mathewhe/aqua_rat huggingface dataset:
Question: If candy bars that regularly sell for $0.40 each are on sale at two for $0.75, what is the percent reduction in the price of two such candy bars purchased at the sale price?
(A) 2 1/2 %
(B) 6 1/4 %
(C) 6 2/3 %
(D) 8%
(E) 12 %
Rationale: Regular price is $0.80, sales price is $0.75.
So, 80-(80 * x%)=75
5 = 80*x%
x% = 5/80 = 1/16 = 6.25%
ANSWER:B
Answer: (B) 6 1/4 %
Question: What is the units digit of the expression 14^7−18^4?
(A) 0
(B) 3
(C) 4
(D) 6
(E) 8
Rationale: Units digit of 14^7−18^4:
Consider the following unit digits:
4^1: 4
4^2: 6
4^3: 4
4^4: 6
⇒ unit digit of 4^7 is: 4
The unit digit of 14^7 will also be 4
Also:
8^1: 8
8^2: 4
8^3: 2
8^4: 6
⇒ unit digit of 8^4 is: 6
The unit digit of 18^4 will also be 6
Finally, 4-6 (or 14-6) = 8
Answer: E)
Answer: (E) 8
Question: The ages of two persons differ by 16 years. If 6 years ago, the elder one be 3 times as old as the younger one, find their present ages.
(A) 14 years
(B) 17 years
(C) 24 years
(D) 29 years
(E) None
Rationale: Solution
Let the age of the younger person be x years.
Then, age of the elder person	= (x + 16) years.
Therefore	‹=› 3 (x - 6) =(x + 16 - 6)
‹=› 3x-18 = x+10
‹=› 2x = 28
x= 14 years.
Answer A
Answer: (A) 14 years
Question: The present ages of three persons in proportions 2 : 2 : 6. Eight years ago, the sum of their ages was 56. Find their present ages (in years).
(A) 8, 20, 28
(B) 16, 16,48
(C) 20, 35, 45
(D) 18, 24, 32
(E) None of these
Rationale: Explanation:
Let their present ages be 2x, 2x and 6x years respectively.
Then, (2x - 8) + (2x - 8) + (6x - 8) = 56
10x = 80
x = 8
Their present ages are 2x = 16 years,2x = 16 years and 6x = 48 years respectively.
Answer: B
Answer: (B) 16, 16,48
Question: Find the sum of first 100 odd numbers
(A) 5500
(B) 2005
(C) 10000
(D) 5800
(E) 4960
Rationale: Explanation:
n2 = 1002 = 10000
Answer: Option C
Answer: (C) 10000
Question: A can do a piece of work in 5 days, and B can do it in 6 days. How long will they take if both work together?
(A) 2 8/11
(B) 2 8/198
(C) 2 8/7
(D) 2 8/18
(E) 2 8/112
Rationale: Sol. A’s 1 day’s work =
1
th
5
part of whole work and
B’s 1 day’s work =
1
th
6
part of whole work
? (A + B)’s one day’s work =
1 1 11 5 6 30 th part of whole work. So, both together will finish the work in 30 days 2 8/ 11 days.
Answer:A
Answer: (A) 2 8/11
Question: Jack and Jill are marathon runners. Jack can finish a marathon (42 km) in 5.5 hours and Jill can run a marathon in 4.2 hours.What is the ratio of their average running speed? (Jack: Jill)
(A) 14/15
(B) 15/14
(C) 4/5
(D) 42/55
(E) Cannot be determined
Rationale: Average Speed of Jack =Distance/ Time
= 42 /(11/2) = 84/11
Average Speed of Jill = 42/(4.2) = 10
Ratio of Average speed of Jack to Jill = (84/11)/10 = 84/110 = 42/55
Answer D
Answer: (D) 42/55
Question: By looking at a rectangular box, a carpenter estimates that the length of the box is between 2 to 2.1 meters, inclusive, the breadth is between 1 to 1.1 meters, inclusive and the height is between 2 to 2.1 centimeters, inclusive. If the actual length, breadth and height of the box do indeed fall within the respective ranges estimated by the carpenter, which of the following is the closest to the maximum possible magnitude of the percentage error Q that the carpenter can make in calculating the volume of the rectangular box?
