mathewhe/aqua_rat huggingface dataset:
Question: In how many ways can a committee consisting of 4 men and 5 women be formed from a group of 7 men and 9 women?
(A) 7C4 9C5
(B) 4C7 5C9
(C) 7C5 9C4
(D) 9C4 7C5
(E) NONE
Rationale: Group consisting of 7 men and 9 women
4 men can be selected from 7 men in 7C4 ways
5 women can be selected from 9 women in 9C5 ways
Therefore, Total number of ways= 7C4 9C5
ANSWER:A
Answer: (A) 7C4 9C5
Question: A series of boxes are placed on a conveyor belt at one end and unloaded at the other. The boxes are each 0.5 meters on each side and are placed immediately adjacent to one another as they are loaded. If the conveyor belt is 30 meters long and moves the boxes at a speed of 0.25 m/s, how long does it take for 100 boxes to be loaded and unloaded?
(A) 4 min 30 sec
(B) 4 min 50 sec
(C) 5 min 20 sec
(D) 5 min 40 sec
(E) 6 min 10 sec
Rationale: C
5 min 20 sec
d = 100 * 0.5 m +30 m = 80 m
T = 80 m / 0.25 m/s = 320 s = 5 min 20 sec
Answer: (C) 5 min 20 sec
Question: The average earning of a mechanic for the first-four days of a week is Rs. 18 and for the last four days is Rs. 22. If he earns Rs . 6 on the fourth day, his average earning for the whole week is ?
(A) Rs . 18.95
(B) Rs 16
(C) Rs. 22
(D) Rs. 25.71
(E) None of these
Rationale: Answer
Total earning for the week = Sum of earning of first four days + Sum of earning of last four days - Earning of 4th day
= 4 x18 + 4 x 22 - 6
= Rs. 154
âˆ´ Average earning = 154 / 7
= Rs. 22
Correct Option: C
Answer: (C) Rs. 22
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 15.7 years. The ration of the number of boys to the number of girls in the class is?
(A) 1:6
(B) 2:3
(C) 2:5
(D) 2:1
(E) 2:4
Rationale: Let the ratio be k : 1. Then,
k * 16.4 + 1 * 15.7 = (k + 1) * 15.8
= (16.4 - 15.8)k = (15.8 - 15.7)
= k = 0.1/0.6 = 1/6
Required ratio = 1/6 : 1 = 1:6.
Answer:A
Answer: (A) 1:6
Question: In a certain egg-processing plant, every egg must be inspected, and is either accepted for processing or rejected. For every 96 eggs accepted for processing, 4 eggs are rejected. If, on a particular day, 12 additional eggs were accepted, but the overall number of eggs inspected remained the same, the ratio of those accepted to those rejected would be 99 to 1. How many E eggs does the plant process per day?
(A)  100
(B)  300
(C)  400
(D)  3,000
(E)  4,000
Rationale: Straight pluggin in for me. As usual, I started with C and got the answer.
Lets' back calculate and see what we get
Let us consider eggs processed each day to be 400
So Initial ratio of eggs processed and rejected is 96:4 or 24:1
So out of 400 eggs, there will be 384 eggs processed and 16 rejected.
Now if the no. of eggs inspected remain and 12 more eggs get accepted that means there E=384+12=396 eggs accepted and 4 rejected...and the ratio will be 99:1
Bingo...this is what the questions says....
Its always a good idea to start with C.
Answer: (C)  400
Question: A man purchases 2 mobiles for $ 1400. He sells one at 20% profit and the other at a loss of 15%. He neither gains nor loses on the whole. Thus, the cost price of two watches are :
(A) $ 600 and $ 1400
(B) $1400 and $ 600
(C) $600 and $800
(D) $800 and $600
(E) $1400 and $ 800
Rationale: x + y = 1400 --- (1)
1.20x + 0.85y = 1400 --- (2)
(2) - (1) --> 0.20x - 0.15y = 0
15x = 10y
x/y = 3/4= (3*200)/(4*200) = 600/800
Answer: C
Answer: (C) $600 and $800
Question: What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 58?
