mathewhe/aqua_rat huggingface dataset:
Question: Running at their respective constant rates, machine X takes 2 days longer to produce w widgets than machine Y. At these rates, if the two machines together produce 5/4 w widgets in 3 days, how many days would it take machine X alone to produce 6w widgets?
(A) 36
(B) 6
(C) 8
(D) 10
(E) 12
Rationale: Let Y produce w widgets in y Days
Hence, in 1 day Y will produce w/y widgets.
Also, X will produce w widgets in y+2 days (given, X takes two more days)
Hence, in 1 day X will produce w/y+2 widgets.
Hence together X and Y in 1 day will produce {w/y + w/y+2} widgets.
Together X and Y in 3 days will produce = 3 * [{w/y + w/y+2}] widgets.
It is given that in 3 days together they produce (5/4)w widgets.
Equating, 3 * [{w/y + w/y+2}] = (5/4)w
Take out w common and move 3 to denominator of RHS
w{1/y + 1/(y+2)} = (5/12)w
Canceling w from both sides
{1/y + 1/(y+2)} = 5/12
2y+2/y(y+2) = 5/12
24y+24=5y^2 + 10y
5y^2-14y-24=0
5y^2-20y+6y-24=0
5y(y-4)+6(y-4)=0
(5y+6)+(y-4)=0
y=-6/5 or y=4
Discarding y=-6/5 as no of days cannot be negative
y=4
hence it takes Y, 4 days to produce w widgets.
Therefore, it will take X (4+2)=6 days to produce w widgets.
Hence it will take X 6*6=36 days to produce 2w widgets.
Answer : A
Answer: (A) 36
Question: In a classroom, the average age of boys (b) is g and the average age of girls (g) is b. The average age of all is b+g. At the time of calculation, the class teacher, who is 42 years old was also present in the class. Can you find the value of b+g?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
Rationale: Solution:
b+g = 8
Explanation:
for b in range(1,99):
for g in range(1,99):
sum1=2*b*g+42
sum2=(b+g)*(b+g+1)
if(sum1==sum2):
print(b,g,sum1)
(b,g)=(3,5) => b+g=8
Answer A
Answer: (A) 8
Question: A can do a piece of work in 10 days and B in 20 days. They began the work together but 5 days before the completion of the work, A leaves. The work was completed in?
(A) 15 days
(B) 10 days
(C) 12 days
(D) 19 days
(E) 13 days
Rationale: B
(x â€“ 5)/10 + x/20 = 1
x = 10 days
Answer: (B) 10 days
Question: A certain city with a population of 180,000 is to be divided into 11 voting districts , and no district is to have a population that is more than 10 percent greater than the population of any other district What is the minimum possible population that the least populated district could have ?
(A) a) 10,700
(B) b) 10,800
(C) c) 10,900
(D) d) 15,000
(E) e) 11,100
Rationale: Let x = number of people in smallest district
x*1.1 = number of people in largest district
x will be minimised when the number of people in largest district is maximised
10*x*1.1 = 11x = total number of people in other districts
So we have 11x + x = 180k
x = 15,000
Answer : D
Answer: (D) d) 15,000
Question: Look at this series: 66, 66, 60, 60, 54, 54, ... What number should come next?
(A) 48
(B) 15
(C) 17
(D) 19
(E) 11
Rationale: In this series, each number is repeated, then 6 is subtracted to arrive at the next number.
The next number should be 48
Answer : A
Answer: (A) 48
Question: A rectangular tiled patio is composed of 160 square tiles. The rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles. After the change in layout, the patio will still have 160 tiles, and it will still be rectangular. How many rows are in the tile patio before the change in layout?
(A) 5
(B) 6
(C) 10
(D) 13
(E) 28
Rationale: Suppose there are c columns and there are r rows
Original Situation
So, Number of tiles = c*r = 160
Also. Reach column has r tiles and each row has c tiles
New Situation
Number of tiles in each column is r-2 and number of tiles in each row is c+4
So, number of rows = r-2 and number of columns is c+4
So, Number of tiles = (r-2)*(c+4) = 160
Comparing both of them we get
c*r = (r-2)*(c+4)
=> 4r -2c = 8
c = 2r - 4
Putting it in c*r=160
(2r-4)*r = 160
2r^2 - 4r - 160=0
r cannot be negative so r = 10
and c = 16
So, Answer will be C
Answer: (C) 10
Question: In the first 20 overs of a cricket game, the run rate was only 4.8. What should be the run rate in the remaining 30 overs to reach the target of 302 runs?
