(3 ¤ 4) ¤ 2 = (3^8) ¤ 2 = (3^8)^4 = 3^32
Correct Option: E
Answer: (E) 3^32
Question: Anthony and Michael sit on the six member board of directors for company X. If the board is to be split up into 2 three-person subcommittees, what percent R of all the possible subcommittees that include Michael also include Anthony?
(A)  20%
(B)  30%
(C)  40%
(D)  50%
(E)  60%
Rationale: The answer is C. Let's look at a committee where Mike belongs (he's person # 1) on that committee. When we choose person #2, there is a 1/5 probability that it's going to be Anthony (then it doesn't matter who the third person is), and 4/5 probability that it's going to be someone else (then person #3 is going to be Anthony with probability 1/4). Total probability R= 1/5+4/5*1/4 = 2/5.C
Answer: (C)  40%
Question: What is the scope including 1/31+1/32+1/33+......+1/40?
(A) 1/6~1/5
(B) 1/5~1/4
(C) 1/4~1/3
(D) 1/3~1/2
(E) 1/2~1
Rationale: For Maximum value : It should be less than 1/31 + 1/31 +1/31... 10 times = 10/31 ~ 1/3
For Minimum Value : It should be greater than 1/40+ 1/40+ 1/40 .. 10 times = 10/40 = 1/4.
Thus, the answer should lie between 1/4 and 1/3. Correct ans : C.
Answer: (C) 1/4~1/3
Question: If x and y are positive integers, and 4x^2=3y, then which of the following must be a multiple of 8?
I. x^2
II. y^2
III. xy
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II and III
Rationale: 4x^2 = 3y
since x,y are positive integers, x^2 = x*x is divisible by 3 -> x is divisible by 3 and y is divisible by x^2
-> x^2 and y is divisible by 9 -> y^2 is divisible by 9
(1),(2), and (3) must be true
Answer is C
Answer: (C) III only
Question: Bert and Rebecca were looking at the price of a condominium. The price of the condominium was 110% more than Bert had in savings, and separately, the same price was also 20% more than Rebecca had in savings. What is the ratio of what Bert has in savings to what Rebecca has in savings.
(A) 1:5
(B) 1:4
(C) 2:3
(D) 4:7
(E) 1:2
Rationale: Suppose bert had 100 so price becomes 210 , this 210 = 1.2 times R's saving .. so R's saving becomes 175
So required ratio is 100:175=4:7
ANSWER:D
Answer: (D) 4:7
Question: If '×' means '+', '+' means '÷', '–' means '×' and '÷' means '–', then 6 × 4 – 5 + 2 ÷ 1 = ?
(A) 11
(B) 14
(C) 15
(D) 17
(E) 18
Rationale: C
6 + 4 × 5 ÷ 2 – 1
= 6 + 4 × 5/2 – 1
= 15
Answer: (C) 15
Question: In how many years does a sum of Rs. 5000 yield a simple interest of Rs. 16500 at 15% p.a.?
(A) 22 years
(B) 17 years
(C) 97 years
(D) 16 years
(E) 14 years
Rationale: T = (100 * 16500)/(15 * 5000)
= 22 years
Answer: A
Answer: (A) 22 years
Question: On the independence day, bananas were be equally distributed among the children in a school so that each child would get two bananas. On the particular day 160 children were absent and as a result each child got two extra bananas. Find the actual number of children in the school?
(A) 600
(B) 320
(C) 500
(D) 520
(E) 720
Rationale: Let the number of children in the school be x. Since each child gets 2 bananas, total number of bananas = 2x.
2x/(x - 160) = 2 + 2(extra)
=> 2x - 320 = x => x = 320.
ANSWER:B
Answer: (B) 320
Question: Find the least number which when divided by 38 and 3 leaves a remainder of 1 in each case.
(A) 107
(B) 109
(C) 111
(D) 113
(E) 115
Rationale: The least number which when divided by different divisors leaving the same remainder in each case
= LCM(different divisors) + remainder left in each case.
Hence the required least number
= LCM(38, 3) + 1 = 115.
ANSWER:E
Answer: (E) 115
Question: On a sum of money, the S.I. for 2 years is $600, while the C.I. is $630, the rate of interest being the same in both the cases. The rate of interest is?
(A) 8%
(B) 10%
(C) 12%
(D) 14%
(E) 16%
Rationale: Difference in C.I. and S.I for 2 years = $630 - $600 = $30
S.I for one year = $300
S.I. on $300 for 1 year = $30
Rate = (100 * 30)/(300) = 10%
The answer is B.