(A) 1%
(B) 3%
(C) 10%
(D) 18%
(E) 22%
Rationale: the dimensions are between 2-2.1, 1-1.1 and 2-2.1..
so MAX error in Volume=?..
IMPORTANT POINTS TO NOTE
1) Max ERROR would be when actuals and estimate are at the extreme ends..
2) BUT what about MAX % ERROR--
It will be when the base is the lowest...
so the ACTUALS should be lowest or at lower end and the ESTIMATE at the higher end..
SOLUTION
Actuals= 2*2*1=4..
Estimate=2.1*2.1*1.1=4.841..
Max % error Q=(4.841-4)/4 *100= 84.1/4 = 21.25%..
21.25% is closest to 22% in the choices..
ans E
Answer: (E) 22%
Question: A sales representative receives a salary of $150 per week and earns a commission of 15% on all sales she makes. How many dollars’ worth of sales does she need to make in order to bring her total weekly income to $750?
(A) $3,000
(B) $3,150
(C) $4,000
(D) $4,150
(E) $5,000
Rationale: We're told that a sales representative receives a salary of $150 per week and earns a commission of 15% on all sales she makes. We're asked how many dollars’ worth of sales will bring her total weekly income to $750.
Since the salesperson receives a $150 salary, the remaining $600 has to be accounted for by the 15% commission. Since those numbers are rather specific, we're likely dealing with a 'round number' for total sales.
Let's TEST Answer C: $4,000
Since 15% of $1,000 = $150
15% of $4,000 = 4($150) = $600
this is an exact MATCH for what we were told, so this MUST be the answer.
Final Answer:
C
Answer: (C) $4,000
Question: Y and Z start a business with Rs.8000 and Rs.12000 respectively. Hoe should they share their profits at the end of one year?
(A) 1:2
(B) 2:1
(C) 3:1
(D) 2:5
(E) 2:3
Rationale: Explanation:
They should share the profits in the ratio of their investments.
The ratio of the investments made by Y and Z =
8000 : 12000 => 2:3
Answer:E
Answer: (E) 2:3
Question: Zinc and copper are melted together in the ratio 9 : 11. What is the weight of melted mixture, if 31.5 kg of zinc has been consumed in it?
(A) 58 kg
(B) 60 kg
(C) 64 kg
(D) 70 kg
(E) None
Rationale: Sol.
For 9 kg Zinc, mixture melted = (9+11) kg.
For 31.5 kg Zinc, mixture, melted = [20/9 x 31.5] kg
= 70 kg.
Answer D
Answer: (D) 70 kg
Question: In how many ways Chief Minister and Minister be elected from a team of 16 members?
(A) 240
(B) 210
(C) 220
(D) 200
(E) 180
Rationale: To do this, if captain is elected first, then we have 16 ways of doing this.
For election of vice-captain, we have only 15 ways left, coz 1 way is already consumed. (Situations like this is called dependent situation. One selection depends upon other selection.)
So, the ans is 16*15 = 240 ways.
A
Answer: (A) 240
Question: Using all the letters of the word "SOME", how many words can be formed, which begin with S and end with E?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: There are four letters in the given word.
Consider 4 blanks ....
The first blank and last blank must be filled with S and E all the remaining two blanks can be filled with the remaining 2 letters in 2! ways.
The number of words = 2! = 2.
ANSWER:A
Answer: (A) 2
Question: In 140 m race, A covers the distance in 36 seconds and B in 45 seconds. In this race A beats B by:
(A) 20 m
(B) 28 m
(C) 22.5 m
(D) 9 m
(E) 12 m
Rationale: Distance covered by B in 9 sec. =	140/45 x 9	m = 28 m.
A beats B by 28 metres.
Answer: Option B
Answer: (B) 28 m
Question: If the money was put in for the same duration of time by A,B and C, three business partners and four times A’s capital is equal to 6 times B’s capital is equal to 10 times C’s capital. Determine that out of a total profit of Rs 4650 what is C’s share?