(A) 5
(B) 6.25
(C) 6.75
(D) 6.87
(E) 7.25
Rationale: Required run rate = 302 - (4.8 x 20)	/30	=	206/30 = 6.87 Option D
Answer: (D) 6.87
Question: Two successive price increase of 10% and 10% of an article are equivalent to a single price increase of:
(A) 26(2/3)
(B) 25%
(C) 21%
(D) 33(1/3)
(E) None
Rationale: Solution: 100----10%↑--→110---10%↑--→121.
Equivalent price increase = 21%.
Answer: Option C
Answer: (C) 21%
Question: If the average marks of three batches of 55, 60 and 45 students respectively is 50, 55 and 60, then the average marks of all the students is
(A) 53.33
(B) 54.68
(C) 55
(D) 57
(E) None
Rationale: Sol.
Required average = [55x50 + 60x55 + 45x60 / 55 + 60 + 45]
= [2750 + 3300 + 2700 / 160]
= 8750 / 160 = 54.68.
Answer B
Answer: (B) 54.68
Question: A mixture of 150 liters of wine and water contains 20% water. How much more water should be added so that water becomes 25% of the new mixture?
(A) 16 liters
(B) 18 liters
(C) 10 liters
(D) 17 liters
(E) 15 liters
Rationale: Number of liters of water in150 liters of the mixture = 20% of 150 = 20/100 * 150 = 30 liters.
P liters of water added to the mixture to make water 25% of the new mixture.
Total amount of water becomes (30 + P) and total volume of mixture is (150 + P).
(30 + P) = 25/100 * (150 + P)
120 + 4P = 150 + P => P = 10 liters.
Answer: C
Answer: (C) 10 liters
Question: A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs.
3200. With the help of C, they completed the work in 3 days. How much is to be paid to C
(A) Rs. 300
(B) Rs. 400
(C) Rs. 500
(D) Rs. 600
(E) None of these
Rationale: Explanation:
C's 1 day's work =
13−(16+18)=(13−724)=124A:B:C=16:18:124=4:3:1CʹsShare=18
∗
3200=400
If you are confused how we multiplied 1/8, then please study ratio and proportion chapter, for small
information, it is the C raƟo divided by total ratio.
Answer: B
Answer: (B) Rs. 400
Question: Vehicle A covers a certain distance in 8hrs at the speed of 63kmph. What is the average speed of another vehicle B which travels a distance of 60km more than thecar in the same time?
(A) 40 kmph
(B) 50 kmph
(C) 55 kmph
(D) 60 kmph
(E) 70 kmph
Rationale: Speed of vehicle A = 58 kmph and
Time taken by Vehicle A = 5 hours
Distance travelled by Vehicle A in 5 hours => Distance= Speed x Time
= 58 x 5 =290
Now distance travelled by vehicle B = 290+60= 350 km
Hence speed of vehicle B = Distance Travelled/Time Taken
=350/5
= 70 kmph
E
Answer: (E) 70 kmph
Question: If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 4 years the amount to be paid is?
(A) 3377
(B) 2688
(C) 2688
(D) 8774
(E) 1268
Rationale: A = 7500(26/25)^4 = 8774
Answer: D
Answer: (D) 8774
Question: Albert borrowed a total of $ 5800 from Brian and Charlie. He paid simple interest at the rate of 7 % Per yr and 9 % per yr respectively.At the end of three years he paid $ 1400 as total interest. What is the interest paid to Brian at the end of three years?
(A) 585
(B) 581
(C) 441
(D) 431
(E) 421
Rationale: Let x be the amount borrowed form Brian. So amount borrowed form Charlie = 5800-x.
1400 = 21/100x + 27/100(5800-x)
=>x = 16600/6.
