mathewhe/aqua_rat huggingface dataset:
Question: The average age of 10 students in a class is 15 years. If the age of teacher is also included, the average becomes 16 years, find the age of the teacher.
(A) 30
(B) 26
(C) 28
(D) 29
(E) 45
Rationale: Explanation:
If teacher's age is 15 years, there is no change in the average. But teacher has contributed 1 year to all the students along with maintaining his age at 16.
Age of teacher = Average age of all + Total increase in age
= 16 + (1 x 10 ) = 26 years
Answer:B
Answer: (B) 26
Question: A man goes to his office from his house at a speed of 3 km/hr and returns at a speed of 2 km/hr. If he takes 5 hours in going and coming, what is the distance between his house and office?
(A) 8
(B) 7
(C) 4
(D) 6
(E) 09
Rationale: If a car covers a certain distance at x kmph and an equal distance at y kmph,the average speed of the whole journey = 2xyx+y kmphHence, average speed = 2×3×22+3=125 km/hrTotal time taken = 5 hours⇒Distance travelled=125×5=12 km⇒Distance between his house and office =122=6 km
Answer : D
Answer: (D) 6
Question: Half a number plus 7 is 17.What is the number?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 20
Rationale: Let x be the number. Always replace "is" with an equal sign
(1/2)x + 7 = 17
(1/2)x = 17 - 7
(1/2)x = 20
x = 20
correct answer is E
Answer: (E) 20
Question: A bike agent buys 30 bicycles, of which 8 are first grade and the rest are second grade, for Rs 3,150, Find at what price he must sell the first grade bikes so that if he sells the second grade bikes at three quarters of the price, he may make a profit of 40% on his outlay.
(A) Rs 200
(B) Rs 240
(C) Rs 180
(D) Rs 210
(E) Rs 230
Rationale: Suppose the price of first grade bike = Rs X
And the price of second grade bike = Rs Y
Therefore, 8X + 22Y = 3150
Suppose he sells the first grade bike at the rate of Rs Z per cycle
Therefore, 8Z + 22 x 3/4Z = 3150 + 40% of 3150
98Z = 17640 => Z = 180
S.P. of the first grade bike = Rs 180
S.P. of the second grade bike = Rs 135
ANSWER:C
Answer: (C) Rs 180
Question: A drawer holds 5 red hats and 5 blue hats. What is the probability of getting exactly three red hats or exactly three blue hats when taking out 8 hats randomly out of the drawer and returning each hat before taking out the next one?
(A) 3/4
(B) 5/8
(C) 7/16
(D) 15/32
(E) 31/64
Rationale: Let's find the probability of getting exactly 3 red hats.
One possible case is red-red-red-blue-blue-blue-blue-blue.
The probability of this is 1/2*1/2*1/2*1/2*1/2*1/2*1/2*1/2 = 1/256
There are 8C3 = 56 such cases so we need to multiply this by 56.
P(exactly 3 red hats) = 56*1/256 = 7/32
Clearly the probability of getting exactly 3 blue hats will also be 7/32.
The sum of the probabilities is 7/32+7/32 = 14/32 = 7/16
The answer is C.
Answer: (C) 7/16
Question: If d is the smallest positive integer such that 3,150 multiplied by d is the square of an integer, then d must be
(A)  2
(B)  5
(C)  6
(D)  7
(E)  14
Rationale: Solution:
This problem is testing us on the rule that when we express a perfect square by its unique prime factors, every prime factor's exponent is an even number.
Let’s start by prime factorizing 3,150.
3,150 = 315 x 10 = 5 x 63 x 10 = 5 x 7 x 3 x 3 x 5 x 2
3,150 = 2^1 x 3^2 x 5^2 x 7^1
(Notice that the exponents of both 2 and 7 are not even numbers. This tells us that 3,150 itself is not a perfect square.)
We also are given that 3,150 multiplied by d is the square of an integer. We can write this as:
2^1 x 3^2 x 5^2 x 7^1 x d = square of an integer
According to our rule, we need all unique prime factors' exponents to be even numbers. Thus, we need one more 2 and one more 7. Therefore, d = 7 x 2 = 14
Answer is E.
Answer: (E)  14
Question: John takes 6 hrs to print 32 pages. Peter takes 5hrs to print 40 pages. In how many hours they will print 110 pages together ?