(A) Rs 2250
(B) Rs 1550
(C) Rs 450
(D) Rs 900
(E) None of these
Rationale: Explanation:
It is given that business partnership is independent of time in this case as all the investors have invested their money for same amount of time.
Let A’s capital be x, B’s capital be y and C’s capital be z.
=>x+y+z = 4650
=> 4x = 6y = 10z
=>C’s share is z so let us solve the question w.r.t. z
=>x = 5z/2
=>y = 5z/3
=>(5z/2)+(5z/3)+(z) = 4650
=>31z = 4650*6
=>z = 900
ANSWER D
Answer: (D) Rs 900
Question: If the quantity (p + 5) is 5 times the quantity (q + 5), then what is the relationship between p and q?
(A) p = 5q + 30
(B) p = 5q − 30
(C) 5p = 5q + 20
(D) p = 5q
(E) p = 5q − 20
Rationale: p+5=5(q+5)
p+5=5q+25
p=5q+20
option C
Answer: (C) 5p = 5q + 20
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 Rs.1400 left with him,find his expenditure on food and conveyance.
(A) 1000
(B) 2000
(C) 3000
(D) 4000
(E) 5000
Rationale: Part of salary left=1-(2/5+3/10+1/8)
Let the monthly salary be Rs.x
Then, 7/40 of x=1400
X=(1400*40/7)
=8600
Expenditure on food=Rs.(3/10*800)=Rs.2400
Expenditure on conveyence=Rs.(1/8*8000)=Rs.1000
Answer is A.
Answer: (A) 1000
Question: At a conference table, 8 employees gather around a table. One of the employees is the manager and he sits at the head of the table. Two of the employees sit on either side of the table. How many different seating arrangements can be made with these 8 employees?
(A) 5060
(B) 5050
(C) 5060
(D) 5040
(E) 5030
Rationale: Head's sit is fixed. Now 7 people is left with 7 seats.
7 people can sit on 7 seats in 7! ways or 5040 ways.
Ans is D
Answer: (D) 5040
Question: A circular mat with diameter 7 inches is placed on a square tabletop, each of whose sides is 8 inches long. Which of the following is closest to the fraction of the tabletop covered by the mat?
(A) 6/7
(B) 4/9
(C) 5/2
(D) 5/3
(E) 1/7
Rationale: SO we are looking for the area of the cloth over the area of the table
Area of the Cloth = (pi)(r)^2 which is about (22/7)(7)(7)
Area of the Table = (8)(8)
So the quick way to estimate is looking at the fraction like this:154/64 nearest to 5/2
Answer: C
Answer: (C) 5/2
Question: The value of x + x(xx) when x = 5 is:
(A) 130
(B) 10
(C) 12
(D) 14
(E) 16
Rationale: x + x(xx)
Put the value of x = 5 in the above expression we get,
= 5 + 5(5 Ã— 5)
= 5 + 125
= 130
ANSWER : A
Answer: (A) 130
Question: In what time will Rs.4000 lent at 3% per annum on simple interest earn as much interest as Rs.5000 will earn in 5 years at 4% per annum on simple interest?
(A) 8 1/3
(B) 8 1/5
(C) 8 1/6
(D) 8 1/2
(E) 8 1/7
Rationale: (4000*3*R)/100 = (5000*5*4)/100
R = 8 1/3.Answer: A
Answer: (A) 8 1/3
Question: Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 sec. What is the length of the fast train?
(A) 25
(B) 24
(C) 26
(D) 27 7/9
(E) 28
Rationale: Relative speed = (40 - 20) = 20 km/hr.
= 20 * 5/ 18 = 50/9 m/sec.
Length of faster train = 50/9 * 5 = 250/9 = 27 7/9 m.
Answer: Option D
Answer: (D) 27 7/9
Question: A train 500 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
(A) 45 km/hr
(B) 50 km/hr
(C) 54 km/hr
(D) 55 km/hr
(E) 185 km/hr
Rationale: Speed of the train relative to man = (500/10) m/sec = 50 m/sec. [50 * (18/5)] km/hr = 180 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 180 ==> x = 185 km/hr.
