mathewhe/aqua_rat huggingface dataset:
Question: A company pays project contractors a rate of a dollars for the first hour and b dollars for each additional hour after the first, where a > b.
In a given month, a contractor worked on two different projects that lasted 6 and 8 hours, respectively. The company has the option to pay for each project individually or for all the projects at the end of the month. Which arrangement would be cheaper for the company and how much would the company save?
(A) Per month, with savings of $(5a + 5b)
(B) Per month, with savings of $(5a - 5b)
(C) The two options would cost an equal amount.
(D) Per project, with savings of $(5a + 5b)
(E) Per project, with savings of $(5a - 5b)
Rationale: Per Project, company will pay as follows:
For 6 hours work = a+5b
For 8 hours work = a+7b
Total = 2a+12b
Per Month, company will pay for 14 hours work = a+13b
Total per contract - total per month
6a+8b - (a+13b)
5a-5b
Since a>b Amount 6a+8b(per contract amount) > a+13b (per project amount) by 5a-5b.
Hence per month payment will be cheaper by 5a-5b .
OA B
Answer: (B) Per month, with savings of $(5a - 5b)
Question: A rectangular field is to be fenced on three sides leaving a side of 30 feet uncovered. If the area of the field is 720 sq. feet, how many feet of fencing will be required?
(A) 78
(B) 40
(C) 68
(D) 88
(E) None
Rationale: EXPLANATION
We have: l = 30 ft and lb = 720 sq. ft.
So, b = 24 ft.
Length of fencing = (l + 2b) = (30 + 48) ft = 78 ft.
Answer A
Answer: (A) 78
Question: Car Z travels 45 miles per gallon of gasoline when driven at a constant rate of 45 miles per hour, but travels 20 percent fewer miles per gallon of gasoline when driven at a constant rate of 60 miles per hour. How many miles does car Z travel on 10 gallons of gasoline when driven at a constant rate of 60 miles per hour?
(A) 320
(B) 360
(C) 400
(D) 408.3
(E) 440
Rationale: The question stem asks us for the distance possible with 10 gallons of fuel at a constant speed of 60 miles per hour. We therefore first calculate the fuel efficiency at that speed.
The stem tells us that at 45 miles/hour, the car will run 45 miles/gallon and at 60 miles/hour, that distance decreases by 20%. We can therefore conclude that the car will travel 36 miles/gallon at a constant speed of 60 miles/gallon. With 10 gallons of fuel, the car can therefore travel 36 miles/gallon * 10 gallons = 360 miles.
Answer B.
Answer: (B) 360
Question: Two cyclist start on a circular track from a given point but in opposite direction with speeds of 7m/s and 8m/s. If the circumference of the circle is 180meters, after what time will they meet at the starting point?
(A) 20sec
(B) 12sec
(C) 30sec
(D) 50sec
(E) 1min
Rationale: They meet every 180/7+8 = 12sec
Answer is B
Answer: (B) 12sec
Question: 5 skilled workers can build a wall in 20days; 8
semi-skilled workers can build a wall in 25 days; 10
unskilled workers can build a wall in 30days. If a te
am has 2 skilled, 6 semi-skilled and 5 unskilled
workers, how long will it take to build the wall?
(A) 15days
(B) 16days
(C) 14days
(D) 18days
(E) 17days
Rationale: For Skilled
5 workers --------20 days
5 workers 1 day work= 1/20
1 worker's 1 day work= 1/(5*20)
Similarly,
For Semi-Skilled------
1 worker's 1 day work= 1/(8*25)
For Unskilled------
1 worker's 1 day work= 1/(10*30)
For 2 skilled,6 semi-skilled and 5 unskilled
workers
One day work= 2*[1/(5*20)] +6*[1/(8*25)] + 5*[ 1/(10*30)] = 1/15
Therefore no. of days taken= 15
ANSWER:A
Answer: (A) 15days
Question: Twenty coins are tossed simultaneously. In how many of the outcomes will the third coin turn up a head?
(A) 2^19
(B) 2^10
(C) 3 * 2^8
(D) 3 * 2^9
(E) 3 * 2^10
Rationale: Fix the third coin as H. The remaining 19 coins have 2^19 outcomes.
