mathewhe/aqua_rat huggingface dataset:
Question: On a test, the boys in the class averaged 90 points and the girls in the class averaged 96 points. If the overall class average was 94 points, what is the ratio of boys to girls in the class?
(A) 1/2
(B) 2/3
(C) 3/4
(D) 3/5
(E) 4/5
Rationale: (96G + 90B) / (G+B) = 94
96G + 90B = 94(G+B)
2G=4B
B/G = 1/2
The answer is A.
Answer: (A) 1/2
Question: From the salary of Rahul, 20% is deducted as house rent, 10% of the rest he spends on children’s education and 10% of the balance, he spends on clothes. After this expenditure he is left with Rs 1,377. His salary is?
(A) Rs 2,125
(B) Rs 2,040
(C) Rs 2,100
(D) Rs 2,200
(E) Rs 2,300
Rationale: Suppose that his salary = Rs 100
House rent = Rs 20, balance = Rs 80
Expenditure on education = Rs (10 x 80)/100 = Rs 8
Balance = Rs 72
Expenditure on clothes Rs (10 x 72)/100 = Rs 7.2
Balance now = Rs 64.8
If balance is Rs 64.8, salary = Rs 100
If balance is Rs 1,377, salary
= Rs (100 x 1377) / 64.8
Rs 2,125
ANSWER:A
Answer: (A) Rs 2,125
Question: The sale price shirts listed for Rs.1000 after successive discount is 15% and 2% is?
(A) 338
(B) 823
(C) 833
(D) 337
(E) 733
Rationale: 1000*(85/100)*(98/100)
= 833
Answer: C
Answer: (C) 833
Question: The area of the largest circle that can be drawn inside a square of side 112 Cm in length is:
(A) 9856
(B) 8646
(C) 2616
(D) 1636
(E) 3606
Rationale: Radius of required circle = 56 Cm
its area = 22/7 × 56 × 56
176 × 56 = 9856 Cm(power)2
Answer is A.
Answer: (A) 9856
Question: Running at the same constant rate, 8 identical machines can produce a total of 240 pens per minute. At this rate, how many pens could 5 such machines produce in 5 minutes?
(A)  114
(B)  108
(C)  192
(D)  750
(E)  777
Rationale: Let's take the approach that uses the answer choices to eliminate wasted time.
240/8 = 30 pens per minute per machine.5 machines = 150 per minute. 5 minutes worth =750 pens.
Looking at the answers it is clear...we can only choose (D).
THE CORRECT ANSWER IS D.
Answer: (D)  750
Question: If 50% of the 880 students at a certain college are enrolled in biology classes, how many students at the college are NOT enrolled in a biology class?
(A) 560
(B) 540
(C) 520
(D) 440
(E) 500
Rationale: We know 50 % people study biology,therefore the no of people not studying = 100 - 50 = 50%
> Therefore the people not studying biology out of a total 880 people are = 50 % of 880
> (50/100)*880 = 440 people
D
Answer: (D) 440
Question: A bag of potatoes weighs 28 lbs divided by half of its weight. How much does the bag of potatoes weight?
(A) 20 lb
(B) 14 lb
(C) 10 lb
(D) 15 lb
(E) 5 lb
Rationale: Sol.
28÷2 = 14.
Answer : B
Answer: (B) 14 lb
Question: If x^2 = y^2, which of the following must be true?
(A) x = y
(B) x = −y
(C) |x| = |y|
(D) x = −|y|
(E) x = |y|
Rationale: Since x^2=y^2 we have 0=x^2 – y^2 =(x-y)*(x+y). So x=y or x=-y.
So only (A) and only (B) cannot be an answer.
The choice (E) tells us that k should be greater than or equal to 0.
Similarly the choice (D) tells us that k should be less than or equal to 0.
So neither (E) nor (D) cannot be the answer.
The answer is, therefore, (C).
Answer: (C) |x| = |y|
Question: a school has 4 maths 3 physics and 3 chemistry teachers each teacher can teach 2 subjects max what is he minimum number of teachers required
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: Total subjects = 4 +3 +3 = 10
Max subjects by 1 teacher = 2
So, min of teachers required = 10/2 = 5
ANSWER:B
Answer: (B) 5
Question: In a 100m race, Sam beats John by 5 seconds. On the contrary, if Sam allowed John to start 15m ahead of Sam, then Sam and John reach the finishing point at the same time. How long does Sam take to run the 100m race?