(A) 8 hours
(B) 8 hours 15 minutes
(C) 9 hours 15 minutes
(D) 11 hours
(E) 12 hours
Rationale: Ram can type 32/6 pages per hour
Shaam can type 8 pages per hourThey can type 32/6 + 8 = 40/3 pages per hour
So they will take 110/40 × 3 = 33/4 hours or 8 hours 15 minutes
B)
Answer: (B) 8 hours 15 minutes
Question: 70,78, 80,85,90,105,105,130,130,130
The list consists of the times in seconds that it took each of the 10 school children to run a distance of 400 mts . If the standard deviation of the 10 running times is 22.4, rounded to the nearest tenth of a second, how many of the 10 running times are more than 1 standard deviation below the mean of the 10 running times.
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: How many of the 10 running times are more than one SD below the meanmeans how many data points from given 10 are less thanmean-1SD.
We are given that SD=22.4, so we should find mean --> mean=100 --> there is only 1 data points below 100-22.4=77.6, namely 70
Answer: A.
Answer: (A) 1
Question: The Shopkeeper increased the price of a product by 25% so that customer finds it difficult to purchase the required amount. But somehow the customer managed to purchase only 70% of the required amount. What is the net difference in the expenditure on that product?
(A) 11%
(B) 12%
(C) 12.5%
(D) 13%
(E) 14%
Rationale: Quantity X Rate = Price
1 x 1 = 1
0.7 x 1.25 = 0.875
Decrease in price = (0.125/1) × 100 = 12.5%
C
Answer: (C) 12.5%
Question: The greatest number of four digits which is divisible by 25, 40, 54 and 75 is:
(A) 5000
(B) 5400
(C) 5600
(D) 5800
(E) 5200
Rationale: Greatest number of 4-digits is 9999.
L.C.M. of 25, 40, 54 and 75 is 600.
On dividing 9999 by 5400, the remainder is 4599.
Required number (9999 - 4599) = 5400.
Answer: Option B
Answer: (B) 5400
Question: The length of a rectangle is increased to 2 times its original size and its width is increased to 3 times its original size. If the area of the new rectangle is equal to 1800 square meters, what is the area of the original rectangle?
(A) 100 square meters
(B) 200 square meters
(C) 300 square meters
(D) 400 square meters
(E) 500 square meters
Rationale: If L and W be the original length and width of the rectangle and its area is given by
L ? W
After increase the length becomes 2 L and the width becomes 3 W. The area is then given by (2 L) ? (3 W) and is known. Hence
(2 L) ? (3 W) = 1800
Solve the above equation to find L ? W
6 L ? W = 1800
L ? W = 1800 / 6 = 300 square meters , area of original rectangle
correct answer C
Answer: (C) 300 square meters
Question: A man invests some money partly in 12% stock at 132 and partly in 10% stock at 80.To obtain equal dividends from both,he must invest the money in the ratio :
(A) 3 : 4
(B) 3 : 5
(C) 11:8
(D) 16 : 15
(E) None
Rationale: Solution
For an income of Rs. 1 in 12% stock at 132, investment = Rs. (132/12)= Rs. 11 .
For an income of Rs. 1 in 10% stock at 80, investment = Rs.(80/10) = Rs. 8.
∴ Ratio of investments = 11:8 =11:8
Answer C
Answer: (C) 11:8
Question: Working alone, Jerry finishes cleaning half the house in a third of the time it takes Nick to clean the entire house alone. Jerry alone cleans the entire house in 6 hours. How many hours will it take Nick and Jerry to clean the entire house if they work together?
(A) 1.5
(B) 2
(C) 2.4
(D) 3
(E) 3.6
Rationale: Answer is 3.6 hours.
Jerry does the complete house in 6 hours while Nick does it in 9 hours. 1/ (1/6+1/9)= 3.6
answer is E
Answer: (E) 3.6
Question: .008/?= .01
(A) .8
(B) .09
(C) .009
(D) .0009
(E) None of them
Rationale: Let .008/x = .01;
Then x = .008/.01
= .8/1
= .8
Answer is A
Answer: (A) .8
Question: I. a3 - 988 = 343,
II. b2 - 72 = 49 to solve both the equations to find the values of a and b?
(A) a > b
(B) a ≥ b
(C) a < b
(D) a ≤ b
(E) a = b or the relationship between a and b cannot be established.
Rationale: Explanation:
a3 = 1331 => a = 11
b2 = 121 => b = ± 11
a ≥ b
B)
Answer: (B) a ≥ b
Question: Tanks Q and B are each in the shape of a right circular cylinder. The interior of tank Q has a height of 10 meters and a circumference of 8 meters, and the interior of tank B has a height of 8 meters and a circumference of 10 meters. The capacity of tank Q is what percent of the capacity of tank B?