Interest paid = 3*7/100*16600/6 = 581.
B
Answer: (B) 581
Question: Car X began traveling at an average speed of 35 miles per hour. After 84 minutes, car Y began traveling at an average speed of 42 miles per hour. When both cars had traveled the same distance, both cars stopped. How many miles did car X travel from the time car Y began traveling until both cars stopped?
(A) 140
(B) 175
(C) 210
(D) 245
(E) 270
Rationale: In 84 minutes, car X travels 49 miles.
Car Y gains 7 miles each hour, so it takes 7 hours to catch car X.
In 7 hours, car X travels 245 miles.
The answer is D.
Answer: (D) 245
Question: A can do a job in 8 days and B can do it in 16 days. A and B working together will finish twice the amount of work in ------- days?
(A) 12 1/8 days
(B) 10 1/3 days
(C) 14 1/3days
(D) 2 1/2 days
(E) 3 1/2 days
Rationale: 1/8+ 1/16= 3/16
16/3 = 16/3 *2 = 10 2/3
Answer: B
Answer: (B) 10 1/3 days
Question: Elena’s bread recipe calls for 2 ounces of butter for each 5 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) 20
Rationale: Solving through algebra route:
2B + 5F = x amount
If we multiply this equation with 4 we get:
8B + 20F =4X
Therefore, we got 8 ounces of butter and 4X amount of quantity when we use 20 ounces of floor.
Ans:E
Answer: (E) 20
Question: Take a number 'x' and follow these steps :
1. Find the sum of its digit
2. If the sum has only one digit , STOP
3. Else , go back to step 1 with the new number.
If x = 1684 ,what is the end result ?
(A) 19
(B) 10
(C) 1
(D) 2
(E) None of these
Rationale: 1+6+8+4=19
sum=19 two digits
so go to step 1
1+9=10 two digits
so go to step 1
1+0=1
ANSWER:C
Answer: (C) 1
Question: A 6-liter solution is 30% alcohol. How many liters of pure alcohol must be added to produce a solution that is 50% alcohol?
(A) 1.8
(B) 2.1
(C) 2.4
(D) 2.7
(E) 3.0
Rationale: Let x be the amount of pure alcohol required.
0.3(6) + x = 0.5(x+6)
0.5x = 3 - 1.8
x = 2.4 liters
The answer is C.
Answer: (C) 2.4
Question: What will come in place of question mark in the following equation ?
54.(?)3 + 543 + 5.43 = 603.26
(A) 6
(B) 1
(C) 9
(D) 8
(E) 10
Rationale: Explanation:
Let x + 543 + 5.43 = 603.26. Then, x = 603.26 - (543 + 5.43) = 603.26 - 548.43 =54.83
Missing digit = 8
ANSWER IS D
Answer: (D) 8
Question: Mr. Bhaskar is on tour and he has Rs. 360 for his expenses. If he exceeds his tour by 4 days, he must cut down his daily expenses by Rs. 3. for how many days is Mr. Bhaskar on tour?
(A) 10
(B) 20
(C) 30
(D) 40
(E) 50
Rationale: If his tour is for x days and he is spending Rs y per day, then
xy= 360 x= 360/y or y= 360/x
(x+4)*(y-3)=360
or
xy +4y -3x-12 =360
or
4y-3x-12=0
4*360/x - 3x -12=0
solving it, we get x=20
ANSWER:B
Answer: (B) 20
Question: A bowl of fruit contains 14 apples and 20 oranges. How many oranges must be removed so that 70% of the pieces of fruit in the bowl will be apples?
(A)  3
(B)  6
(C)  14
(D)  17
(E)  20
Rationale: Number of apples = 14
number of oranges = 20
let number of oranges that must be removed so that 70% of pieces of fruit in bowl will be apples = x
Total number of fruits after x oranges are removed = 14+(20-x) = 34-x
14/(34-x) = 7/10
=>20 = 34-x
=>x= 14
Answer C
Answer: (C)  14
Question: The H.C.F of two numbers is 23 and the other two factors of their L.C.M are 15 and 16. The larger of the two numbers is:
(A) 338
(B) 278
(C) 322
(D) 368
(E) 121
Rationale: Clearly, the numbers are (23 * 15) and (23 * 16). Larger number
= (23 * 16) = 368.