(A) 4 seconds
(B) 25 seconds
(C) 29 seconds
(D) 21 seconds
(E) 17 seconds
Rationale: Their difference is 5 second but this difference is 0 if john allows Sam to start the race from 15m ahead . that means Jhon was 15m away from finishing line when they started together . so He will cover 15 m in 5 seconds . so his speed =15/5=3 metre / second . so time taken =100/5=20 seconds . so Sam took = 17 seconds .
correct answer = E
Answer: (E) 17 seconds
Question: A candidate got 35% of the votes and lost to the rival by 1800 votes. How many votes were cast?
(A) 5500
(B) 6000
(C) 6500
(D) 7000
(E) 7500
Rationale: 35%-----------L
65%-----------W
------------------
30% = 1800
10% = 600
100% of the votes = 6000
Answer: B
Answer: (B) 6000
Question: The roots of the equation x / (x + 2) + 3 / (x - 4) = (4x + 2) / (x 2 - 2x - 8) are
(A) x = 4 and x = 1
(B) x = 4 only
(C) x = 1 only
(D) x = -4 only
(E) None
Rationale: We first note that
(x + 2)(x - 4) = x 2 - 2x - 8
We now multiply all terms of the given equation by (x + 2)(x - 4) and simplify to get
x (x - 4) + 3 (x + 2)= (4x + 2)
Expand, group and solve
x 2 - x + 6 = 4x + 2
x 2 - 5x + 4 = 0
(x - 1)(x - 4) = 0
Roots: x = 1 and x = 4
Check answer: only x = 1 is a solution since the given equation is not defined at x = 4.
Answer C
Answer: (C) x = 1 only
Question: Suppose that there is a rubber ball which has a property of bouncing back to the original height from which it was dropped and it keeps doing that until it is stopped by any external force.
Can you calculate the fraction of height to which the ball would have bounced if it has bounced four times after dropping from a certain height without being stopped?
(A) 16/81
(B) 15/90
(C) 18/88
(D) 15/79
(E) 13/85
Rationale: A
16/81
Explanation:
It is a question of geometric progression but we can solve it step by step as well in case you are not aware of the formula.
At first bounce
The height at which the ball would have reached = 2/3 of the original height from which it was dropped.
At second bounce
The height at which the ball would have reached = 2/3 * 2/3 of the original height from which it was dropped.
At third bounce
The height at which the ball would have reached = 2/3 * 2/3 * 2/3 of the original height from which it was dropped.
At fourth bounce
The height at which the ball would have reached = 2/3 * 2/3 * 2/3 * 2/3 of the original height from which it was dropped.
Now, 2/3 * 2/3 * 2/3 * 2/3 = 16/81
Therefore, 16/81 of the original height from which the ball was dropped is the required fraction height.
Answer: (A) 16/81
Question: If a farmer sells 15 of his hens, his stock of feed will last for 4 more days than planned, but if he buys 20 more hens, he will run out of feed 3 days earlier than planned. If no hens are sold or bought, the farmer will be exactly on schedule. How many hens does the farmer have?
(A) 60
(B) 40
(C) 80
(D) 70
(E) 50
Rationale: Let x = total feed required for the planned period
n= number of hen
t = total time of the planned feed
x = nt
1) x = (n-15) * (t+4)
2) x = (n+20) * (t-3)
equating 1&2
(n-15) * (t+4) = (n+20) * (t-3) or nt +4n -15t -60 = nt -3n +20t-60
7n = 35t
n =5t
x= n * n/5
substituting this value in 1
n * n/5 = (n-15) * (n/5+4)
5n = 300
n =60
A
Answer: (A) 60
Question: It takes Joey the postman 1 hours to run a 2 mile long route every day. He delivers packages and then returns to the post office along the same path. If the average speed of the round trip is 6 mile/hour, what is the speed with which Joey returns?
(A) 9
(B) 12
(C) 13
(D) 14
(E) 15
Rationale: let his speed for one half of the journey be 3 miles an hour
let the other half be x miles an hour
now,
avg speed =5 mile an hour
2*2*x/3+x=6
4x=6x+18=>2x=18
x=9
A
Answer: (A) 9
Question: When a number is divided by 13, the remainder is 6. When the same number is divided by 7, then remainder is 1. What is the number ?
(A) 243
(B) 253
(C) 312
(D) 432
(E) None of these
Rationale: Explanation:
Take 243
243 ÷ 7 = 34, remainder = 5
Hence this is not the answer
Take 312
312 ÷ 7 = 44, remainder = 4
Hence this is not the answer
Take 253
253 ÷ 7 = 36, remainder = 1.