A
Answer: (A) 2^19
Question: The manufacturing cost of a shoe is Rs.180 and the transportation lost is Rs.500 for 100 shoes. What will be the selling price if it is sold at 20% gains
(A) Rs 222
(B) Rs 216
(C) Rs 220
(D) Rs 210
(E) Rs 217
Rationale: Explanation :
Total cost of a watch = 180 + (500/100) = 185.
Gain = 20% => SP = 1.2CP = 1.2 X 185 = 222
Answer : A
Answer: (A) Rs 222
Question: Shopkeeper rise price by 33% and gives successive discount of 10% and 15%. What is overall % gain or loss?
(A) 1.745%
(B) 4.745%
(C) 3.745%
(D) 6.745%
(E) 7.745%
Rationale: Let d initial price be 100
33 % rise
now price = 133/100*100 = 133
10% discount
Then price = 133 * 90/100 = 119.7
15 % discount
Then price = 119.7 * 85/100 = 101.745
So Gain = 101.745 - 100 = 1.745
Gain % = Gain * 100 /CP
==> 1.745 * 100 /100 = 1.745%
ANSWER:A
Answer: (A) 1.745%
Question: A relay race covers 1 1/2 miles,and each runner on a team will run 1/4 of a mile. How many runners are needed for a team?
(A) 9
(B) 6
(C) 3
(D) 10
(E) 4
Rationale: Number of runners=total distance/distance each runner runs
=1 1/2 ÷ 1/4
=3/2 ÷ 1/4 = 3/2*4/1
=12/2
= 6.
Answer is B.
Answer: (B) 6
Question: Today Jennifer, who is 30 years old, and her daughter, who is 6 years old, celebrate their birthdays. How many years will pass before Jennifer’s age is twice her daughter’s age?
(A) 18
(B) 20
(C) 22
(D) 24
(E) 25
Rationale: Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.
After x years passes Jennifer’s age will be (30+x) years old, and her daughter’s age will be (6+x) years old. Since the Jennifer’s age is twice her daughter’s age (30+x)= 2 * (6+x) ---> 30+x=12+2x ---> x= 18.
The answer is (A).
Answer: (A) 18
Question: A 3-digit positive integer consists of non zero digits. If exactly two of the digits are the same, how many such integers are possible?
(A) 72
(B) 144
(C) 216
(D) 283
(E) 300
Rationale: here is the answer in pure probability terms.
let the 3 digit number be XYZ
now none of them contain zero --> they can vary from 1 - 9
so lets take the value of X, X can be from 1 - 9, hence X can be selected in 9 ways
since Y =X, after selecting X you can select Y in 1 way only
Z can be an selected from 1 -9 (minus 1 because it cannot be the same as X) in exactly 8 ways
hence total number of ways of selecting the number is 9 * 8 = 72.
BUT we are asked for all possible numbers that can be formed.
So XYZ ( or XXZ in this case) can be moved around in 3 ways
XXZ
XZX
ZXX
hence the total number of numbers is 72 *3 = 216
ANSWER:C
Answer: (C) 216
Question: There were 35 students in a hostel. Due to the admission of 7 new students, ;he expenses of the mess were increased by Rs. 42 per day while the average expenditure per head diminished by Rs 1. Wbat was the original expenditure of the mess?
(A) 320
(B) 120
(C) 400
(D) 420
(E) 514
Rationale: Sol. Let the original average expenditure be Rs. x. Then,
42 (x - 1) - 35x=42	ïƒ³	7x= 84	ïƒ³	x =12.
Original expenditure = Rs. (35 x 12) =Rs. 420. .
ANSWER D
Answer: (D) 420
Question: How many odd numbers are possible between 1 to 10000000? find out the number of odd number of digits?
(A) 2999
(B) 3500
(C) 4000
(D) 4599
(E) 4999999
Rationale: There are always one odd and one even no. And the question is odd no. Between 1 to 10000000
So we have to find no. Between 1 to 10000 so we should not includes 1
10000000/2 -1=4999999
ANSWER:E
Answer: (E) 4999999
Question: A train of length L is traveling at a constant velocity and passes a pole in t seconds. If the same train travelling at the same velocity passes a platform in 3.5t seconds, then what is the length of the platform?