Answer: D
Answer: (D) 368
Question: Suzie’s Discount Footwear sells all pairs of shoes for one price and all pairs of boots for another price. On Monday the store sold 22 pairs of shoes and 16 pairs of boots for $460. On Tuesday the store sold 8 pairs of shoes and 32 pairs of boots for $560. How much more do pairs of boots cost than pairs of shoes at Suzie’s Discount Footwear?
(A) 15
(B) 18
(C) 21
(D) 23
(E) 25
Rationale: Let X be pair of shoes and Y be pair of boots.
22x+16y = 460 ... eq1
8x +32y = 560....eq 2.
Now multiply eq 1 by 2 and sub eq 2.
44x =920
8x = 560.
36x = 360 => x = 10.
Sub x in eq 2.... we get 80 + 32y = 560... then we get 32y = 480 then y = 25
Differenece between X and Y is 15
Answer : A
Answer: (A) 15
Question: How many integers are between 9 and 67/5, inclusive?
(A) 5
(B) 7
(C) 9
(D) 10
(E) 11
Rationale: 67/5 = 13.xx
We are not concerned about the exact value of 67/5 as we just need the integers.
Since the values are small, we can write down the integers.
The different integers between 9 and 67/5 would be 9, 10, 11, 12,13
Total number of integers = 5
Option A
Answer: (A) 5
Question: Suppose son name is 120,his brother name is 150 and his mother name is 230.find out his father's name???
(A) 190
(B) 210
(C) 230
(D) 240
(E) 260
Rationale: since difference between all name is =30
so father's name will be 230+30=260.
ANSWER:E
Answer: (E) 260
Question: Find the average of all numbers between 3 and 86 which are divisible by 5
(A) 15
(B) 20
(C) 25
(D) 30
(E) 45
Rationale: Explanation:
Average=(5+10+15+20+25+30+35+40+45+50+55+60+65+70+75+80+85)/17=765/17=45
Answer: Option E
Answer: (E) 45
Question: Eddy and Freddy start simultaneously from city A and they travel to City B and City C respectively. Eddy takes 3 hours and Freddy takes 4 hours to complete the journey. If the distance between City A and City B is 510 kms and City A and City C is 300 kms. What is the ratio of their average speed of travel? (Eddy: Freddy)
(A) 8/3
(B) 3/8
(C) 8/5
(D) 5/8
(E) 34/15
Rationale: Distance traveled by Eddy = 510 km
Time taken by Eddy = 3 hours
Average speed of Eddy = 510/3 = 170 km/hour
Distance traveled by Freddy = 300 km
Time taken by Freddy = 4 hours
Average speed of Freddy = 300/4 = 75 km/hour
Ratio of average speed of Eddy to Freddy = 170/75 = 34/15
Answer E
Answer: (E) 34/15
Question: Speed of a boat in standing water is 14 kmph and the speed of the stream is 1.2 kmph. A man rows to a place at a distance of 4864 km and comes back to the starting point. The total time taken by him is:
(A) 600
(B) 500
(C) 700
(D) 900
(E) 800
Rationale: Speed downstream = (14 + 1.2) = 15.2 kmph
Speed upstream = (14 - 1.2) = 12.8 kmph
Total time taken =4864/15.2+4864/12.8 = 320 + 380 = 700 hours
Answer is C.
Answer: (C) 700
Question: The value of 99^(98/99) x 99 is:
(A) 9989
(B) 9899
(C) 9890
(D) 9809
(E) 9810
Rationale: (100 â€“ 1/99) x 99 = 9900 â€“ 1
= 9899.
ANSWER:B
Answer: (B) 9899
Question: The average attendance in a school for the first 4 days of the week is 30 and for the first 5 days of the week is 32. The attendance on the fifth day is
(A) 32
(B) 40
(C) 38
(D) 36
(E) None of the above
Rationale: Attendance on the fifth day = 32 × 5 – 30 × 4
= 160 – 120 = 40
Answer B
Answer: (B) 40
Question: A car is traveling 72 kilometers per hour. How many meters does the car travel in one minute?