253 ÷ 13 = 19, remainder = 6
This satisfies both the conditions given in the question. Hence it is the answer.
Answer: B
Answer: (B) 253
Question: For any positive number x, the function [x] denotes the greatest integer less than or equal to x. For example, [1] = 1, [1.367] = 1 and [1.996] = 1. If k is a positive integer such that k^2 is divisible by 45 and 80, what is the units digit of k^3/4000 ?
(A) 0
(B) 1
(C) 0
(D) 54
(E) Cannot be determined
Rationale: K=[lCM of 80 and 45] * (any integer)
however minimum value of k is sq.rt of 3^2*4^2*5^2 = 60 * any integer
for value of k(60) * any integer unit value will be always zero .
C
Answer: (C) 0
Question: The speed of a train is 90 kmph. What is the distance covered by it in 10 minutes?
(A) 15 kmph
(B) 18 kmph
(C) 85 kmph
(D) 17 kmph
(E) 99 kmph
Rationale: 90 * 10/60
=15 kmph
Answer:A
Answer: (A) 15 kmph
Question: A large research project was scheduled over the course of a 25-month period, and a budget of $100,000 was allotted for the course of the entire project. After 9 months, the project had spent $35,800. Was the project at this point over budget or under budget, and by how much?
(A) under, $200
(B) under, $1200
(C) under, $7000
(D) over $1800
(E) over $5800
Rationale: cost per month = 100,000/25 = 4,000.
Now, multiply by nine months: 9*($4000) = $36,000. That would be the budgeted amount, the amount theoretically supplied to the project. The real amount spent is less than this, so it is under budget.
$36,000 â€“ #35,800 = $200
Answer = (A)
Answer: (A) under, $200
Question: A town's oldest inhabitant is x years older than the sum of the ages of the Lee triplets. If the oldest inhabitants is now J years old, how old will one of the triplets Q be in 20 years?
J-X-40/3 is my answers.
J = X + L + L + L is the initial situation
After 20 years
J + 20 = X + L + L + L + 60 ...20 years for each triplet so 60 years totally.
J - X - 40/ 3 = L is my answer.
What wrong am i doing ? Since the age asked is after 20 years i also consider adding 20 years to J .
(A) (J - 50)/3
(B) 3(J + 20)/x
(C) (J + x - 50)/3
(D) (J - x + 60)/3
(E) (J + x - 20)/3
Rationale: here it goes:
Oldest inhabitant = sum of age of triplets + X
J = 3L + X so L = (J - X)/3
After 20 years = L + 20
Q= (J - X)/3 + 20
= (J - X + 60)/3=D
Answer: (D) (J - x + 60)/3
Question: There are two numbers. If 30% of the first number is added to the second number, then the second number increases to its five-fourth. Find the ratio of the first number to the second number?
(A) 5/9
(B) 5/6
(C) 5/3
(D) 5/8
(E) 5/1
Rationale: Let the two numbers be x and y.
30/100 * x + y = 5/4y
=> 3/10 x = 1/4 y => x/y
= 5/6
Answer: B
Answer: (B) 5/6
Question: John had $100 to buy drinks and sandwiches for his birhtday party. He bought 5 small boxes of drinks at $4 each box and 8 boxes of sandwiches at $6 each box. How much money was left after the shopping?
(A) $68
(B) $45
(C) $57
(D) $34
(E) $77
Rationale: Money spent on drinks
5 * 4 = $20
Money spent on sandwiches
8 * 6 = $48
Total money spent
20 + 48 = $68
Money left after shopping
100 - 68 = $32
correct answer A
Answer: (A) $68
Question: A credit card number has 6 digits (between 1 to 9 inclusive). The first two digits are 12 in that order, the third digit is bigger than 6, the fourth digit is divisible by 2, and the fifth digit is 2 times the sixth. How many different credit card numbers are possible?
(A) 24
(B) 36
(C) 48
(D) 60
(E) 72
Rationale: The first two digits are fixed.
The third digit can be 7, 8, or 9 so there are 3 choices.
The fourth digit can be 2, 4, 6, or 8 so there are 4 choices.
The fifth digit depends entirely on the sixth digit.
The sixth digit can be 1, 2, 3, or 4 so there are 4 choices.
The number of possibilities is 3*4*4 = 48
The answer is C.
Answer: (C) 48
Question: Car A runs at the speed of 80km/hr & reaches its destination in 5hr. Car B runs at the speed of 100 km/h & reaches its destination in 2h. What is the respective ratio of distances covered by Car A & Car B?