(A) 75%
(B) 80%
(C) 100%
(D) 120%
(E) 125%
Rationale: B.
For Q, r=8/2pi. Its capacity = (4pi)^2 * 10= 160pi
For B, r=10/pi. Its capacity = (5pi)^2 *8 = 200pi
Q/B = 160pi/200pi = 0.8
Answer: (B) 80%
Question: 4 dice are thrown simultaneously on the board. Find the probability show the same face.
(A) 1/115
(B) 2/113
(C) 1/216
(D) 2/121
(E) 3/114
Rationale: The total number of elementary events associated to the random experiments of throwing four dice simultaneously is:
=6×6×6×6=64=6×6×6×6=64
n(S)=64n(S)=64
Let XX be the event that all dice show the same face.
X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}
n(X)=6n(X)=6
Hence required probability,
=n(X)n(S)=664=n(X)n(S)=664
=1/216
C
Answer: (C) 1/216
Question: 10 men, working 4 hours a day can complete a work in 18 days. How many hours a day must 15 men work to complete the work in 12 days ?
(A) 4 hours a day
(B) 5 hours a day
(C) 6 hours a day
(D) 7 hours a day
(E) 8 hours a day
Rationale: Explanation:
More Men, Less Hours {Indirect Proportion}
Less Days, More Hours {Indirect Proportion}
[men 15 10
days 12 18] ::4:x
=>xâˆ—15âˆ—12=10âˆ—18âˆ—4
=>x=10âˆ—18âˆ—4/ 15âˆ—12
=>x=4
Option A
Answer: (A) 4 hours a day
Question: If (x + 10)^2 = 144, which of the following could be the value of 2x?
(A) –26
(B) –22
(C) –44
(D) 66
(E) 13
Rationale: You can also get to the answer by backsolving using answer choices
Starting with x= -22
(x + 10)^2 = 144
(-22 + 10)^2 = 144 =====> (-12)^2 = 144 Bingo, Clearly, among the answer choices only -22 will result in 144 in the equation so x must be -22,
Then 2x = 2 * -22 = -44
Answer: C
Answer: (C) –44
Question: Let f(x,y) be defined as the remainder when (x–y)! is divided by x. If x=36, what is the maximum value of y for which f(x,y)=0?
(A) 9
(B) 12
(C) 18
(D) 20
(E) 30
Rationale: The question is finding y such that (36-y)! is a multiple of 36. That means we need to have 2^2*3^2 in (36-y)!
6! is the smallest factorial number with 2^2*3^2 as a factor.
36-y = 6
y = 30
The answer is E.
Answer: (E) 30
Question: What percent is 6 gm of 1 kg?
(A) 0.06%
(B) 0.6%
(C) 0.006%
(D) 6%
(E) None of these
Rationale: Explanation:
1 kg = 1000 gm
6/1000 * 100 = 600/1000
=3/5 = 0.6 %
Answer: Option B
Answer: (B) 0.6%
Question: Ten years ago A was half of B in age. If the ratio of their present ages is 3 : 4, what will be the total of their present ages
(A) 30
(B) 35
(C) 37
(D) 41
(E) 42
Rationale: Explanation:
Let A's age 10 years ago = x years.
Then, B's age 10 years ago = 2x years.
(x + 10) / (2x+ lO) = 3/4
=> x = 5.
So, the total of their present ages =(x + 10 + 2x + 10)
= (3x + 20) = 35 years
Option B
Answer: (B) 35
Question: The least number, which when divided by 12, 15, 20 and 54 leaves in each case a remainder of 5 is:
(A) 545
(B) 488
(C) 542
(D) 548
(E) 560
Rationale: Required number = (L.C.M. of 12, 15, 20, 54) + 5
= 540 + 5
= 545.
answer :A
Answer: (A) 545
Question: A can do a piece of work in 12 days. He worked for 15 days and then B completed the remaining work in 10 days. Both of them together will finish it in.
(A) 12 1/2 days
(B) 12 1/9 days
(C) 12 8/2 days
(D) 17 1/2 days
(E) 32 1/2 days
Rationale: 15/25 + 10/x = 1 => x = 25
1/25 + 1/25 = 2/25
25/2 = 12 1/2 days
Answer: A
Answer: (A) 12 1/2 days
Question: The average age of students of a class is 15.8 years. The average age of boys in the class is 16.4 years and that of the girls is 15.4 years. The ration of the number of boys to the number of girls in the class is?