(A) 1,200 meters / minute
(B) 1,300 meters / minute
(C) 1,450 meters / minute
(D) 1,550 meters / minute
(E) 1,650 meters / minute
Rationale: Convert hour into minutes ( 1 hour = 60 minutes) and kilometers into meters (1 km = 1000 m) and simplify
72 kilometers per hour = 72 km/hr
= (72 * 1000 meters) / (60 minutes) = 1,200 meters / minute
correct answer A
Answer: (A) 1,200 meters / minute
Question: If X = 2 + 1/(1+1/(1-1/2))then the value of 7x+7/3?
(A) 9 2/3
(B) 10 1/3
(C) 11
(D) 11 2/3
(E) 18
Rationale: X = 2 + 1/(1+1/(1-1/2))
= 2 + 1/(1+2)
= 2 + 1/3
X = 7/3 ==> 7X + 7/3 => 7(7/3) + 7/3
==> 49/3 + 7/3
==> 56/3
==> 18.
E)
Answer: (E) 18
Question: A is twice as good a workman as B and they took 6 days together to do the work B alone can do it in.
(A) 18 days
(B) 12 days
(C) 29 days
(D) 25 days
(E) 27 days
Rationale: WC = 2:1
2x + x = 1/6
x = 1/18 => 18 days
ANSWER:A
Answer: (A) 18 days
Question: For an employee to qualify for early retirement at a certain company, the sum of the employee’s age and years of service must be at least 60, If Sue was K years old when she was hired by the company, what is the minimum age at which she could possibly qualify for early retirement.
(A) K+35
(B) 2K+35
(C) (60+K)/2
(D) (70-K)/2
(E) 2(70-K)
Rationale: Say Sue was hired when she was already 60 years old (k=60), then she could retire right away, at the age of 60. Now, plug k=60 in the answer choices and see which yields 60. Only C fits.
Answer: C.
Answer: (C) (60+K)/2
Question: Jill is dividing her 14-person class into two teams of equal size for a basketball game. If no one will sit out, how many different match-ups between the two teams are possible?
(A) 1110
(B) 1125
(C) 1716
(D) 2152
(E) 1630
Rationale: With 14 players, the process of figuring out how many groups of 7 can be formed is pretty straight-forward....
14C7 = 14!/(7!7!) = 3432 possible groups of 7
Once forming that first group of 7, the remaining 7 players would all be placed on the second team by default.
The 'twist' is that the two teams of 7 canshow upin either order:
C
Answer: (C) 1716
Question: A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good.
(A) 125/128
(B) 125/125
(C) 125/126
(D) 125/121
(E) 125/122
Rationale: Required probability = 1 - 1/126
= 125/126
Answer: C
Answer: (C) 125/126
Question: If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 6-letter code words to the number of 5-letter code words?
(A) 5 to 4
(B) 3 to 2
(C) 2 to 1
(D) 5 to 1
(E) 6 to 1
Rationale: Number of ways to form 6-letter code: 10!/4! = 10*9*8*7*6*5
Number of ways to form 5-letter code: 10!/5! = 10*9*8*7*6
Ratio: 5 to 1
Answer : D
Answer: (D) 5 to 1
Question: How many terms are in the G.P. 3, 6, 12, 24, ......., 384,768
(A) 8
(B) 9
(C) 67
(D) 5
(E) 2
Rationale: Explanation:
Here a = 3 and r = 6/3 = 2. Let the number of terms be n.
Then, t = 768 => a * r^(n-1) = 768
=> 3 * 2^(n-1) = 768 => 2^(n-1) = 256 = 2^(8)
=> n-1 = 8 => n = 9.
Answer: B
Answer: (B) 9
Question: If the selling price of 50 articles is equal to the cost price of 40 articles, then the loss or gain percent is?
(A) 20
(B) 98
(C) 66
(D) 54
(E) 12
Rationale: Let C.P. of each article be Re. 1.
Then, C.P. of 50 articles = Rs. 50;
S.P. of 50 articles = Rs. 40.