(A) 11 : 5
(B) 11 : 8
(C) 2 : 1
(D) 15 : 7
(E) 16 : 9
Rationale: Sol. Distance travelled by Car A = 80 × 5 = 400 km
Distance travelled by Car B = 100 × 2 = 200 km
Ratio = 400/200 = 2 : 1
Answer : C
Answer: (C) 2 : 1
Question: In how many different number of ways 5 men and 4 women can sit on a shopa which can accommodate persons?
(A) 200
(B) 230
(C) 240
(D) 9
(E) 260
Rationale: 9p1 = 9
D
Answer: (D) 9
Question: Total of ages of A,B and C at present is 90 years. If ratio of this ages is 2 : 3 : 4 what will be the age of C after 8 years?
(A) 45 years
(B) 42 years
(C) 40 years
(D) 48 years
(E) None of the above
Rationale: 2+3+4=9
4*(90/9)=40yrs
after 8 yrs=48
ANSWER:D
Answer: (D) 48 years
Question: In a survey of 345 employees, 104 of them are uninsured, 54 work part time, and 12.5 percent of employees who are uninsured work part time. If a person is to be randomly selected from those surveyed, what is the probability that the person will neither work part time nor be uninsured?
(A) 7/12
(B) 8/41
(C) 9/348
(D) 1/8
(E) 40/69
Rationale: ---------UI----------------NUI-------Total
PT----(12.5/100)*104 = 13----------- --54
NPT---104-13-------------- x--------291
Total--104----------------------------345
we have to find not part time and not uninsured . in other words not part time and insured = x/345 = (291-104+13)/345
= 40/69
Answer is E.
Answer: (E) 40/69
Question: The ratio of present age of A and B is 4:3. A will be 26yrs old in 6yrs from now. How old is B now?
(A) 15yrs
(B) 20yrs
(C) 25yrs
(D) 10yrs
(E) 18yrs
Rationale: present age of A is 20yrs(26-6).
4/3=20/x;
x=15
ANSWER:A
Answer: (A) 15yrs
Question: A shopkeeper sold sarees at 266 each after giving 5% discount on labelled price. Had he not given the discount, he would have earned a profit of 12% on the cost price. What was the cost price of each saree?
(A) 280
(B) 260
(C) 38 mph
(D) Data inadequate
(E) None of these
Rationale: Marked price = 266 × 100⁄95 × 280
Cost Price = 280 × 100⁄112 = 250
Answer E
Answer: (E) None of these
Question: It takes Avery 4 hours to build a brick wall while Tom can do it in 2 hours. If the two start working together and after an hour Avery leaves, how much time will it take Tom to complete the wall on his own?
(A) 20
(B) 40
(C) 30
(D) 50
(E) 60
Rationale: Avery takes 4 hours
Tom takes 2 hours
Efficiency of Avery is 1/4 units/hr
Efficiency of Tom is 1/2 units/hr
Combined efficiency of Tom and Avery is 1/4 +1/2 = 3/4 units/hr
Since they worked for 1 hour they completed 3/4 units of work and 1/4 units of work is left which is to be completed by Tom ( Since Avery left )
So Time taken by Tom to complete the remaining work will be 1/4/1/2 hours => 1/2*60 = 30 minutes...
Answer will be (C)
Answer: (C) 30
Question: Some persons can do a piece of work in 12 days. Two times the number of these people will do half of that work in?
(A) 3 days
(B) 3.5 days
(C) 4.5 days
(D) 5.5 days
(E) 2.5 days
Rationale: 14/ (2 * 2) = 3.5 days
ANSWER:B
Answer: (B) 3.5 days
Question: x, y, a, and b are positive integers. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 18. Which of the following is NOT a possible value for y + b?
(A) 24
(B) 21
(C) 20
(D) 17
(E) 15
Rationale: Important note: remainder is ALWAYS less than divisor, thus y>6 and b>18 --> y+b>24.
Answer: A.
Answer: (A) 24
Question: What is (21^7+21) / 21?
(A) 82216043
(B) 83786095
(C) 84316108
(D) 85766122
(E) 86426237
Rationale: (21^7+21) / 21 =
21*(21^6+1) / 21 =
21^6 + 1
Clearly this is a number which ends with a 2 in the units place.
The answer is D.
Answer: (D) 85766122
Question: Local trains leave from a station at an interval of 15 minutes at a speed of 16 km/h. A man moving from opposite side meets the trains at an interval of 12 minutes. Find the speed of the man.