(A) Rs.3944
(B) Rs.3988
(C) Rs.3928
(D) Rs.3928
(E) Rs.3943
Rationale: Let the side of the square plot be a ft.
a2 = 289 => a = 17
Length of the fence = Perimeter of the plot = 4a = 68 ft.
Cost of building the fence = 68 * 58 =Rs.3944.
Answer: A
Answer: (A) Rs.3944
Question: A goods train runs at the speed of 72 km/hr and crosses a 300 m long platform in 26 sec. What is the length of the goods train?
(A) 278
(B) 166
(C) 151
(D) 220
(E) 109
Rationale: Speed = 72 * 5/18 = 20 m/sec.
Time = 26 sec.
Let the length of the train be x meters.
Then, (x + 300)/26 = 20
x = 220 m.
Answer:D
Answer: (D) 220
Question: An athlete takes 10 seconds to run 100m. What is his avg. speed in miles per hour?
(A) 22.37
(B) 26.66
(C) 24.35
(D) 36.0
(E) 42.44
Rationale: His average speed is 10m/s. which is 36 km/hr.
But 36km=22.37 miles. The average speed of the athlete is 22.37mph
Answer: A
Answer: (A) 22.37
Question: There are 7 dozen mangoes in a box. If there are 29
such boxes, how many mangoes are there in all the
boxes together?
(A) 516
(B) 2436
(C) 6192
(D) 628
(E) None
Rationale: Number of mangoes = 7 dozens
= 7 × 12 = 84
∴ Number of mangoes in 29 boxes
= 29 × 84 = 2436
Answer B
Answer: (B) 2436
Question: If (5^13)(9^7)=3(15^x), what is the value of x?
(A) 7
(B) 9
(C) 11
(D) 13
(E) 15
Rationale: (5^13)(9^7)=3(15^x)
=> 5^13 * 3^14 = 3 * 3^x * 5^x
=> 5^13 * 3^14 = 3^(x+1) * 5^x
Value of x = 13
Answer D
Answer: (D) 13
Question: If Q is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3^k is a factor of Q?
(A) 10
(B) 12
(C) 14
(D) 16
(E) 18
Rationale: Q = 30!
8
Q = 30 x 29 x 28 x 27 x 26 x 25 x 24 x 24 x 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 09 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
Out of these 30 , 27 , 24 , 21 , 18, 15 , 12 , 09 , 06 , 3 are factors of 3
3 x 10 , 3 x 3 x 3 , 3 x 8 , 3 x 3 x 2, 3 x 5 , 3 x 4 , 3 x 3 x 3 , 3 x 2 , 3
So we have a total of 14 three's ...
Therefore the maximum value of K can be 14 (C)
Answer: (C) 14
Question: .05% of cans of beans that go down a conveyor belt are sealed improperly and must be disposed of. How many cans of beans must pass down a conveyor belt for 5 cans to be sealed improperly?
(A) 500
(B) 5000
(C) 4000
(D) 2500
(E) 10000
Rationale: Let the number of total cans of beans be x
Then, .05% of x=5
(5/100)*(1/100)*x=5
x=10000
Answer is E
Answer: (E) 10000
Question: a light flashes every 15 seconds, how many times will it flash in ? of an hour?
(A) 550
(B) 600
(C) 240
(D) 700
(E) 750
Rationale: 1flash=15sec
for 1 min=4flashes
so for 1 hour=4*60=240 flashes.
ANSWER:C
Answer: (C) 240
Question: Solve for x and check: 6x = 54
(A) 12
(B) 15
(C) 5
(D) 9
(E) None of these
Rationale: Solution : Dividing each side by 6, we obtain
(6x/6)=(54/6)
Therefore : x=9
Check :
6x=54
(6*9)=54
54=54
ANSWER : D
Answer: (D) 9
Question: which is odd one
3, 5, 7, 12, 17, 19
(A) 19
(B) 17
(C) 5
(D) 12
(E) 14
Rationale: Each of the numbers is a prime number except 12.