Loss % = 10/50 * 100 = 20%
Answer: A
Answer: (A) 20
Question: If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance traveled by him is:
(A) 50 km
(B) 56 km
(C) 60 km
(D) 70 km
(E) 80 km
Rationale: Let the actual distance travelled be x km.
x/10 = (x+20)/14
14x = 10x + 200
4x = 200
x = 50 km.
answer :A
Answer: (A) 50 km
Question: Gold is 19 times as heavy as water and copper is 9 times as heavy as water. In what ratio should these be mixed to get an alloy 15 times as heavy as water?
(A) 1:2
(B) 3:2
(C) 4:1
(D) 5:2
(E) 6:5
Rationale: G = 19W
C = 9W
Let 1gm of gold mixed with x gm of copper to get 1+x gm of the alloy
1gm gold + x gm copper = x+1 gm of alloy
19W+9Wx = x+1 * 15W
19+9x = 15(x+1)
x = 2/3
Ratio of gold with copper = 1:2/3 = 3:2
Answer is B
Answer: (B) 3:2
Question: The average height of 35 boys in a class was calculated as 180cm. It has later found that the height of one of the boys in the class was wrongly written as 156 cm whereas his actual height was 106 cm. Find the actual average height of the boys in the class (Round off your answer to two decimal places).
(A) 168.58 cm
(B) 158.58 cm
(C) 179.29 cm
(D) 168.58 cm
(E) 178.58 cm
Rationale: Calculated average height of 35 boys = 180 cm.
Wrong total height of 35 boys = 180 * 35 cm. This was as a result of an actual height of 106 cm being wrongly written as 156 cm. Correct total height of 35 boys = 180 * 35 cm - 156 cm + 106 cm
= 180 * 35 cm - 156 cm + 106 cm/35 = 180 cm - 50 /35 cm
= 180 cm - 1.42 cm = 178.58 cm.
ANSWER:E
Answer: (E) 178.58 cm
Question: The average of four consecutive even numbers is one-fourth of the sum of these numbers. What is the difference between the first and the last number?
(A) 4
(B) 6
(C) 2
(D) Cannot be determined
(E) None of these
Rationale: Let the four consecutive even nos. be 2x, 2x + 2, 2x + 4 and 2x + 6 respectively.
Reqd difference = 2x + 6 – 2x = 6
Answer B
Answer: (B) 6
Question: A 25 cm wide path is to be made around a circular garden having a diameter of 4 meters. Approximate area of the path is square meters is?
(A) 3.34
(B) 3.36
(C) 3.39
(D) 3.35
(E) 3.31
Rationale: Area of the path = Area of the outer circle - Area of the inner circle = ∏{4/2 + 25/100}2 - ∏[4/2]2
= ∏[2.252 - 22] = ∏(0.25)(4.25) { (a2 - b2 = (a - b)(a + b) }
= (3.14)(1/4)(17/4) = 53.38/16
= 3.34 sq m
Answer: A
Answer: (A) 3.34
Question: A car covers a distance of 526 km in 9 hours. Find its speed?
(A) 104 kmph
(B) 289 kmph
(C) 58 kmph
(D) 277 kmph
(E) 177 kmph
Rationale: 526/9
= 58 kmph
Answer: C
Answer: (C) 58 kmph
Question: How many words can be formed by using all letters of the word “BIHAR”
(A) 523
(B) 190
(C) 145
(D) 450
(E) 120
Rationale: The word BIHAR contains 5 different letters.
Required number of words = 5p5 = 5! = (5x4x3x2x1) = 120
Ans: E
Answer: (E) 120
Question: A group of men decided to do a work in 40 days, but 5 of them became absent. If the rest of the group did the work in 60 days, Find the original number of men?
(A) 60
(B) 15
(C) 40
(D) 10
(E) 25
Rationale: Original number of men = 5*60 / (60-40) = 15
Answer is B
Answer: (B) 15
Question: 6 + 6+ 6 + 2 × 6^2 + 2 × 6^3 + 2 × 6^4 + 2 × 6^5 + 2 × 6^6 + 2 × 6^7 =
(A) 6^3
(B) 6^8
(C) 6^2
(D) 6^1
(E) 6^7
Rationale: We have the sum of 9 terms. Now, if all terms were equal to the largest term 2*6^7 we would have: sum=9*(2*6^7)=18*6^7=~6^9, so the actual sum is less than 6^9 and more than 6^7 (option E) as the last term is already more than that. So the answer is clearly B.