(A) 4 km/h
(B) 3.5 km/h
(C) 4.5 km/h
(D) 3 km/h
(E) None of these
Rationale: Let speed of man = S km/h. Then,
Distance covered in 15 min = Distance covered in 12 min
16 × 15⁄60 = 12⁄60[16 + S]
⇒ 16 + S = 20 ⇒ S = 4 km/h
Answer A
Answer: (A) 4 km/h
Question: The average weight of A, B and C is 45 kg. If the average weight of A and B be 42 kg and that of B and C be 43 kg, then the weight of B is:
(A) 33 kg
(B) 31 kg
(C) 32 kg
(D) 36 kg
(E) 35 kg
Rationale: Let A, B, C represent their respective weights.
Then, we have: A + B + C = (45 x 3) = 135 .... (i)
A + B = (42 x 2) = 84 .... (ii)
B + C = (43 x 2) = 86 ....(iii)
Adding (ii) and (iii), we get: A + 2B + C = 170 .... (iv)
Subtracting (i) from (iv), we get : B = 35
B's weight = 35 kg.
E
Answer: (E) 35 kg
Question: A man invested Rs. 4455 in Rs. 10 shares quoted at Rs. 8.25. If the rate of dividend be 12%, his annual income is:
(A) Rs. 207.40
(B) Rs. 534.60
(C) Rs. 648
(D) Rs. 655.60
(E) Rs. 755.60
Rationale: No. of shares= 4455/8.25 =540
income on shares=540*10=5400
annual income=12*5400/100=648
ANSWER:C
Answer: (C) Rs. 648
Question: A circular swimming pool is surrounded by a concrete wall 4ft wide. If the area of the concrete wall surrounding the pool is 11/25 that of the pool, then the radius of the pool is?
(A) 22
(B) 20
(C) 88
(D) 387
(E) 19
Rationale: let the radius of the pool be Rft
Radius of the pool including the wall = (R+4)ft
Area of the concrete wall = {\color{Black} \Pi \left [ (R+4)^{2} -R^{2}\right ]}={\color{Black} \Pi \left [ (R+4+R)(R+4-R) \right ] =8\Pi (R+2)} sq feet
{\color{Black} \Rightarrow 8\Pi (R+2)=\frac{11}{25}\Pi R^{2}\Rightarrow 11R^{2}=200(R+2)}
Radius of the pool R = 20ft
Answer: B) 20ft
Answer: (B) 20
Question: Harry started a 4-mile hike with a full 6-cup canteen of water and finished the hike in 2 hours with 1 cup of water remaining in the canteen. If the canteen leaked at the rate of 1 cup per hour and Harry drank 1 cups of water during the last mile, how many cups did he drink per mile during the first 3 miles of the hike?
(A) 1/3
(B) 2/3
(C) 3/4
(D) 5/4
(E) 4/3
Rationale: No of cups leaked during the trip = 2 cups.
No of cups Harry drank = 3 cups.
No of cups harry drank during the first 3 miles = 2.
drink / mile = 2/3
Answer:B
Answer: (B) 2/3
Question: The average age of 3 girls is 40 years and their ages are in the proportion 1:2:3. The age of the youngest girl is?
(A) 22 years
(B) 23 years
(C) 21 years
(D) 20 years
(E) 25 years
Rationale: Total age of 3 boys = 40*3 =120
ratio of their ages = 1:2:3
Age of the youngest =120*1/6 = 20 years
Answer is D
Answer: (D) 20 years
Question: A group of 10 people consists of 3 married couples and 4 single men. A committee of 4 is to be formed from the 10 people. How many different committees can be formed if the committee can consist of at most 1 married couple?
(A) 105
(B) 207
(C) 210
(D) 540
(E) 5,040
Rationale: Total number of possibilities of selecting 4 people out of 10 without any restrictions = 10C4 = 10!/(4!*6!)
= (10*9*8*7)/4*3*2*1
= 10*3*7
= 210
Number of possibilities of selecting 2 married couples = 3C2 = 3!/2! = 3
Number of different committees with atmost 1 married couple that can be formed = 210 - 3 = 207
Answer B
Answer: (B) 207
Question: A train cross a 450 m bridge in 42 s and another bridge 650 m length in 50 s what is approximate speed of train in km/h?
(A) 90 Km /hr.
(B) 25 Km /hr.
(C) 30 Km /hr.
(D) 20 Km /hr.
(E) None of these
Rationale: Explanation:
Let the length of the train be L.
Then,
=> (450 + L)/42 = (650+L)/50.