Answer: Option D
Answer: (D) 12
Question: If the complement of a certain angle is seven times the measure of that certain angle, then what is the measure of that certain angle?
(A) 45°
(B) 30°
(C) 22.5°
(D) 18°
(E) 11.25°
Rationale: Thecomplementof angle A is the angle which, when added to angle A, gives 90 degrees. The two acute angles of a right triangle are complements, for example.
The original angle is x, so the complement is 7x, and together, these add up to 90 degrees.
x + 7x = 90
8x = 90
x = 11.25°
Answer = (E)
Answer: (E) 11.25°
Question: How much time will it take for an amount of 500 to yield 100 as interest at 5% per annum of simple interest?
(A) 3 year
(B) 4 year
(C) 6 year
(D) 5 year
(E) 7 year
Rationale: Time = (100 x 100)/(500 x 5) years = 4 years.
answer B
Answer: (B) 4 year
Question: find the average of first 40 natural numbers?
(A) 12.3
(B) 15.4
(C) 63.2
(D) 45.2
(E) 20.5
Rationale: sum of first n natural numbers=n(n+1)/2;
So,sum of 40 natural numbers=(40*41)/2 =820.
Therefore the required average=(820/40) =20.5.
Ans: E
Answer: (E) 20.5
Question: Each light bulb at a hotel is either incandescent or fluorescent. At a certain moment, thirty percent of the incandescent bulbs are switched on, and eighty percent of the fluorescent bulbs are switched on. If 70 percent of all the bulbs are switched on at this moment, what percent of the bulbs that are switched on are incandescent?
(A) 4.5%
(B) 8.6%
(C) 12.3%
(D) 16.7%
(E) 20%
Rationale: Let I be the number of incandescent bulbs.
Let F be the number of fluorescent bulbs.
0.3I + 0.8F = 0.7(I+F)
0.1F = 0.4I
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:
0.3I / (0.3I + 0.8F) = 0.3I / (0.3I + 0.8*4I) = 0.3I / 3.5I = 3/35 which is about 8.6%.
The answer is B.
Answer: (B) 8.6%
Question: Which of the following is not a multiple of 3!+4?
(A) 5!+20
(B) 4!+1
(C) 5!-60
(D) 4!+36
(E) 5!+20
Rationale: The factorial 3! means 3*2
therefore 3!+4=(3*2)+4
Which gives 6+4=10
all the options except option b) 4!+1 are multiples of 3!+4
The correct option is B)
Answer: (B) 4!+1
Question: A tradesman by means of his false balance defrauds to the extent of 22%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?
(A) 56.25%
(B) 49.56%
(C) 84.46%
(D) 24.50%
(E) 45.35%
Rationale: g% = 25 + 25 + (25*25)/100
= 56.25%
Answer: A
Answer: (A) 56.25%
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 225 m and they cross each other in 18 sec, then the speed of each train is?
(A) 22
(B) 77
(C) 36
(D) 88
(E) 45
Rationale: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (225 + 225)/18 => x = 25/2
Speed of each train = 25/2 m/sec.
= 25/2 * 18/5 =- 45 km/hr.Answer: E
Answer: (E) 45
Question: Divide $1000 among A,B in the ratio 1:3. How many $ that A get?
(A) $50
(B) $500
(C) $150
(D) $250
(E) $600
Rationale: Sum of ratio terms = 1+3 = 4
A = 1000*1/4 = $250
Answer is D
Answer: (D) $250
Question: Elena’s bread recipe calls for 3 ounces of butter for each 4 cups of flour used. She needs to make 4 times the original recipe. If 12 ounces of butter is used, then how many cups of flour are needed?
(A) 1
(B) 4
(C) 9
(D) 13
(E) 16
Rationale: Number of cups flour needed for 3 ounces of butter = 4
Number of cups flour needed for 1 ounce of butter = 4/3
Number of cups flour needed for 12 ounces of butter = 4/3 * 12 = 16
Answer E
Answer: (E) 16
Question: Average temperature of first 4 days of a week is 6°C and that of the last 4 days is 40.3°C. If the average temperature of the week be 39.1°C, the temperature on 4th day is?