(A) 2:6
(B) 2:3
(C) 2:5
(D) 2:1
(E) 2:4
Rationale: Let the ratio be k : 1. Then,
k * 16.4 + 1 * 15.4 = (k + 1) * 15.8
= (16.4 - 15.8)k = (15.8 - 15.4)
= k = 0.4/0.6 = 2/3
Required ratio = 2/3 : 1 = 2:3.
Answer:B
Answer: (B) 2:3
Question: If 7875 / 5.25 = 1500, then 787.5 / 52.5 is equal to ?
(A) 15
(B) 19
(C) 12
(D) 14
(E) 16
Rationale: Answer
Given expression 787.5 / 52.5 = 7875 / 525
= 7875 / (525 x 100)
= 1500 / 100
15
Correct Option: A
Answer: (A) 15
Question: The ratio of number of boys and girls in a school is 2:5. If there are 490 students in the school, find the number of girls in the school?
(A) 150
(B) 350
(C) 300
(D) 370
(E) 280
Rationale: Let the number of boys and girls be 2x and 5x
Total students = 490
Number of girls in the school = 5*490/7 = 350
Answer is B
Answer: (B) 350
Question: What percent is 320 gm of 1 kg?
(A) 25%
(B) 40%
(C) 10%
(D) 8%
(E) 32%
Rationale: 1 kg = 1000 gm
320/1000 Ã— 100 = 32000/1000
=32 %
Answer is E
Answer: (E) 32%
Question: A train moves 100m in 2 sec and then find the speed travelled?
(A) 28
(B) 900
(C) 50
(D) 180
(E) none
Rationale: Length = Speed * time
Speed = L/T
S = 100m/2sec
S = 50 M/Sec
Speed= 50*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 180Kmph.Answer:D
Answer: (D) 180
Question: A selection committee is to be chosen consisting of 5 ex-technicians. Now there are 12 representatives from four zones. It has further been decided that if Mr. X is selected, Y and Z will not be selected and vice-versa. In how many ways it can be done?
(A) 572
(B) 672
(C) 472
(D) 372
(E) None
Rationale: Solution:
10C5: when both are not included.
10C4: when one of them is included.
Number of ways = 10C5 +10C4+ 10C4 = 672
Answer: Option B
Answer: (B) 672
Question: 7 men and 2 boys working together can do four times as much work as a man and a boy. Working capacity of man and boy is in the ratio
(A) 1:2
(B) 1:3
(C) 2:1
(D) 2:3
(E) None of these
Rationale: Explanation:
Let 1 man 1 day work = x
1 boy 1 day work = y
then 7x + 2y = 4(x+y)
=> 3x = 2y
=> x/y = 2/3
=> x:y = 2:3
Option D
Answer: (D) 2:3
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If four marbles are picked at random, what is the probability that none is blue?
(A) 33/16
(B) 33/91
(C) 33/29
(D) 33/18
(E) 33/11
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. When four marbles are picked at random, then the probability that none is blue is
= ¹²C₄/¹⁵C₄
= (12 * 11 * 10 * 9)/(15 * 14 * 13 * 12)
= 33/91
Answer: B
Answer: (B) 33/91
Question: An empty pool being filled with water at a constant rate takes 8hours to fill to 4/5 of its capacity.how much more time will it take to finish filling the pool?
(A) 5hr 30min
(B) 5hr 20min
(C) 4hr 48min
(D) 3 hr 12min
(E) 5hr 40 min
Rationale: As pool is filled to 3/5 of its capacity then 2/5 of its capacity is left to fill.
To fill 3/5 of the pool took 8 hours --> to fill 2/5 of the pool will take 8/(3/5)*2/5=16/3 hours = 5 hours 20 minutes (because if t is the time needed to fill the pool then t*3/5=8 --> t=8*5/3 hours --> to fill 2/5 of the pool 8*5/3*2/5=16/3 hours will be needed).
Or plug values: take the capacity of the pool to be 5 liters --> 3/5 of the pool or 3 liters is filled in 8 hours, which gives the rate of 3/8 liters per hour --> remaining 2 liters will require: time = job/rate = 2/(3/8) = 16/3 hours = 5 hours 40 minutes.
Answer: E.
Answer: (E) 5hr 40 min
Question: The radii of two cones are in ratio 2:1, their volumes are equal. Find the ratio of their heights.