=> L= 600 m.
Now, speed = (450+600)/42 or (650+600)/50 = 25 m/s i.e. 25*(18/5) = 90 Km /hr.
ANSWER IS A
Answer: (A) 90 Km /hr.
Question: Anderson has a phone plan that charges a
monthly rate of $50 for the first 1,000 minutes
plus $0.25 for each additional minute.
Which of the following functions models
Anderson’s plan for all m > 1,000, with m as
the number of minutes per month and f(m)
as the monthly charge?
(A) f(m) = 0.25m
(B) f(m) = 0.25m + 50
(C) f(m) = 0.25m – 200
(D) f(m) = 0.25m – 950
(E) f(m) = 0.25m + 1,000
Rationale: For m > 1,000 — that is, beyond 1,000 minutes of usage — the plan charges a usage fee
based on the number of minutes used plus a flat rate of $50. With this information, you can
create the following function:
f(m) = Usage fee + 50
The usage fee is $0.25 per minute; however, the first 1,000 minutes are already paid for. So
the usage fee is 0.25(m – 1,000). Plug this value into the preceding function and simplify:
f(m) = 0.25(m – 1,000) + 50
f(m) = 0.25m – 250 + 50
f(m) = 0.25m – 200
correct answer C)f(m) = 0.25m – 200
Answer: (C) f(m) = 0.25m – 200
Question: At a certain committee meeting only associate professors and assistant professors are present. Each associate professor has brought 2 pencils and 1 chart to the meeting, while each assistant professor has brought 1 pencil and 2 charts. If a total of 7 pencils and 11 charts have been brought to the meeting, how many people are present?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: Say there are 'A' associate professors. So we have 2A pencils and A charts.
Say there are 'B' assistant professors. So we have B pencils and 2B charts.
Total pencils are 10 so 2A + B = 7
Total charts are 11 so A + 2B = 11
Add both: 3A + 3B = 18 so A + B = 6
Total number of people = 6
A
Answer: (A) 6
Question: If the President and Vice President must sit next to each other in a row with 3 other members of the Board, how many different seating arrangements are possible?
(A) 12
(B) 26
(C) 20
(D) 48
(E) 32
Rationale: We need to take President and VP as one unit. Therefore we have 4 people to arrange=4! ways
Also, we both President and VP can be arranged in 2 ! ways.
Reqd no of ways=4!*2!=48 ways
Answer D
Answer: (D) 48
Question: A sum of money placed at C.I. interest doubles itself in 5 years. It will amount to eight times itself at the same rate of interest in
(A) 17 years
(B) 87 years
(C) 15 years
(D) 16 years
(E) 19 years
Rationale: P(1 + R/100)5 = 2P => (1 + R/100)5 = 2
Let P(1 + R/100)n = 8P
=> (1 + R/100)n = 8 = 23 = {(1 + R/100)5}3
=> (1 + R/100)n = (1 + R/100)15 => n = 15 Required time
= 15 years.
Answer:C
Answer: (C) 15 years
Question: Anil can do a work in 15 days while Sunil can do it in 25 days. How long will they take if both work together?
(A) 9 3/8 days
(B) 4 2/8 days
(C) 17 9/8 days
(D) 12 7/8 days
(E) 16 9/8 days
Rationale: 1/15 + 1/25 = 8/75
75/8 = 9 3/8 days
ANSWER:A
Answer: (A) 9 3/8 days
Question: In a competitive examination in State A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 80 more candidates got selected than A. What was the number of candidates appeared from each State?
(A) 7000
(B) 7200
(C) 7400
(D) 7600
(E) 8000
Rationale: State A and State B had an equal number of candidates appeared.
In state A, 6% candidates got selected from the total appeared candidates
In state B, 7% candidates got selected from the total appeared candidates
But in State B, 80 more candidates got selected than State A
From these, it is clear that 1% of the total appeared candidates in State B = 80
=> total appeared candidates in State B = 80 x 100 = 8000
=> total appeared candidates in State A = total appeared candidates in State B = 8000
E)
Answer: (E) 8000
Question: If 0 < x > 7 and 5 < y < 9, then the lowest possible value for xy is
(A) between 60 and 70
(B) between 0 and 60
(C) 0
(D) between 0 and -70
(E) less than -70
Rationale: If 0 < x > 7 and 5 < y < 9, then the lowest possible value for xy is
Say y = 8 (y<9)
x = 8
So xy =64 which is more than 60.
Answer is A.
Answer: (A) between 60 and 70