(A) 0.5L
(B) 1.5L
(C) 2.5L
(D) 3.5L
(E) 4.5L
Rationale: The train passes a pole in t seconds, so velocity v = L/t
(L+P)/v = 3.5t
(L+P) / (L/t) = 3.5t
P = 2.5L
The answer is C.
Answer: (C) 2.5L
Question: In how many days does B alone complete the work
1. B and C together can complete the work in 8 days
2. A and B together can complete the work in 12 days
(A) Statement 1 alone is sufficient
(B) Statement 2 alone is sufficient
(C) Statement 1 and 2are sufficient
(D) Statement 1 and 2are not sufficient
(E) None of these
Rationale: Explanation:
We cannot find the work done by B.
If C+A work is given we can find it by
B’s work = (A+B+C) work - (A+C) work
Answer: Option D
Answer: (D) Statement 1 and 2are not sufficient
Question: A project scheduled to be carried out over a single fiscal year has a budget of $12,600, divided into12 equal monthly allocations. At the end of the fourth month of that fiscal year, the total amount actually spent on the project was $5,580. By how much was the project over its budget?
(A)  $380
(B)  $540
(C)  $1,050
(D)  $1,380
(E)  $1,430
Rationale: Difficulty level: 600
Each month's budget = 12600/12 = 1050
Budget for 4 months = 4*1050 = 4200
Actual amount spent = 5580
Amount spent over the budget = 5580 - 4200 = 1380
Answer (D),
Regards,
Answer: (D)  $1,380
Question: A student's mark was wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by 1/2. What is the number of students in the class?
(A) 20
(B) 30
(C) 10
(D) 40
(E) 50
Rationale: Let the total number of students = x
The average marks increased by 1/2 due to an increase of 83 - 63 = 20 marks.
But total increase in the marks = (1/2)x=x/2
Hence we can write as
x/2=20
⇒x=20×2=40
Answer is D.
Answer: (D) 40
Question: The length of a rectangle is halved, while its breadth is tripled. Wat isthe % change in area?
(A) 20%
(B) 40%
(C) 50%
(D) 60%
(E) 70%
Rationale: Let original length = x and original breadth = y.
Original area = xy.
New length = x .
2
New breadth = 3y.
New area = x x 3y = 3 xy.
2 2
Increase % = 1 xy x 1 x 100 % = 50%.
2 xy
C
Answer: (C) 50%
Question: In 1998 the profits of company N were 10 percent of revenues. In 1999, the revenues of company N fell by 20 percent, but profits were 10 percent of revenues. The profits in 1999 were what percent of the profits in 1998?
(A) 80%
(B) 105%
(C) 120%
(D) 124.2%
(E) 138%
Rationale: 0,08R = x/100*0.1R
Answer A
Answer: (A) 80%
Question: Can you solve it?
2+3=8,
3+7=27,
4+5=32,
5+8=60,
6+7=72,
7+8=??
(A) 68
(B) 78
(C) 88
(D) 98
(E) 56
Rationale: 2+3=2*[3+(2-1)]=8
3+7=3*[7+(3-1)]=27
4+5=4*[5+(4-1)]=32
5+8=5*[8+(5-1)]=60
6+7=6*[7+(6-1)]=72
therefore
7+8=7*[8+(7-1)]=98
x+y=x[y+(x-1)]=x^2+xy-x
correct answer is D)98
Answer: (D) 98
Question: If x and y are positive integers, and 3x^2=3y, then which of the following must be a multiple of 9?
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 A
Answer: (A) I only
Question: Find the unit's digit in (264)^102 + (264)^103
(A) 4
(B) 1
(C) 5
(D) 0
(E) 2
Rationale: Required unit's digit = unit's digit in (4)^102 + (4)^103.
Now, 4^2 gives unit digit 6.
Therefore, (4)^102 gives unit digit 6.
Therefore, (4)^103 gives unit digit of the product (6 x 4) i.e., 4.
Hence, unit's digit in (264)m + (264)103 = unit's digit in (6 + 4) = 0.
Answer is D.
Answer: (D) 0
Question: The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water?
(A) 7
(B) 2
(C) 8
(D) 6
(E) 3
Rationale: S = 4
M = x
DS = x + 4
US = x - 4
6/(x + 4) + 6/(x - 4) = 2
x = 8
Answer:C
Answer: (C) 8
Question: For which of the following does g(a)−g(b)=g(a−b) for all values of a and b?