Answer: (B) 10%
Question: Which of the following options must be positive, given 2 negative integers e and f?
(A) ef
(B) e/f
(C) (e + f)^3
(D) B and C
(E) A and B above
Rationale: A.ef
-ve*-ve= +ve
will be positive
B. e/f
-ve/-ve=+ve
will be positive
C. (e + f)^3=-ve
D. (e + f)^5
= -ve
E. A and B option are positive so both are correct
Answer E
Answer: (E) A and B above
Question: kamal finish a work in 15 days.vimal is 50% more efficient than kamal.then how much time vimal take to finish the work?
(A) 10 days
(B) 21/2 days
(C) 12 days
(D) 14 days
(E) 11 days
Rationale: work of kamal in 1 days=1/15
work of vimal in 1 days=1/15*150%=[1/15*150/100]=1/10
hence,vimal take 10 days to finish the work
answer A
Answer: (A) 10 days
Question: When Rahul was born, his father was 35 years older than his brother and his mother was 27 years older than his sister. If Rahul's brother is 6 years older than him and his mother is 3 years younger than his father, how old was Rahul's sister when he was born ?
(A) 10 years
(B) 11 years
(C) 9 years
(D) 8 years
(E) 7 years
Rationale: When Rahul was born, his brother's age = 6 years; his father's age = (6 + 35) years = 41 years,
his mother's age = (41 - 3) years = 38 years;
his sister's age = (38 - 27) years = 11 years.
Answer: Option B
Answer: (B) 11 years
Question: A certain protective additive increases from 45 days to 60 days the time between required maintenance checks on an industrial vehicle. By what percent is the time between maintenance checks increased by using the additive?
(A) 25%
(B) 33 1/3%
(C) 50%
(D) 66 2/3%
(E) 75%
Rationale: General formula for percent increase or decrease, (percent change):
percent=Change/Original∗100
So, the time between maintenance checks increased by 60−45/45∗100=33 1/3
Answer: B.
Answer: (B) 33 1/3%
Question: Robert spent $55 in buying raw materials, $125 in buying machinery and 10% of the total amount he had as cash with him. What was the total amount?
(A) A)$150
(B) B)$210
(C) C)$250
(D) D)$160
(E) E)$200
Rationale: Let the total amount be x
then, (100-10)% of x = 55+125
90% of x = 180
90x/100 = 180
x = $200
Answer is E
Answer: (E) E)$200
Question: If the wheel is 14 cm then the number of revolutions to cover a distance of 1056 cm is?
(A) 14
(B) 86
(C) 16
(D) 12
(E) 18
Rationale: 2 * 22/7 * 14 * x = 1056 => x
= 12
Answer:D
Answer: (D) 12
Question: The mean of 25 values was 190. It was detected on rechecking that one value 165 was wrongly copied as 130 for the computation of the mean. Find the correct mean.
(A) 151
(B) 149
(C) 152
(D) 191.4
(E) None of the above
Rationale: Corrected mean = 190×25−130+165/25
= 4750+35/25
=4785/25=191.4
Answer D
Answer: (D) 191.4
Question: A project manager needs to select a group of 3 people from a total of 3 men and 3 women. How many possible group combinations exist such that no group has all men or all women?
(A) 18
(B) 24
(C) 74
(D) 82
(E) 48
Rationale: Since the order in which the group is selected does not matter, we are dealing with a combinations problem (and not a permutations problem).
The formula for combinations is:
N!/((N-K)!K!)
Where N = the total number of elements from which we will select, 6 people in this case.
Where K = the total number of elements to select, 3 people in this case.
The total number of combinations is therefore:
6!/((6-3)!3!) = 20
However, two of these combinations are not valid since they have all members of one gender.
The correct answer is 20-2 = 18. Ans A
Answer: (A) 18
Question: A part-time employee whose hourly wage was increased by 20 percent decided to reduce the number of hours worked per week so that the employee's total weekly income would remain unchanged. By what percent should the number of hours worked be reduced?
(A) 11
(B) 15
(C) 16.66
(D) 17
(E) 18
Rationale: Let original hourly wage be x and let the no of hours worked be y
Total wage will be =x*y
After the increment the wage will be=1.2 x
Now we need to find number of hours worked so that
x*y=1.2x*z i.e z= 1/1.2 y
%decrease = (y-1/1.2y)/y *100=16.66
Thus my answer is C.
Answer: (C) 16.66
Question: If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same sum at the rate and for the same time?