(A) 36.7°C
(B) 38.6°C
(C) 39.8°C
(D) 41.9°C
(E) 51.9°C
Rationale: Let temperature on 4th day be X°C
Therefore, 4 x 38.6 + 4 x 40.3 - X = 7 x 39.1
=> X = 41.9
Therefore, temperature on 4th day = 41.9°C.
ANSWER:D
Answer: (D) 41.9°C
Question: If the price of an item is decreased by 40% and then increased by 40%, the net effect on the price of the item is
(A) A decrease of 99%
(B) No change
(C) A decrease of 16%
(D) A increase of 1%
(E) none
Rationale: initially assume 100 rupees
40% discount in 100 gives price of 60 rupees
then 40% raise in 60 is only 24 rupees.
therefore total price =84 rupees.
hence 16% is the loss
ANSWER:C
Answer: (C) A decrease of 16%
Question: What is the rate percent when the simple interest on Rs.800 amount to Rs.160 in 4 Years?
(A) 5%
(B) 8%
(C) 9%
(D) 4%
(E) 1%
Rationale: 160 = (180*4*R)/100
R = 5%
Answer: A
Answer: (A) 5%
Question: In a box, there are 20 red, 15 blue and 10 green balls. One ball is picked up randomly. What is the probability that it is green?
(A) 1/3
(B) 2/5
(C) 3/7
(D) 2/9
(E) 1/5
Rationale: Total number of balls = 20+15+10 = 45
E = event that the ball drawn is green = 10
n(E) = 10
P(E) = 10/45 = 2/9
Answer is D
Answer: (D) 2/9
Question: A cab driver 5days income was $40, $50, $60, $65 , $80. Then his average income is?
(A) A)$58
(B) B)$42
(C) C)$65
(D) D)$59
(E) E)$62
Rationale: avg = sum of observations/number of observations
avg income=(40+50+60+65+80)/5 = 59
Answer is D
Answer: (D) D)$59
Question: A 18% stock yielding 12% is quoted at:
(A) s. 83.33
(B) s. 110
(C) s. 112
(D) s. 120
(E) s. 150
Rationale: Income of Rs 12 on investment of Rs 100
Income of Rs 18 on investment of ?
= (18*100)/12=150
ANSWER:E
Answer: (E) s. 150
Question: The area of a square is 4096 sq cm. Find the ratio of the breadth and the length of a rectangle whose length is twice the side of the square and breadth is 24 cm less than the side of the square.
(A) 5 : 12
(B) 5 : 13
(C) 5 : 167
(D) 5 : 19
(E) 5 : 16
Rationale: Let the length and the breadth of the rectangle be l cm and b cm respectively. Let the side of the square be a cm.
a2 = 4096 = 212
a = (212)1/2 = 26 = 64
L = 2a and b = a - 24
b : l = a - 24 : 2a = 40 : 128 = 5 : 16
Answer: Option E
Answer: (E) 5 : 16
Question: An article was bought for 2000 and sold for 2200. Find the gain or loss.
(A) 200
(B) 300
(C) 400
(D) 500
(E) 600
Rationale: Sol. C.P. of the article = 2000
S.P. of the article = 2200
Since S.P. > C.P. So there is gain.
Gain (profit) = S.P. – C.P.
=2200 –2000 =200 Answer A
Answer: (A) 200
Question: One out of every 4000 computer chips is defective. If 2 out of every 30 defective chips have defective processors and there are 30 defective processors in the first batch, how many computer chips are there in the first batch?
(A) 450
(B) 900
(C) 90,000
(D) 1800,000
(E) 900,000
Rationale: (D) Read the whole question to get the feel of what they are asking you to find. Then start with the smallest amount and work your way outwards. We are told that two out of every 30 defective chips have a defective processor. Let x be the total number of defective processors in the batch. Because we know 2 out of every 30 defective chips will have defective processors, and the total number of defective processors in the batch is 30, we can write out an equation: (2/30)x = 30. This can be simplified to (1/15)x = 30. Multiplying each side by 15, we arrive at x = 450. This tells us that there are 450 defective chips in the whole batch. Because we know that 1 out of every 1000 chips is defective, we can set up a proportion. If 1 out of every 4000 chips is defective, then 450 out of y chips would be defective, where y is the total number of chips in the batch. This can be set up as an equation as follows: 1/4000 = 450/y. Solve for y and you will get the total number of chips in the batch: 1800,000.