(A) g(x)=x^2
(B) g(x)=x/2
(C) g(x)=x+5
(D) g(x)=2x−1
(E) g(x)=|x|
Rationale: To solve this easiest way is just put the value and see that if it equals or not.
with option 1. g(a) = a^2 and g(b) = b^2
so L.H.S = a^2 - b^2
and R.H.S = (a-b)^2 ==> a^2 + b^2 -2ab.
so L.H.S not equal to R.H.S
with option 2. g(a) = a/2 and g(b) = b/2
L.H.S = a/2 - b/2 ==> 1/2(a-b)
R.H.S = (a-b)/2
so L.H.S = R.H.S which is the correct answer.
answer:B
Answer: (B) g(x)=x/2
Question: Find the simple interest on Rs.500 for 9 months at 6 paisa per month?
(A) Rs.345
(B) Rs.270
(C) Rs.275
(D) Rs.324
(E) Rs.300
Rationale: Explanation:
I = (500*9*6)/100 = 270
Answer IS B
Answer: (B) Rs.270
Question: The cost price of 13 articles is equal to the selling price of 11 articles. Find the profit percent?
(A) 18 2/17
(B) 18 2/11
(C) 18 2/15
(D) 18 2/19
(E) 18 2/12
Rationale: 13 CP = 11 SP
11 --- 2 CP
100 --- ?
=>18 2/11%
Answer:B
Answer: (B) 18 2/11
Question: 3+33+333+3.33=?
(A) 362.33
(B) 372.33
(C) 702.33
(D) 702
(E) None of them
Rationale: 3
33
333
3.33
----------
372.33
----------
Answer is B
Answer: (B) 372.33
Question: How long will it take for a sum of money to grow from Rs.1250 to Rs.10,000, if it is invested at 12.5% p.a simple interest?
(A) 38
(B) 56
(C) 22
(D) 088
(E) 11
Rationale: Explanation:
Simple interest is given by the formula SI = (pnr/100), where p is the principal, n is the numberof years for which it is invested, r is the rate of interest per annum
In this case, Rs. 1250 has become Rs.10,000.
Therefore, the interest earned = 10,000 – 1250 = 8750.
8750 = [(1250 x n x 12.5)/100]
=> n = 700 / 12.5 = 56 years.
Answer: B) 56years
Answer: (B) 56
Question: If the operation Ø is defined for all positive integers x and w by x Ø w = (2^x)/(2^w) then (3 Ø 1) Ø 2 = ?
(A) 2
(B) 4
(C) 8
(D) 16
(E) 32
Rationale: 3 Ø 1 = 2^3/2^1 = 4
4 Ø 2 = 2^4/2^2 = 4
The answer is B.
Answer: (B) 4
Question: The profit obtained by selling an article for Rs. 66 is the same as the loss obtained by selling it for Rs. 52. What is the cost price of the article?
(A) Rs. 40
(B) Rs. 50
(C) Rs. 49
(D) Rs. 59
(E) None of these
Rationale: S.P 1- C.P = C.P – S.P 2
66 - C.P = C.P - 52
2 C.P = 66 + 52;
C.P = 118/2 = 59
ANSWER:D
Answer: (D) Rs. 59
Question: If 13 = 13w/(1-w) ,then (2w)2 =
(A) 1/4
(B) 1/2
(C) 1
(D) 2
(E) 3
Rationale: 13-13w=13w
26w=13
w=1/2
2w=1
2w*2=1*2=2
ANSWER:D
Answer: (D) 2
Question: If a*b*c=130, b*c*d = 65, c*d*e=750 and d*e*f=250 the (a*f)/(c*d) = ?
(A) 1/2
(B) 2/3
(C) 3/4
(D) 4/3
(E) None of these
Rationale: Explanation :
aâˆ—bâˆ—c/bâˆ—câˆ—d= 130/65 => a/d = 2
dâˆ—eâˆ—f/câˆ—dâˆ—e= 250/750 => f/c = 1/3
a/d* f/c = 2 * 1/3 = 2/3
Answer : B
Answer: (B) 2/3
Question: A can do a piece of work in 7 days of 9 hours each and B alone can do it in 6 days of 7 hours each.how long will they take it to do working together
8 2/5 hours a day?