(A) Rs. 51.25
(B) Rs. 51.22
(C) Rs. 51.219
(D) Rs. 51.18
(E) Rs. 51.11
Rationale: Explanation:
Sum = (50 * 100) / (2 * 5) = Rs. 500
Amount = [500 * (1 + 5/100)2] = Rs. 551.25
C.I. = (551.25 - 500) = Rs. 51.25.
Answer:A
Answer: (A) Rs. 51.25
Question: In a mixture of milk and water, the proportion of milk by weight was 80%. If, in a 180 gm mixture, 36 gms of pure milk is added, what would be the percentage of milk in the mixture formed?
(A) 80
(B) 83.33
(C) 85
(D) 90
(E) 42
Rationale: Percentage of milk in the mixture formed = [80/100 (180) + 36] / (180 + 36) * 100% = (144 + 36)/216 * 100% = 5/6 * 100% = 83.33%.
ANSWER B
Answer: (B) 83.33
Question: A, B and C have Rs.500 between them, A and C together have Rs.200 and B and C Rs.340. How much does C have?
(A) 50
(B) 40
(C) 267
(D) 29
(E) 27
Rationale: A+B+C = 500
A+C = 200
B+C = 340
--------------
A+B+2C = 540
A+B+C = 500
----------------
C = 40
Answer: B
Answer: (B) 40
Question: How many pieces of 85 cm length can be cut from a rod of 38.25 meters long?
(A) 25
(B) 35
(C) 45
(D) 55
(E) 65
Rationale: Number of pieces = 3825/85 = 45
The answer is C.
Answer: (C) 45
Question: A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
(A) 12
(B) 27
(C) 36
(D) 28
(E) 23
Rationale: Speed of train relative to jogger = 45 - 9 = 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Distance to be covered = 240 + 120 = 360 m.
Time taken = 360/10
= 36 sec.
Answer: C
Answer: (C) 36
Question: What is 3 2/3 - 2 1/4 divided by 6/7 - 2/5 ?
(A) 17/36
(B) 36/17
(C) 17/64
(D) 15/4
(E) 14/4
Rationale: 3 2/3 - 2 1/4 = 11/3 - 9/4 = (44 - 27)/12 = 17/12
6/7 - 2/5 = (30-14)/35 = 16/35
So 17/12/16/3 = 17/12 * 3/16 = 17/64
Answer - C
Answer: (C) 17/64
Question: A discount cloth store normally sells all merchandise at a discount of 10 percent to 25 percent off the suggested retail price. If, during a special sale, an additional 30 percent were to be deducted from the discount price, what would be the lowest possible price of an item costing $1000 before any discount?
(A) $180.00
(B) $545.60
(C) $750.00
(D) $525.00
(E) $1000.00
Rationale: Original price : 1000 $
Max first discount = -25%
Thus : 1000âˆ—(1âˆ’25/100)=750
Second discount on the discounted price = -30%
Thus : 750âˆ—(1âˆ’30/100)=525
Answer D
Answer: (D) $525.00
Question: If f(x) = 6x − √x and g(x) = x^2, what is f(g(4))?
(A) -4
(B) 8
(C) 16
(D) 32
(E) 92
Rationale: g(x) = x²
g(4) = 4² = 16
So, f(g(4)) = f(16)
f(x) = 6x − √x
So, f(16) = 6(16) − √16
= 96 - 4
= 92
= E
Answer: (E) 92
Question: The population of a city increases at the rate of 4% p.a. but there is an additional annual increase of 1% in the population due to some job seekers. The percentage increase in the population after 2 years is?
(A) 10.29%
(B) 10.22%
(C) 10.25%
(D) 12.25%
(E) 11.25%
Rationale: 100
5 ---- I
5
0.25 --- II
-----------
10.25%
Answer:C
Answer: (C) 10.25%
Question: Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 36 kmph and 72 kmph. After how much time will the trains meet?
(A) 10/3 sec
(B) 20/7 sec
(C) 33/7 sec
(D) 21/7 sec
(E) 32/7 sec
Rationale: They are moving in opposite directions, relative speed is equal to the sum of their speeds.
Relative speed = (36 + 72)*5/18 = 6*5 = 30 mps.
The time required = d/s = 100/30 = 10/3 sec.
Answer : A
Answer: (A) 10/3 sec
Question: A feed store sells two varieties of birdseed: Brand A, which is 40% millet and 60% sunflower, and Brand B, which is 65% millet and 35% safflower. If a customer purchases a mix of the two types of birdseed that is 50% millet, what percent of the mix is Brand B?