The answer is (D).
Answer: (D) 1800,000
Question: At an art exhibit the entrance costs is $1.15 per person, and every print sold costs $5. Assuming that you bought prints that came in a bag that could hold 12, and another that holds %50 more. How much money do you end up spending all together at the exhibition?
(A) 180
(B) 181.15
(C) 1.15
(D) 81.15
(E) 200.15
Rationale: Entrance fee is $1.15.
total prints bought is 12 + (1.50*12)= 36
Total prints cost 36* $5= $180.
Total spent at exhibit is $1.15 + $180= $181.15
Answer is B.
Answer: (B) 181.15
Question: A 450 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec. What is the length of the platform?
(A) 600
(B) 525
(C) 360
(D) 370
(E) 380
Rationale: Speed = 450/18 = 25 m/sec.
Let the length of the platform be x meters.
Then, (x + 450)/39 = 25
=> x = 975 m.
L=975-450=525
Answer: Option B
Answer: (B) 525
Question: Look at this series: 7, 10, 8, 11, 9, 12, 10, 13, 11, ... What number should come next?
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Rationale: This is a simple alternating addition and subtraction series. In the first pattern, 3 is added; in the second, 2 is subtracted.
The answer is C.
Answer: (C) 14
Question: How many 1's are there preceded by 2 but not followed by 0?
5 9 3 2 1 7 4 2 6 9 7 4 2 1 3 2 8 7 0 1 3 8 3 2 5 6 7 4 3 9 5 8 2 2 1 0 7 4 6 3
(A) 4
(B) 2
(C) 6
(D) 8
(E) 9
Rationale: 2 1 7
2 1 3
Only at these places 2 is preceded by 2 but not followed by 0
Answer: B
Answer: (B) 2
Question: Pipe A can fill a tank in 6 hours. Due to a leak at the bottom, it takes 9 hours for the pipe A to fill the tank. In what time can the leak alone empty the full tank?
(A) 13
(B) 17
(C) 18
(D) 19
(E) 12
Rationale: Let the leak can empty the full tank in x hours 1/6 - 1/x = 1/9
=> 1/x = 1/6 - 1/9 = (3 - 2)/18 = 1/18
=> x = 18.
Answer: C
Answer: (C) 18
Question: Three coins are tossed. What is the probability of getting at most two tails?
(A) 5/6
(B) 2/3
(C) 7/8
(D) 8/7
(E) 6/9
Rationale: Explanation :
Total number of outcomes possible when a coin is tossed = 2 (∵ Head or Tail)
Hence, total number of outcomes possible when 3 coins are tossed, n(S) = 2 × 2 × 2 = 8
E = event of getting at most two Tails = {TTH, THT, HTT, THH, HTH, HHT, HHH}
Hence, n(E) = 7
P(E)=n(E)/n(S)=7/8
Answer:C
Answer: (C) 7/8
Question: In the Olympic track represented above 8 runners are going to compete to reach the finish line in the shortest amount of time. Between Tom in line 1 and Jack in line 2 there's a distance of 1.2 meters, the same as in the subsequent lanes. If each runner is to race onto their assigned line (and not in the middle of the lane), and Tom is to run on line 1 and Bob on line 8. Bob will have to start-position himself approximately how many meters in front of Tom for the two to run the same distance before reaching the finishing line?
(A) 37
(B) 51
(C) 53
(D) 64
(E) 85
Rationale: first perimeter:402 meters, second perimeter:455, for the two of them to run 402 meters the second athlete will have to start 53 meters ahead.
ANSWER:C
Answer: (C) 53
Question: The average of first five multiples of 4 is?