(A) 3 days
(B) 4 days
(C) 5 days
(D) 6 days
(E) 7 days
Rationale: A's work per hour=1/63
B's work per hour=1/42
A & B's work per hour together=(1/63)+(1/42)=5/126
so a & B together complete the work in 126/5 hours...
if they work 8 2/5=42/5 hours a day,
it will take (126/5)/(42/5) days=(126/5)*(5/42)=3 days...
ANSWER:A
Answer: (A) 3 days
Question: Find value of x from given equation 2x + 1 = -17
(A) -8
(B) -9
(C) -7
(D) 7
(E) 6
Rationale: 1. Subtract 1 from both sides:
2x + 1 - 1 = -17 - 1
2. Simplify both sides:
2x = -18
3. Divide both sides by 2:
4. Simplify both sides:
x = -9
B
Answer: (B) -9
Question: For any integer k greater than 1, the symbol k* denotes the product of all integers between 1 and k, inclusive. If k* is a multiple of 1701 what is the least possible value of k?
(A) 8
(B) 10
(C) 12
(D) 14
(E) 16
Rationale: 1701 = 3*3*3*3*3*7
Thus k must include numbers at least up to the number 12 so that there are at least five appearances of 3 (that is: 3, 6, 9=3*3, and 12).
The answer is C.
Answer: (C) 12
Question: A, B, K start from the same place and travel in the same direction at speeds of 30 km/hr, 40 km/hr, 100 km/hr respectively. B starts two hours after A. If B and K overtake A at the same instant, how many hours after A did K start?
(A) 4.2
(B) 4.8
(C) 5.6
(D) 6.4
(E) 7.2
Rationale: In 2 hours, A travels 60 km.
B can catch A at a rate of 10 km/hr, so B catches A 6 hours after B starts.
So A and B both travel a distance of 240 km.
C needs 2.4 hours to travel 240 km, so C leaves 5.6 hours after A.
The answer is C.
Answer: (C) 5.6
Question: What is the solution of the equations x - y = 10 and (x + y)-1 = 2 ?
(A) x = 3.2, y = 2.3
(B) x = 5.25, y = 4.75
(C) x = 2, y = 1.1
(D) x = 1.2, y = 0.3
(E) None
Rationale: Answer
x - y = 10 ...(i)
and 1/(x + y)-1=2
⇒ 1/ (x + y) = 2
⇒ 2(x + y) =1
⇒ x + y = 1/2 ...(ii)
On solving Eqs.(i) and (ii),we get
x = 5.25
and y = 4.75
Correct Option: B
Answer: (B) x = 5.25, y = 4.75
Question: The sum of the ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?
(A) 4 years
(B) 8 years
(C) 10 years
(D) None of these
(E) 15 years
Rationale: Explanation:
Let the ages of the children be x, (x + 3), (x + 6), (x + 9) and (x +12) years.
Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50
5x = 20 => x = 4.
Age of youngest child = x = 4 years.
ANSWER IS A
Answer: (A) 4 years
Question: If X+Y = 2X-2Z, X-2Y = 4Z and X+Y+Z = 21, what is the value of Y/Z?
(A) -4.5.
(B) -2.
(C) -1.7.
(D) 3.
(E) 2.5.
Rationale: Given : X+Y = 2X-2Z, --> eq 1
X-2Y = 4Z --> eq 2
X+Y+Z = 21 -->eq 3.
Now we are asked to find the value of Y/Z.
Now let choose some option randomly,
Take C , which is 3, I randomly chose this value as it is positive :)
Y/Z = 3 , this is the value we need to get.
Then Y = 3Z -- eq 4
Sub this in eq 1.
X + 3Z = 2X - 2Z
=> X = 5Z -->eq 5.
Sub X and Y value in eq 3.
5Z + 3Z + Z = 21
=> Z = 21/9. Now sub this value to get Y , we get Y = 21/3.
Then Y/Z = 21/3 / 21/9 = we get 3 again. So this option is correct.
Answer: option C is correct.
Answer: (C) -1.7.