ANSWER: E
Answer: (E) 185 km/hr
Question: 252 Ã· ? Ã— 15 + 270 = 405
(A) 24
(B) 25
(C) 28
(D) 39
(E) 43
Rationale: Explanation:
252 Ã· ? Ã— 15 = 405 - 270 = 135
(252 Ã— 15)/? = 135
? = (252 Ã— 15)/135 = 28
Answer: Option C
Answer: (C) 28
Question: In a group of 100 adults, 50 percent of the women are left-handed. If there are 12 right-handed women in the group, how many men are in the group?
(A) 48
(B) 52
(C) 54
(D) 60
(E) 76
Rationale: 12 left-haded women compose 100-50=50% (or 1/2) of all women, so there are total of 2*12=24 women --> 100-24=76 men.
Answer: E.
Answer: (E) 76
Question: Free notebooks were distributed in a class among all the students. Each student got notebooks which were 1/8th of the number of student. If number of student been half, then each child would have received 16notebooks in total. Find the total number of books distributed among students?
(A) 430
(B) 450
(C) 460
(D) 480
(E) 512
Rationale: Let suppose total number of students in class are X.
Then from the question we can conclude it that,
X∗18X=X2∗16=>X=64Total notebooks,=18X2=(18∗64∗64)=512
E
Answer: (E) 512
Question: A fair 2 sided coin is flipped 6 times. What is the probability that tails will be the result at least twice, but not more than 4 times?
(A) 25/32
(B) 13/4
(C) 17/8
(D) 57/64
(E) 15/16
Rationale: at least twice, but not more than 5 timesmeans exactly 2 times, 3 times, 4 times
The probability of getting exactly k results out of n flips is nCk/2^n
6C2/2^6+6C3/2^6+6C4/2^6=(20+15+15)/2^6=25/32
Option: A
Answer: (A) 25/32
Question: A high school has 400 students 1/2 attend the airthmetic club, 5/8 attend the biology club and 3/4 attend the chemistry club. 1/8 attend all 3 clubs. If every student attends at least one club how many students attend exactly 2 clubs.
(A) 300
(B) 200
(C) 250
(D) 150
(E) 160
Rationale: Basically, this question is asking you to figure out how many students are being double-counted.
A-Club has 200 members (1/2 of 400)
B-Club has 250 members (5/8 of 400)
C-Club has 300 members (3/4 of 400)
We can create an equation to solve this:
200+250+300 = n + x + 2y
where n is the number of students, x is the number of students in two clubs, and y is the number of students in three clubs.
The question provides y for us (50).
750 = 400 + x + 100
x =250
C
Answer: (C) 250
Question: Worker A takes 5 hours to do a job. Worker B takes 15 hours to do the same job. How long it take both A & B, working together but independently, to do the same job?
(A) 15/4
(B) 40/9
(C) 50/9
(D) 60/9
(E) 80/9
Rationale: one day work of A = 1/5
one day work of B = 1/15
so one day work of A and B together = 1/5 + 1/15 = 4/15
so total days required = 15/4
ANSWER:A
Answer: (A) 15/4
Question: An analysis of the monthly incentives received by 5 salesmen : The mean and median of the incentives is $7000. The only mode among the observations is $12,000. Incentives paid to each salesman were in full thousands. What is the difference Z between the highest and the lowest incentive received by the 5 salesmen in the month?
(A) $4000
(B) $5000
(C) $9000
(D) $11,000
(E) $13,000
Rationale: Break down the question in to steps:
Step #1: incentives received by 5 salesmen -->abcde
Step #2: mean and median of the incentives is $7000: via number properties --> total incentives = 7,000 * 5 = 35, 000ab7,000de
Step #3: only mode among the observations is $12,000: mode is the value that appears most often in a set of data. Therefore 12,000 must occur more then once and since 12,000 is larger than the mean (7,000) the most it can occur is twice in our list. If we place the numbers in ascending order we haveab7,00012,00012,000
Step #4: What is the difference Z between the highest and the lowest incentive:
- The total paid has to equal mean * # of numbers = 7,000 * 5 = 35 000.