(A) 6
(B) 8
(C) 9
(D) 5
(E) 12
Rationale: Average = 4(1 + 2 + 3 + 4 + 5)/5
= 60/5
= 12.
Answer:E
Answer: (E) 12
Question: A man can row a boat three quarters of a kilometre in 11.25 minutes. What is the speed of the boat in still water?
(A) 4 kmph
(B) 8 kmph
(C) 6 kmph
(D) 5 kmph
(E) 12 kmph
Rationale: Explanation:
Simple Division.
No stream current mentioned.
Trick question.
Speed= Distance/Time.
Speed= 3/4 km / (11.25/60) hr
Therefore, Speed = 4 km/hr
ANSWER:A
Answer: (A) 4 kmph
Question: Two men Amar and Bhuvan have the ratio of their monthly incomes as 6 : 5. The ratio of their monthly expenditures is 3 : 2. If Bhuvan saves one-fourth of his income, find the ratio of their monthly savings?
(A) 4:10
(B) 3:10
(C) 3:17
(D) 3:20
(E) 3:60
Rationale: Let the monthly incomes of Amar and Bhuvan be 6x and 5x respectively.
Let the monthly expenditure of Amar and Bhuvan be 3y and 2y respectively.
Savings of Bhuvan every month = 1/4(5x)
= (His income) - (His expenditure) = 5x - 2y.
=> 5x = 20x - 8y => y = 15x/8.
Ratio of savings of Amar and Bhuvan
= 6x - 3y : 1/4(5x) = 6x - 3(15x/8) : 5x/4 = 3x/8 : 5x/4
= 3 : 10.
Answer:B
Answer: (B) 3:10
Question: If u r genius solve it:-
40 * 14 = 11
30 * 13 = 12
20 * 12 = 6
10 * 11 = ?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Rationale: A
2
Logic :
40*14=560=5+6+0=11
30*13=390=3+9+0=12
20*12=240=2+4+0=6
So 10*11=110=1+1+0=2
Answer: (A) 2
Question: YES bank offers an interest of 5% per annum compounded annually on all its deposits. If $10,000 is deposited, what will be the ratio of the interest earned in the 4th year to the interest earned in the 5th year?
(A) 1:5
(B) 625:3125
(C) 100:105
(D) 100^4:105^4
(E) 725:3225
Rationale: Hi Bunuel,
Here is my approach: is this correct?
YES bank offers an interest of 5% per annum compounded annually on all its deposits.
Interest earned in 4 year= 10000(1+0.05)^4
Interest earned in 5 year= 10000(1+0.05)^5
Ratio= {10000(1.05)^4}/{10000(1.05^5)} =>1.05^4/1.05^5 =>1/1.05 Multiplied by 100 in both numerator and denominator gives 100:105
Hence Ans:C
Answer: (C) 100:105
Question: 3 men and 2 women are lined up in a row. What is the number of cases where they stand with each other in turn? (The number of cases in which men (or women) do not stand next to each other)
(A) 12
(B) 15
(C) 18
(D) 21
(E) 24
Rationale: The list should be WMWMW. Hence, from women 2! And men 3!, we get (2!)(3!)=12. Therefore, the correct answer is A.
Answer: (A) 12
Question: The ratio of the length and the breadth of a rectangle is 4 : 3 and the area of the rectangle is 6912 sq cm. Find the ratio of the breadth and the area of the rectangle?
(A) 1: 96
(B) 1: 98
(C) 1: 97
(D) 1: 95
(E) 1: 91
Rationale: Let the length and the breadth of the rectangle be 4x cm and 3x respectively.
(4x)(3x) = 6912
12x2 = 6912
x2 = 576 = 4 * 144 = 22 * 122 (x > 0)
=> x = 2 * 12 = 24
Ratio of the breadth and the areas = 3x : 12x2 = 1 : 4x = 1: 96.
Answer:A
Answer: (A) 1: 96
Question: Ayesha's father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
(A) 2 years
(B) 4 years
(C) 6 years
(D) 7 years
(E) 8 years
Rationale: Mother's age when Ayesha's brother was born = 36 years.