(A) 1:4
(B) 1:3
(C) 1:2
(D) 1:5
(E) None of these
Rationale: Explanation:
Let their radii be 2x, x and their heights be h and H resp.
Then,
Volume of cone =1/3πr2h
1/3∗π∗(2x)2∗h /1/3∗π∗x2∗H
=>hH=14
=>h:H=1:4
Option A
Answer: (A) 1:4
Question: A sum of Rs.312 was divided among 100 boys and girls in such a way that the boy gets Rs.3.60 and each girl Rs. 2.40 the number of girls is
(A) 35
(B) 40
(C) 45
(D) 50
(E) 55
Rationale: Explanation:
Step (i): Let x be the number of boys and y be the number of girls.
Given total number of boys and girls = 100
x+y=100 -------------- (i)
Step (ii): A boy gets Rs. 3.60 and a girl gets Rs. 2.40
The amount given to 100 boys and girls = Rs. 312
3.60x + 2.40y = 312 -------------- (ii)
Step (iii):
Solving (i) and (ii)
3.60x + 3.60y = 360 --------- Multiply (i) by 3.60
3.60x + 2.40y = 312 --------- (ii)
1.20y = 48
y = 48 / 1.20
= 40
Number of girls = 40
Answer: B
Answer: (B) 40
Question: A and B together can do a piece of work in 6 days and A alone can do it in 13 days. In how many days can B alone can do it?
(A) 12 days
(B) 15 days
(C) 78/7 days
(D) 21 days
(E) 22/7 days
Rationale: Explanation:
A and B can do work 1/6 in 1 day
A alone can do 1/13 work in 1 day
B alone can do (1/6 -1/13) =7/78 work in 1 day
=> complete work can be done in 78/7 days by B
Answer: Option C
Answer: (C) 78/7 days
Question: From a Group of 8 People, Including Gary and Nina, 3 people are to be selected at random to work on a certain project. What is the probability that 3 people selected will include Gary but not Nina
(A) 5/56
(B) 9/56
(C) 15/56
(D) 21/56
(E) 25/56
Rationale: Number of ways of selecting 3 people out of 8 people = 8C3
In the three members Gary will always be there in the team. At this step we have vacancy for 2 more members and 7 members are available. Nina cannot be there in the team. So 2 members have to be selected and the number of available members = 7 - Nina = 6
Number of ways to form a 3 member team that includes Gary and excludes Nina = 6C2
Probability = 6C2/8C3 = 15/56
Answer: C
Answer: (C) 15/56
Question: A family consisting of one mother, one father, two daughters and a son is taking a road trip in a sedan. The sedan has two front seats and three back seats. If one of the parents must drive and the two daughters refuse to sit next to each other, how many possible seating arrangements are there?
(A) 28
(B) 32
(C) 48
(D) 60
(E) 120
Rationale: Sisters can sit separately in two ways:
1. one of them is on the front seat (2 ways). Others (including second sister) can be arranged in: 2 (drivers seat)*3! (arrangements of three on the back seat)=12 ways. Total for this case: 2*12=24
Or
2. both by the window on the back seat (2 ways). Others can be arranged in: 2 (drivers seat)*2 (front seat)*1(one left to sit between the sisters on the back seat)=4 ways. Total for this case: 2*4=8.
Total=24+8=32. ANS:B
Answer: (B) 32
Question: How many bricks each measuring 20cm x 10cm x 8cm, will be needed to build a wall 10m x 8m x 24.5m
(A) 12250
(B) 13400
(C) 12500
(D) 14340
(E) None of these
Rationale: Explanation:
no. of bricks= volume of the wall/volume of 1 brick = (1000 x 800 x 24.5) / (20 x 10 x 8) = 12250
Answer: A
Answer: (A) 12250
Question: In Richard's office one half of the workers are Indians,quarter are from America,one-fifth are from Canada and the other 100 are China. How many workers total are there in the company?
(A) 250
(B) 500
(C) 750
(D) 1000
(E) 2000
Rationale: 1/2x + 1/4x +1/5x = 19/20x
Remaining 1/20 x= 100
x= 100*20= 2000
E is the answer.
Answer: (E) 2000
Question: Rahim bought 32 books for Rs.1500 from one shop and 60 books for Rs.340 from another. What is the average price he paid per book ?