(A) 40%
(B) 45%
(C) 50 %
(D) 60 %
(E) 55 %
Rationale: Yes there is a simple method :
Consider the following method
Brand A : 40% millet and 60% sunflower
Brand B : 65% millet and 35% safflower
Mix : 50% millet
Here the weighted average is 50%,
Now Brand A has 40% millet, which is 10% less than the weighted average of mix = - 0.10 A --------------- I
Similarly, Brand B has 65 % millet, which is 15 % more than the weighted average of mix = + 0.15 B ------------ II
Now, both Brand A and Brand B are combined to give a 50% mix containing millet, so equate I and II
implies, 0.10 A = 0.15 B
Therefore A/B = 0.15/0.10 = 3/2
A : B : (A + B) = 3 : 2 : (3+2) = 3 : 2 : 5
We have to find, percent of the mix is Brand B i.e. B : (A + B) = 2 : 5 = (2 / 5) * 100 = 40 %
Here is a pictorial representation :
Brand A= 40%------------------------10% or 0.10 below average, A times-----------------Total below = - 0.10 A
----------------------------------------------------------------------------------------Average = 50% or 0.50
Brand B = 65 %--------------------------15% or 0.15 above average, B times-----------------Total above = + 0.15 B
Since the amount below the average has to equal the average above the average; therefore,
0.10 A = 0.15 B
A/B = 3/2
A:B: Total = 3:2:5
Therefore
B/Total = 2:5 = 40 %
Answer: A
Answer: (A) 40%
Question: A bicycle wheel has a diameter of 0.51m. How many complete revolutions does it make in 1km?
(A) 246
(B) 448
(C) 1408
(D) 710
(E) 624
Rationale: 1 revolution = 3.14 * diameter.
Number of revolutions in 1km = 1000m / ( 3.14 * 0.51m ) = 624.5. Hence 624 complete revolutions.
Answer E
Answer: (E) 624
Question: If money is invested at r percent interest, compounded annually, the amount of investment will double in approximately 70/r years. If Pat's parents invested $ 5000 in a long term bond that pays 8 percent interest, compounded annually, what will be the approximate total amount of investment 18 years later, when Pat is ready for college?
(A) $20000
(B) $15000
(C) $12000
(D) $10000
(E) $9000
Rationale: Since investment doubles in 70/r years then for r=8 it'll double in 70/8=~9 years (we are not asked about the exact amount so such an approximation will do). Thus in 18 years investment will double twice and become ($5,000*2)*2=$20,000 (after 9 years investment will become $5,000*2=$10,000 and in another 9 years it'll become $10,000*2=$20,000).
Answer: A.
Answer: (A) $20000
Question: Find large number from below question The difference of two numbers is 1500. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder
(A) 1234
(B) 1345
(C) 1456
(D) 1797
(E) 1635
Rationale: Let the smaller number be x. Then larger number = (x + 1500).
x + 1500 = 6x + 15
5x = 1485
x = 297
Large number = 297+1500 = 1797
D
Answer: (D) 1797
Question: Meera purchased two three items from a shop. Total price for three items is Rs.3200/- She have given Rs. 6000/- What is the balance amount meera got?
(A) 650
(B) 1400
(C) 1350
(D) 8200
(E) 2800
Rationale: Total cost of Items : 3200/-
amount Paid : 6000/-
Balance receivable : 6000 - 3200 = 2800/-
Answer is E
Answer: (E) 2800
Question: Randy'sbar serves customers every weeknight from 3 pm to 1 am. In Randy's bar,Silvermoonbeer is sold at a constant rate except during happy hour, from 6:30 to 7:30 pm, when the rate triples.
If a keg of Silvermoon beer is half empty at 5pm on Monday, and two-thirds empty at the beginning of the happy hour, when will it be completely empty?
(A) Monday, 7:30 pm
(B) Monday, 9 pm
(C) Monday, 7 pm
(D) Monday, 6:45 pm
(E) Monday, 9:30 pm
Rationale: Let the keg be a 150 Litre keg
At 5 pm.. There are 75 litres
At 6:30 pm there are 50 litres.
So, consumption rate is 25 litres per 1.5 hours.
So it will take 3 hours to finish 50 litres at this rate.
During happy hour it sells 3 times faster. So, rate = 1 hour per 50 litres.
So, keg becomes empty at 6:30 + 1 hour = 9:30 pm
Answer is E.