- The three values we have so far (12,000 12,000 and 7, 000) equal 31,000.
- Therefore the first two numbers( ab) must equal 4, 000
- There is only one mode which is 12,000, therefore 4,000 must be equal to a set of two numbers that are not the and a < b
if a = 1,000 b = 3,000 --> difference between the highest and the lowest incentive = 12,000 - 1,000 =11, 000
no other options for a or b to fit the criteria
Final List:1,0003,0007,00012,00012,000
Answer D
Answer: (D) $11,000
Question: The slant height of a right circular cone is 10 m and its height is 8 m. Find the area of its curved surface.
(A) 30 m2
(B) 40 m2
(C) 60 m2
(D) 80 m2
(E) 90 m2
Rationale: l = 10 m,
h = 8 m.
So, r = l2 - h2 = (10)2 - 82 = 6 m.
Curved surface area = rl = ( x 6 x 10) m2 = 60 m2.
Answer: Option C
Answer: (C) 60 m2
Question: A manufacturer of a certain type of screw rejects any screw whose length is less than 2.5 — 0.03 centimeters or greater than 2.53 centimeters. If k represents the length of a screw, in centimeters, which of the following inequalities specifies all the lengths of screws that are acceptable?
(A) |k + 0.03| > 2.5
(B) |k — 0.03| <= 2.5
(C) |k — 2.5| > 0.03
(D) |2k — 5| <= 0.06
(E) |k — 2.5| >= 0.09
Rationale: So, let's go through this step by step:
rejects any screw whose length is less than 2.5 — 0.03 centimeters or greater than 2.5 + 0.03 centimeters.
In other words, any screw that is less than: 2.50 - 0.03 =2.47or greater than 2.53 will be rejected.
If k represents the length of a screw
In other words,Kis an acceptable screw that must fall within the acceptable range of 2.47 to 2.53, So:
2.47 ≤ K ≤ 2.53
You can rule out answers with < or > as opposed to ≤ or ≥ because the length cannot be LESS than 2.47 or GREATER than 2.53. In other words, 2.47 and 2.53 are acceptable lengths.
Let's look at (D): |2k — 5| <= 0.06 or dividing by 2
|k — 2.5| <= 0.03
For the positive case: k - 2.5 ≤ 0.03 ===>k ≤ 2.53
For the negative case: -(k - 2.5) ≤ 0.03 ===> -k +2.5 ≤ 0.03 ===> - k ≤ -2.47 ===>k ≥ 2.47
2.47 ≤ k ≤ 2.53
(D)
Answer: (D) |2k — 5| <= 0.06
Question: A letter lock consists of three rings each marked with seven different letters. The number of distinct unsuccessful attempts to open the lock is at the most ?
(A) 177
(B) 199
(C) 342
(D) 168
(E) 167
Rationale: Since each ring consists of seven different letters, the total number of attempts possible with the three rings is
= 7 * 7 * 7 = 343. Of these attempts, one of them is a successful attempt.
Maximum number of unsuccessful attempts
= 343 - 1
= 342
Answer: C
Answer: (C) 342
Question: Lee Colle insures its students for thefts up to $1000. The college makes no profit but sets the premium to cover administrative costs of 10% on average claim of $120. If the annual premium per students is 24$. What is the expected number of thefts per 100 students per year?
(A) 12
(B) 14
(C) 16
(D) 18
(E) 20
Rationale: assume x is number of theft per year
24*100=120*1.1*x -> x = ~18
ANSWER:D
Answer: (D) 18
Question: There has been successive increases of 25% and then 10% in the price of gas from the previous month. By what percentage should a driver reduce gas consumption so that the expenditure does not change?
(A) 23%
(B) 27%
(C) 31%
(D) 35%
(E) 39%
Rationale: Let P be the original price per unit of gas.
Let x be the original gas consumption.