Father's age when Ayesha's brother was born = (38 + 4) years = 42 years.
Required difference = (42 - 36) years = 6 years.
Answer: Option C
Answer: (C) 6 years
Question: A small, rectangular park has a perimeter of 560 feet and a diagonal measurement of 300 feet. What is its area, in square feet?
(A) 43,200
(B) 19,600
(C) 20,000
(D) 20,400
(E) 20,800
Rationale: you can avoid a lot of work in this problem by recognizing that, with the info provided, the diagonal forms a triangle inside the rectangle with sides that have a 3:4:5 ratio.
diagonal = 200
2x + 2y = 560, or x + y = 280
a^2 + b^2 = c^2 for each the sides of the triangle
using the ratio 3:4:5 for sides, and knowing c = 300, you can deduce the following
a=180
b=240
180x240=43,200
A is the answer.
Answer: (A) 43,200
Question: Right triangle ABC is the base of the prism in the figure above. If AB=AC=√2 and the height of the prism is 3, what is the volume of the prism?
(A) 1
(B) 3/2
(C) 2
(D) 3
(E) 6
Rationale: Volume of prism = Area of base * height = 1/2* (square root of 2) * (square root of 2)*3 = 3
Answer: D
Answer: (D) 3
Question: A,B,C invested the capitals in a business. If A invested Rs. 5000 more than B and C invested Rs.20,000 more than A, then how should a profit of Rs.36,000 be divided among A,B and C? Given : Capital of B is Rs.10,000
(A) 3250, 2250, 6500
(B) 3500, 2000, 6500
(C) 3000, 2500, 6500
(D) 3000, 2000, 7000
(E) 3500, 2000, 6250
Rationale: A==15,000
B==10,000
C==35,000
so, ration are 3:2:7
profit 14000
so,, 12000/12==1000
so,, A==3000, B==2000,, C==7000
ANSWER:D
Answer: (D) 3000, 2000, 7000
Question: John want to buy a $100 Trouser at the store, but he think it’s too expensive. Finally, it goes on sale for $30. What is the percent decrease?
(A) 20%
(B) 30%
(C) 40%
(D) 70%
(E) 80%
Rationale: The is always the difference between our starting and ending points. In this case, it’s 100 – 30 = 70. The “original” is our starting point; in this case, it’s 100. (70/100)*100 = (0.7)*100 = 70%.
D
Answer: (D) 70%
Question: The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %?
(A) 18
(B) 19
(C) 81
(D) 16
(E) 13
Rationale: 1500 ---- 270
100 ---- ? => 18%
Answer: A
Answer: (A) 18
Question: A man and his wife appear in an interview for two vacancies in the same post. The probability of husband's selection is (1/7) and the probability Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5? of wife's selection is (1/5). What is the probability that only one of them is selected ?
(A) 9/19
(B) 9/20
(C) 11/21
(D) 11/23
(E) 12
Rationale: Here, S = {1, 2, 3, 4, ...., 19, 20}.
Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}.
P(E) = n(E)/n(S) = 9/20.
B)
Answer: (B) 9/20
Question: A book club rented the party room of a local restaurant to meet and discuss its current novel over dinner. The total charge, including food and service, was $ 900. If each member of the club paid at least $ 40, then what is the greatest possible number of members in the club?
(A) 19
(B) 20
(C) 21
(D) 23
(E) 25
Rationale: Given: Each person spends $40
By looking at the options, we see that if there were 20 members, each person will spend atleast $40
Hence the greatest number of members = 22.5 Option D
Answer: (D) 23
Question: When 28 is divided by the positive integer a, the remainder is 1. What is the sum of all the possible values of a for which this is true?
(A) 2
(B) 3
(C) 9
(D) 30
(E) 39
Rationale: The only possible values of the form 28=ap+1 are 3,9 or 27
The sum = 3+9+27 =39. E is the correct answer. We dont need to look for values >28 as all these values will leave a remainder of 28 and not 1.
Answer: (E) 39