Question: A garrison of 150 men has provisions for 31 days. At the end of 16 days, a reinforcement arrives, and it is now found that the provisions will last only for 5 days more. What is the reinforcement?
(A) 150
(B) 450
(C) 400
(D) 600
(E) 300
Rationale: 150 ---- 31
150 ---- 15
x -----5
x*5 = 150*15
x = 450
150
-------
300
Answer: E
Answer: (E) 300
Question: The probability that a convenience store has no iced tea is 50%. If Karl is stopping by 2 convenience stores on his way to work, what is the probability thatat least oneof the stores will not have a can of iced tea?
(A) 1/8
(B) 1/4
(C) 1/2
(D) 3/4
(E) 7/8
Rationale: p=1-1/2^2(all stores have iced tea)=3/4
D
Answer: (D) 3/4
Question: The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) 267 m
(B) 256 m
(C) 245 m
(D) 627 m
(E) 167 m
Rationale: Speed
= (45 * 5/18) m/sec = (25/2) m/sec. Time
= 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30 = 25/2 ==> 2(130 + X)
= 750 ==> X
= 245 m.
Answer: C
Answer: (C) 245 m
Question: A searchlight on top of the watch-tower makes 3 revolutions per minute. What is the probability that a man appearing near the tower will stay in the dark for at least 5 seconds?
(A) 1/4
(B) 1/3
(C) 1/2
(D) 2/3
(E) 3/4
Rationale: 3 revolutions per minute = 1 revolution every 20 seconds
So no matter what anybody appearing at the tower cannot stay in the dark for more than 20 seconds. This will be our total number of possibilities i.e the denominator.
P(man in dark for at least 5 seconds) = 1 - P (man in dark for max of 5 seconds) = 1 - 5/20 = 1 - 1/4 = 3/4
or the other way would be:
P(man in dark for at least 5 seconds) is like saying he can be in dark for 5,6,7...all the way to 20 seconds because that is the max. In this approach it would be 15/20 seconds = 3/4.
Answer: (E) 3/4
Question: A and B working saperately can do a piece of work in 12 and 18 hours respectively. If they work for 6 hour alternately with B beginning, in how many hours will the work be completed?
(A) 9 hours
(B) 15 hours
(C) 13 ½ hours
(D) 12 ½ hours
(E) 16 hours
Rationale: Explanation:
A and B 2 hours work = 1/12 + 1/18 = 5/36
work done by A and B during 6 pairs
i.e 12 hours = 6 * 5/36 = 5/6
Remaining work = 1 – 5/6 = 1/6
1/6 of work and this work done by B only = 18* 1/6 = 3 hours
Hence the total time take is 15 hours
Answer: Option B
Answer: (B) 15 hours
Question: At the end of a business conference, ten people present shake hands with each other once. How many handshakes will be there all together?
(A) 20
(B) 45
(C) 55
(D) 90
(E) None
Rationale: Explanation : . Total no. of handshakes = (9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1) = 45
Answer B
Answer: (B) 45
Question: What is the smallest of six consecutive odd integers whose average (arithmetic mean) is c + 2?
(A) c - 5
(B) c - 3
(C) c- 1
(D) c
(E) c + 1
Rationale: Since the numbers are consecutive odd integers, mean = median = 3rd integer + 4th integer /2
And 1st integer= 3rd integer- 4
let's say 3rd integer = n and 4th integer = n+2
2n+2/2= c+2
n= c+1
1st integer= c+1-4= c-3
B is the answer
Answer: (B) c - 3
Question: A relay has a series of 5 circuits in a line. The even-numbered circuits are control circuits; the odd are buffer circuits. If both a control circuit and the buffer circuit immediately following it both fail in that order, then the relay fails. The probability of circuit one failing is 3/8; circuit two, 1/9; circuit three, 3/10; circuit four, 3/4; and circuit five, 2/5 .What is the probability that the relay fails?
(A) 9/80
(B) 3/10
(C) 303/800
(D) 97/300
(E) 497/800
Rationale: The first circuit doesn't matter.
Prob(relay fails) = 1 - Prob(relay succeeds)
Prob(2+3 work) = 1 - 1/30 = 29/30
Prob(4+5 work) = 1 - 3/10 = 7/10
Prob(relay fails) = 1 - Prob(2+3 work AND 4+5 work) = 1 - (29/30)(7/10) = 1 - 203/300 = 97/800
D
Answer: (D) 97/300
Question: A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 650 m long?