Let y be the reduced gas consumption.
y*1.1*1.25*P = x*P
y = x / (1.1*1.25) which is about 0.73x which is a decrease of about 27%.
The answer is B.
Answer: (B) 27%
Question: A vessel of capacity 2 litre has 35% of alcohol and another vessel of capacity 6 litre had 50% alcohol. The total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water. What is the new concentration of Mixture?
(A) 31%.
(B) 71%.
(C) 49%.
(D) 29%.
(E) 37%.
Rationale: 35% of 2 litres = 0.7 litres
50% of 6 litres = 3 litres
Therefore, total quantity of alcohol is 3.7 litres.
This mixture is in a 10 litre vessel. Hence, the concentration of alcohol in this 10 litre vessel is 37%
E
Answer: (E) 37%.
Question: Tough and Tricky questions: Functions. Let a be a positive integer. Let n#a equal n^(2a) if a is odd and n^(a) if a is even. Then (2#3) + (3#2) – (3#3) is equal to
(A) -656
(B) 82
(C) 128
(D) 512
(E) 1522
Rationale: Answer:
2^6 + 3^2 - 3^6 = -656
ANs A
Answer: (A) -656
Question: If x and y are positive integers and (5^x)−(5^y)=(2^y−1)∗(5^x−1), what is the value of xy?
(A) 48
(B) 36
(C) 24
(D) 18
(E) 12
Rationale: x and y are positive integers which means we will have clean numbers. On the right hand side, you have a 2 as a factor while it is not there on the left hand side. Can a 2 be generated on the left hand side by the subtraction? Here I am thinking that if we take 5^y common on the left hand side, I might be able to get a 2.
56y(56^x−y −1)=2^y−1∗5^x−1
Now I want only 2s and 5s on the left hand side. If x-y is 1, then (5^x−y−1) becomes 4 which is 2^2. If instead x - y is 2 or more, I will get factors such as 3, 13 too. So let me try putting x - y = 1 to get
5^y(2^2)=2^y−1∗5^x−1
This gives me y - 1 = 2
y = 3
x = 4
Check to see that the equations is satisfied with these values. Hence xy = 12
Answer (E)
Answer: (E) 12
Question: Find the invalid no.from the following series 15, 16, 34, 105, 424, 2123, 12756
(A) 16
(B) 34
(C) 105
(D) 424
(E) 2123
Rationale: 2nd term = (1st term) * 1 + 1 = 15 *1 + 1 = 16.
3rd term = (2nd term) * 2 + 2 = 16 * 2 + 2 = 34
4th term = (3th term) *3 + 3 = 34 * 3 + 3 = 105
5th term = (4th term) * 4 + 4 = 105 * 4 + 4 = 424
6th term = (5th term) * 5 + 5 = 424 * 5 + 5 = 2125
6th term should 2125 instead of 2123.
E
Answer: (E) 2123
Question: If the simple interest on a sum of money for 5 years at 18% per annum is Rs. 900, what is the compound interest on the same sum at the rate and for the same time?
(A) Rs. 1287.76
(B) Rs. 1284.76
(C) Rs. 1587.76
(D) Rs. 1266.76
(E) Rs. 1283.76
Rationale: Sum = (900 * 100) / (5 * 18) = Rs. 1,000.00
C.I. on Rs. Rs. 1,000.00 for 5 years at 18% = Rs. 2,287.76.
= Rs. 2,287.76 - 1,000.00 = Rs. 1287.76
ANSWER:A
Answer: (A) Rs. 1287.76
Question: If x = -12/5 and y = -6/7, what is the value of the expression -2x – y^2?
(A) 741/357
(B) 456/789
(C) 636/735
(D) 564/263
(E) -636/735
Rationale: x = -12/15 and y = -6/7
==> -2(-12/15) - (-6/7)^2 = 24/15 - 36/49 = 636/735
Ans: C
Answer: (C) 636/735
Question: What is the difference between the compound interest on Rs.12000 at 20% p.a. for one year when compounded yearly and half yearly?