Answer: B
Answer: (B) 6^8
Question: Hari purchased 20 dozen notebook at Rs. 48 per dozen. He sold 8 dozen at 10% profit and remaining 12 dozen with 20% profit. What is his profit percentage in the transaction?
(A) 8%
(B) 15%
(C) 16%
(D) none of the above
(E) Cannot be determined
Rationale: Explanation :
C.P of 20 dozen = Rs.(48 x 20) = Rs.960
C.P of 8 dozen = Rs. (48 x8) = Rs. 384.
C.P of 12 dozen =Rs. (960 384) = Rs. 576
Total S.P = Rs. (110/100 x 384 +120/100 x 576) = Rs.1113.60
Profit % = (153.60/960 x 100)% =16%
Answer : C
Answer: (C) 16%
Question: If a 3-member subcommittee is to be formed from a certain 4-member committee, how many different such subcommittee are possible?
(A) 4
(B) 18
(C) 20
(D) 108
(E) 216
Rationale: Another way:
1st member can be selected in 4 ways
2nd can be selected in 3 ways
3rd can be selected in 2 ways
So total ways : 24
But to avoid the similar scenarios 24/3!=4
A
Answer: (A) 4
Question: Anand and Deepak started a business investing Rs. 3500 and Rs. 7000 respectively. Out of a total profit of Rs. 2000, Deepak's share is:
(A) 1333.3
(B) 2687.1
(C) 1200.6
(D) 1580.2
(E) 2671
Rationale: Ratio of their shares = 3500 : 7000 = 1:2
Deepak's share = 2000* 2/3 = Rs. 1333.3.
Answer: A
Answer: (A) 1333.3
Question: Before lunch, a painter can paint a wall at a rate of r square feet per minute. The same painter, after lunch and a cup of coffee, can paint the same wall at a rate r + 1 square feet per minute, and the same wall would be finished in 30 seconds less time. What is the value of r?
(A) 1/3
(B) 3
(C) 1/2
(D) 1
(E) 2
Rationale: Convert 30 seconds to 1/2 minute
Equation: 1/r = 1/(r + 1) + 1/2
Plug options into the equation:
D fits: 1/1 = 1/(1 + 1) + 1/2
Answer: D
Answer: (D) 1
Question: A rectangular plot measuring 90 metres by 50 metres is to be enclosed by wire fencing. If the poles of the fence are kept 10 metres apart, how many poles will be needed ?
(A) 28
(B) 56
(C) 57
(D) 58
(E) None of these
Rationale: Solution
Perimeter of the plot = 2(90 + 50) = 280 m.
∴ Number of poles = [280/10] =28m Answer A
Answer: (A) 28
Question: The value of a machine depreciates at 20% per annum. If its present value is Rs. 1,50,000, at what price should it be sold after two years such that a profit of Rs. 20,000 is made?
(A) 328897
(B) 120000
(C) 877888
(D) 116000
(E) 188871
Rationale: The value of the machine after two years = 0.8 * 0.8 * 1,50,000 = Rs. 96,000
SP such that a profit of Rs. 20,000 is made = 96,000 + 20,000 = Rs. 1,16,000
Answer: D
Answer: (D) 116000
Question: A truck covers a distance of 240 km at a certain speed in 8 hours. How much time would a car take at an average speed which is 18 kmph more than that of the speed of the truck to cover a distance which is 0 km more than that travelled by the truck ?
(A) 6 hours
(B) 5 hours
(C) 7 hours
(D) 8 hours
(E) None
Rationale: Explanation :
Speed of the truck = Distance/time = 240/8 = 30 kmph
Now, speed of car = (speed of truck + 18) kmph = (30 + 18) = 48 kmph
Distance travelled by car = 240 + 0 = 240 km
Time taken by car = Distance/Speed = 240/48 = 5 hours.
Answer –B
Answer: (B) 5 hours