(A) 65 sec
(B) 89 sec
(C) 100 sec
(D) 150 sec
(E) 250 sec
Rationale: Speed = 240/24 = 10 m/sec.
Required time = (240 + 650)/10 = 89 sec
ANSWER:B
Answer: (B) 89 sec
Question: Which of the following does NOT have a divisor greater than 1 that is the square of an integer?
(A) 28
(B) 32
(C) 49
(D) 62
(E) 25
Rationale: Prime Factorization
28=2*2*7=2^2*7. Includes a perfect square of 4.
32=2*2*2*2*2=4^2*2. Includes the perfect square of 16.
49=7*7. Is a perfect square.
62=2*31. No perfect square here, so a possibility.
25= 5*5. Is a perfect square.
All but 62 have perfect squares as a factor so D is the correct answer.
28=2*2*7=2^2*7. Perfect square of 4.
32=2*2*2*2*2=4^2*2. Perfect square of 16.
49=7*7. Perfect square.
62=2*31. No perfect square.
25= 5*5. Perfect square.
Answer: (D) 62
Question: A 340-liter solution of Kola is made from 88% water, 5% concentrated Kola and the rest is made from sugar. If 3.2 liters of sugar, 10 liter of water and 6.8 liters of concentrated Kola were added to the solution, what percent of the solution is made from sugar?
(A) 6%.
(B) 7.5%.
(C) 9.2%.
(D) 10.5%.
(E) 11%.
Rationale: Denominator:
340+10+3.2+6.8=360
Numerator:
340(1-.88-.05)+3.2
340(0.07)+3.2
23.8+3.2
27
Ratio:
27/360=3/40
Answer: B
Answer: (B) 7.5%.
Question: 7 men, 5 women and 8 children were given as assignment of distributing 2000 books to students in a school over a period of 3 days. All of them distributed books on the 1st day. One of the 2nd day 2 women and 3 children remained absent and on the 3rd day 3 men and 5 children remained absent. If the ratio of the no. of books distributed in a day by a man, a woman & a child was 5 : 4 : 2 respectively, a total of approximately how many books were distributed on the second day?
(A) 340
(B) 450
(C) 600
(D) 650
(E) 700
Rationale: Sol. Let the books distributed by man, a woman and a child be 5x, 4x and 2x respectively.
∴ No. of books distributed in 1st day
= 7×5x+5×4x+8×2x=71x
No. of books distributed in 1Ind day
=7×5x+3×4x+5×2x=57x
And no. of books distributed in IIIrd day
=4×5x+5×4x+3×2x=46x
71x + 57x + 46x = 2000, x = 2000/174
57x=2000/174×57=650
D
Answer: (D) 650
Question: -24*29+1240=?
(A) -544
(B) 584
(C) 544
(D) 345
(E) None of these
Rationale: => -24*(30-1)+1240;
=> -(24*30)+24+1240;
=> -720+1264=544.
Correct Option: C
Answer: (C) 544
Question: In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?
(A) 14
(B) 25
(C) 63
(D) 74
(E) 36
Rationale: Required number of ways = (7C5 x 3C2) = (7C2 x 3C1) = = 63.
Ans: C
Answer: (C) 63
Question: What is the sum of the numbers between 1 and 12, inclusive?
(A) 99
(B) 65
(C) 79
(D) 78
(E) 80
Rationale: Sol. add the numbers between 1 and 12.
answer is D, 78.
Answer: (D) 78
Question: The area of a parallelogram is 128sq m and its altitude is twice the corresponding base. Then the length of the base is?
(A) 8
(B) 9
(C) 5
(D) 3
(E) 2
Rationale: 2x * x = 128 => x
= 8
Answer:A
Answer: (A) 8
Question: If a(a + 2) = 99 and b(b + 2) = 99, where a ≠ b, then a + b =
(A) -2
(B) -5
(C) -8
(D) -10
(E) -12
Rationale: i.e. if a = 9 then b = -11
or if a = -11then b = 9
But in each case a+b = -11+9 = -2
Answer: A
Answer: (A) -2