(A) 272
(B) 120
(C) 277
(D) 2898
(E) 212
Rationale: When compounded annually, interest
= 12000[1 + 20/100]1 - 12000 = Rs.2400
When compounded semi-annually, interest
= 12000[1 + 10/100]2 - 12000 = Rs.2520
Required difference = 2520 - 2400 = Rs.120.Answer: B
Answer: (B) 120
Question: If grapes are 92% water and raisins are 20% water, then how many kilograms did a quantity of raisins, which currently weighs 5 kilograms, weigh when all the raisins were grapes? (Assume that the only difference between their raisin-weight and their grape-weight is water that evaporated during their transformation.)
(A) 50
(B) 54
(C) 55
(D) 56
(E) 60
Rationale: Let x be the original weight.
The weight of the grape pulp was 0.08x.
Since the grape pulp is 80% of the raisins, 0.08x = 0.8(5).
Then x = 50 kg.
The answer is A.
Answer: (A) 50
Question: In a vehicle's repair shed, 3 men and 8 boys can do a piece of work in 15 days; 4 men and 9 boys can do the same work in 12 days. Then, 5 men and 5 boys can do double the amount of this work in :
(A) 20 days
(B) 33 days
(C) 24 days
(D) 28 days
(E) None of these
Rationale: Explanation :
Solution: (3*15) men + (8*15) boys= (4*12) men + (9*12) boys
45 M + 120 B = 48 M+ 108 B <=> 3 M = 12 B => 1 M = 4 B.
.'. 3 M + 8 B = (3*4) B+ 8 B = 20 B.
5 M + 5 B = (5*4) B + 5 B = 25 B.
Let the required number of days be x.
now, more boys, less days (IP)
more work, more days (DP)
boys 25 : 20
} : :15: x
work 1 : 2
.'. (25*1*x) = (20*2*15)
=> x = 40*15/25 = 24.
Answer : C
Answer: (C) 24 days
Question: A bag contains 20 purple jellybeans, 18 green jellybeans, and 12 yellow jellybeans; these jellybeans are the only items in the bag. If a person picks a jellybean at random out of the bag, what is the probability that the jellybean will be green?
(A) 15%
(B) 20%
(C) 25%
(D) 30%
(E) 36%
Rationale: Probability of green beans = 18 / (20 + 18 + 12) = 18/50 = 36%
Answer is E
Answer: (E) 36%
Question: consider a sequence of numbers is such that a1 = 11, a2 =16, and each subsequent an = an-2 + 9. Which of the following numbers is a member of the sequence?
(A) 216
(B) 246
(C) 289
(D) 299
(E) 368
Rationale: each odd term(1st , 3rd, 5th,...) of the sequence is given by 11 + 9*(something)
each even term(2nd, 4th, 6th...) of the sequence is given by 16 + 9*(something)
So if you subtract the numbers by 11 or 16 then it should be divisible by 9
216-11(=205) or 216-16(=200) are not divisible by 9
246-11(=235) or 246-16(=240) are not divisible by 9
289-11(=278) or 289-16(=273) are not divisible by 9
299-11(=288) is divisible by 9ANSWER, 299-16(=283) are not divisible by 9
368-11(=357) or 368-16(=352) are not divisible by 9
So, Answer is D
Answer: (D) 299
Question: Mr. Yutaro’s class contains 10 boys and 6 girls. If two students are chosen, one at a time, from the class, what is the probability that a boy and a girl are chosen?
(A) 9/48
(B) 9/20
(C) 11/24
(D) 27/48
(E) 1/2
Rationale: Probability of a girl being chosen first, then a girl:
6/16 * 10/15
Probability of a boy being chosen first, then a boy:
10/16 * 6/15
Probability of a boy and a girl being chosen:
(6*10+6*10) / (15*16)
=1/2
Answer:E
Answer: (E) 1/2
Question: A and B together can do a piece of work in 8 days. If A alone can do the same work in 12 days, then B alone can do the same work in?
(A) 76 days
(B) 68 days
(C) 24 days
(D) 97 days
(E) 17 days
Rationale: B = 1/8 – 1/2 = 1/24
=> 24 days
Answer: C
Answer: (C) 24 days