(A) s.17
(B) s.18
(C) s.12
(D) s.11
(E) s.20
Rationale: Average price per book
= (1500+ 340) / (32 + 60) = 1840/ 92
= Rs.20
Answer:E
Answer: (E) s.20
Question: Each day a man meets his wife at the train station after work, and then she drives him home. She always arrives exactly on time to pick him up. One day he catches an earlier train and arrives at the station an hour early. He immediately begins walking home along the same route the wife drives. Eventually his wife sees him on her way to the station and drives him the rest of the way home. When they arrive home the man notices that they arrived 30 minutes earlier than usual. How much time did the man spend walking?
(A) 45 minutes
(B) 50 minutes
(C) 40 minutes
(D) 55 minutes
(E) 35 minutes
Rationale: As they arrived 30 minutes earlier than usual, they saved 30 minutes on round trip from home to station (home-station-home) --> 15 minutes in each direction (home-station) --> wife meets husband 15 minutes earlier the usual meeting time --> husband arrived an hour earlier the usual meeting time, so he must have spent waking the rest of the time before their meeting, which is hour-15 minutes= 45 minutes.
Answer: A
Answer: (A) 45 minutes
Question: How much time will a train of length 200 m moving at a speed of 72 kmph take to cross another train of length 300 m, moving at 36 kmph in the same direction?
(A) sec
(B) sec
(C) sec
(D) sec
(E) sec
Rationale: The distance to be covered = Sum of their lengths = 200 + 300 = 500 m.
Relative speed = 72 -36 = 36 kmph = 36 * 5/18 = 10 mps.
Time required = d/s = 500/10 = 50 sec.
Answer: A
Answer: (A) sec
Question: How many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 8 m x 6 m x 22.5 cm?
(A) 5600
(B) 6000
(C) 6400
(D) 7200
(E) 8600
Rationale: Number of bricks =Volume of the wall/Volume of 1 brick =	(800 x 600 x 22.5)/(25 x 11.25 x 6) = 6400.
Answer: Option C
Answer: (C) 6400
Question: A can do a work in 14 days. B is 40% more efficient than A. How many days does B alone take to do the same job?
(A) 9
(B) 10
(C) 11
(D) 12
(E) 8
Rationale: Ratio of times taken by A and B = 140:100 = 7:5
suppose B alone to take x days to do the work
then, 7:5::14:x
7x= 5*14
x=10 days
correct option is B
Answer: (B) 10
Question: Each light bulb at a hotel is either incandescent or fluorescent. At a certain moment, forty percent of the incandescent bulbs are switched on, and eighty percent of the fluorescent bulbs are switched on. If 72 percent of all the bulbs are switched on at this moment, what percent of the bulbs that are switched on are incandescent?
(A) 24%
(B) 16%
(C) 11%
(D) 7%
(E) 5%
Rationale: Let I be the number of incandescent bulbs.
Let F be the number of fluorescent bulbs.
0.4I + 0.8F = 0.72(I+F)
0.08F = 0.32I
F = 4I
This means that for every 1 incandescent bulb, there are 4 fluorescent bulbs.
The percent of bulbs that are switched on which are incandescent is:
0.4I / (0.4I + 0.8F) = 0.4I / (0.4I + 0.8*4I) = 0.4I / 3.6I = 1/9 which is about 11%.
The answer is C.
Answer: (C) 11%
Question: A crate of mangoes contains one bruised mango for every thirty mango in the crate. If three out of every four bruised mango are considerably unsaleable and there are 12 unsaleable mangoes in the crate then how many mango are there in the crate?
(A) 321
(B) 430
(C) 530
(D) 172
(E) 480
Rationale: Let the total no of mangoes in the crate be x
Then the no of bruised mango = 1/30 x
Let the no of unsalable mangoes =3/4 (1/30 x)
1/40 x =12
x=480
Option E
Answer: (E) 480
Question: If -1 < x < 1, which of the following must be true?
I. x^3 < x^2
II. x^5 < 1 – x
III. x^4 < x^2
(A) I only
(B) I and II only
(C) II and III only
(D) I and III only
(E) I, II and III
Rationale: I. x^3 < x^2 --> from -1 < x < 1 x must be a decimal so multiplying it by itself makes it a smaller value positive or negative. x^2 is always positive so x^3 being a small value always makes x^3<x^2 so this statement is true.
II. x^5 < 1 – x --> x(x^4+1) < 1 --> since 1(1+1)=2 > 1, so this statement is false.
III. x^4 < x^2 --> reduce by x^2 (we can safely do that since from -1 < x < 1 is follows that x^2>0): x^2 < 1. Again, as -1 < x < 1, then x^2 must be less than 1. Hence, this statement is also true.
Answer: D.
Answer: (D) I and III only