Answer: (E) Monday, 9:30 pm
Question: If the simple interest on a sum of money at seventeen percent per annum for two years is Rs.10500, compound interest on the same sum for the same period at the same rate of interest is
(A) 10,396.50
(B) 11,392.50
(C) 10,500.50
(D) 10,892.50
(E) 10,500.00
Rationale: S I for 2 years = 10500 ie for one year =5250
The compound interest for Rs.5250 for the second year = 5250*17/100 = 892.50
The CI for two years 10500+892.50 = 11,392.50
ANSWER:B
Answer: (B) 11,392.50
Question: An article is bought for Rs.600 and sold for Rs.400, find the loss percent?
(A) 33 1/4%
(B) 33 4/3%
(C) 33 2/3%
(D) 33 1/3%
(E) 33 8/3%
Rationale: 600 ---- 200
100 ---- ? => 33 1/3%
Answer: D
Answer: (D) 33 1/3%
Question: In 2005, 25 percent of the math department’s 40 students were female, and in 2007, 40 percent of the math department’s 65 students were female. What was the percent increase from 2005 to 2007 in the number of female students in the department?
(A) 15%
(B) 50%
(C) 62.5%
(D) 115%
(E) 160%
Rationale: in 2005 25% of 40= 10 students were female
in 2007 40% of 65 = 26 were female
% increase= (26-10)/10 *100= 160%
E is the answer
Answer: (E) 160%
Question: How many two element subsets of {5,6,7,8,9} are there that do not contain the elements 6,7 and 9?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Required subsets are = {5,8}= 1
Answer: A
Answer: (A) 1
Question: A monkey ascends a greased pole 14 metres high. He ascends 2 metres in first minute and slips down 1 metre in the alternate minute. In which minute, he reaches the top ?
(A) 25th
(B) 22nd
(C) 23rd
(D) 24th
(E) None of these
Rationale: In 2 minutes, he ascends = 1 metre
âˆ´ 12 metres, he ascends in 24 minutes.
âˆ´ He reaches the top in 25th minute.
Answer A
Answer: (A) 25th
Question: Cereal A is 10% sugar by weight, whereas healthier but less delicious Cereal B is 4% sugar by weight. To make a delicious and healthy mixture that is 5% sugar, what should be the ratio of Cereal A to Cereal B, by weight?
(A) 2:9
(B) 2:7
(C) 1:6
(D) 1:4
(E) 1:5
Rationale: Ratio of A / Ratio of B = (Average Wt of Mixture - Wt of B)/(Wt of A - Average Wt of Mixture)
=> Ratio of A / Ratio of B = (5 - 4)/(10 - 5) = 1/5
So they should be mixed in the ratio 1:5
Answer - E
Answer: (E) 1:5
Question: Working simultaneously at their respective constant rates, Machines A and B produce 800 nails in x hours. Working alone at its constant rate, Machine A produces 800 nails in r hours. In terms of x and r, how many hours does it take Machine B, working alone at its constant rate, to produce 800 nails?
(A) x/(x+y)
(B) y/(x+y)
(C) xy/(x+y)
(D) xy/(x-y)
(E) xr/(r-x)
Rationale: Pick some smart numbers for x and r.
Say x=1 hour and r=2 hours (notice that r must be greater than x, since the time for machine A to do the job, which is r hours, must be more than the time for machines A and B working together to do the same job, which is x hours).
In this case, the time needed for machine B to do the job must also be 2 hours: 1/2+1/2=1.
Now, plug x=1 and r=2 in the options to see which one yields 2. Only option E fits.
Answer: E.
Answer: (E) xr/(r-x)
Question: Find the sum The difference between the compound and S.I. on a certain sum of money for 4 years at 20% per annum is Rs.50 of money?
(A) 1000
(B) 6000
(C) 5000
(D) 8000
(E) 1900
Rationale: P = 50(100/20)4 => P = 1000
Answer: A
Answer: (A) 1000
Question: The average salary of workers in an industry is Rs.200 the average salary of technicians being Rs.400 and that of non-technicians being Rs.125. What is the total number of workers?
(A) 288
(B) 672
(C) 299
(D) 277
(E) 121
Rationale: 8 * 84 = 672 – 7 = 665.Answer: B
Answer: (B) 672
Question: The banker's gain on a sum due 6 years hence at 12% per annum is Rs. 828. What is the banker's discount?
(A) 1240
(B) 1120
(C) 1190
(D) 1978
(E) None of these
Rationale: Explanation :
TD = (BG ×100)/TR = (828×100)/(6×12) = Rs. 1150
BG = BD – TD
=> 828= BD - 1150
=> BD = 1978 Answer : Option D
Answer: (D) 1978