mathewhe/aqua_rat huggingface dataset:
Question: If n is a positive integer and the product of all the integers from 1 to n, inclusive, is a multiple of 8, what is the least possible value of n?
(A) 7
(B) 4
(C) 5
(D) 3
(E) 6
Rationale: We need 3 factors of 2, so n must be at least 4. Therefore, the answer is B.
Answer: (B) 4
Question: A third of Paul's marks in Mathematics exceeds a half of his marks in English by 30. If he got 240 marks in the two subjects together, how many marks did he get in English?
(A) 50
(B) 40
(C) 45
(D) 60
(E) 55
Rationale: Let Paul's marks in Mathematics and English be x and y respectively.
Then, x/3 - y/2 = 30, the LCM of 3,2 is 6 by cross multiplying we get 2x - 3y = 180 -- (I)and we know (x + y = 240) * 2 ==>
2x +2y = 480 --(II)
subtract (I) from (II) we get 5y = 300 ==> y = 60.
so Paul's marks in English is 60.
The correct answer is option D) 60.
Answer: (D) 60
Question: If A : B : C = 3 : 4 : 7, then what is the ratio of (A / B) : (B / C) : (C / A)?
(A) 63 : 48 : 196
(B) 66 : 49 : 190
(C) 56 : 40 : 186
(D) 46 : 38 : 160
(E) 43 : 20 : 170
Rationale: EXPLANATION:
Hint: If a = kb for some constant k, then we can say that a is directly proportional to b.
A : B : C = 3 : 4 : 7
Assume, A = 3 k, B = 4 k, C = 7 k
Therefore,
A/B	=	(3k)/(4K)	,	B/C	=	(4k)/(7K)	,	C/A	=	(7k)/(3K)
A/B	=	(3)/(4)	,	B/C	=	(4)/(7)	,	C/A	=	(7)/(3)
L.C.M of 3, 4, 7 is 84
(3 x 84) / 4 = 63
(4 x 84) / 7 = 48
(7 x 84) / 3 = 196
Ratio of (A/B) : (B/C) : (C/A) = 63:48:196
ANSWER IS A
Answer: (A) 63 : 48 : 196
Question: In how many ways 4 boys and 1 girls can be seated in a row so that they are alternate.
(A) 144
(B) 288
(C) 24
(D) 256
(E) None
Rationale: Solution: Let the Arrangement be,
B B B B G
4 boys can be seated in 4! Ways.
Girl can be seated in 1! Ways.
Required number of ways,
= 4!*1! = 24.
Answer: Option C
Answer: (C) 24
Question: How long will it take for a sum of money to grow from Rs.5000 to Rs.20,000, if it is invested at 10% p.a simple interest?
(A) 30 years
(B) 64 years
(C) 72 years
(D) 56 years
(E) None
Rationale: In this case, Rs. 5000 has become Rs.20,000.
Therefore, the interest earned = 20,000 – 5000 =15000
Interest for Rs 5000 @ 10% for 1 year = 500
500 - 1
15000 - ? => 30 years
Answer : A
Answer: (A) 30 years
Question: Find the area of the quadrilateral of one of its diagonals is 20 cm and its off sets 9 cm and 6 cm?
(A) 128 cm2
(B) 150 cm2
(C) 172 cm2
(D) 177 cm2
(E) 167 cm2
Rationale: 1/2 * 20(9 + 6)
= 150 cm2
Answer:B
Answer: (B) 150 cm2
Question: By selling an article for $100 a man gains $20 then his gain%?
(A) 25%
(B) 30%
(C) 50%
(D) 20%
(E) 10%
Rationale: S.P. = $100
Gain = $20
C.P. = 100-20 = 80
Gain% = 20/80 * 100 = 25%
Answer is A
Answer: (A) 25%
Question: 1, 2, 9, 24, 120, 36,?
(A) 4040
(B) 5040
(C) 3040
(D) 2040
(E) 556
Rationale: 1!=1
2!=2
3^2=9
4!=24
5!=120
6^2=36
and according to the sequence now
7!=5040
ANSWER:B
Answer: (B) 5040
Question: A cab driver 5 days income was $200, $150, $750, $400 , $500. Then his average income is?
(A) $420
(B) $410
(C) $400
(D) $390
(E) $380
Rationale: avg = sum of observations/number of observations
avg income=(200+150+750+400+500)/5 = 400
Answer is C
Answer: (C) $400
Question: At a school, three-fifths of the male students and two-thirds of the female students speak a foreign language. If the number of males is equal to the number of females, what fraction of the students speak a foreign language?
(A) 17/30
(B) 19/30
(C) 11/15
(D) 7/15
(E) 2/5
Rationale: Let x be the number of students in the school.
The number of males who speak a foreign language is (3/5)(1/2)x = (3/10)x
The number of females who speak a foreign language is (2/3)(1/2)x = (1/3)x
The total number of students who speak a foreign language is (3/10)x + (1/3)x = (19/30)x
The answer is B.
Answer: (B) 19/30
Question: In a urban village of india named "owlna" , 90% people have refrigerator , 86% people have television , 80% people got computers and 80% got Air-conditionor. how many people(minimum) got all these luxury.
(A) 23%
(B) 36%
(C) 30%
(D) 34%
(E) 42%
Rationale: B
10%
100 - [ (100-90)+(100-86)+(100-80) +(100-80)]
=100-(10+14+20+20)
=100-64
Answer: (B) 36%
Question: If a man lost 1% by selling oranges at the rate of 16 a rupee at how many a rupee must he sell them to gain 44%?
(A) 12
(B) 14
(C) 7
(D) 11
(E) 10
Rationale: 99% ---- 16
144% ---- ?
99/144* 16 = 11
Answer: D
Answer: (D) 11
Question: A man purchased 2 blankets @ Rs.100 each, 5 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.150. Find the unknown rate of two blankets?
(A) A)300
(B) B)350
(C) C)450
(D) D)470
(E) E)550
Rationale: Explanation:
10 * 150 = 1500
2 * 100 + 5 * 150 = 950
1500 – 950 = 550
E
Answer: (E) E)550
Question: If a farmer wants to plough a farm field on time, he must plough 340 hectares a day. For technical reasons he ploughed only 85 hectares a day, hence he had to plough 2 more days than he planned and he still has 40 hectares left. What is the area of the farm field and how many days the farmer planned to work initially?
(A) 280
(B) 490
(C) 720
(D) 435
(E) 679
Rationale: Let x be the number of days in the initial plan. Therefore, the whole field is 340â‹…x hectares. The farmer had to work for x+2 days, and he ploughed 85(x+2) hectares, leaving 40 hectares unploughed. Then we have the equation:
340x=85(x+2)+40
255x=210
x=0.823
So the farmer planned to have the work done in 6 days, and the area of the farm field is 340(0.823)=280 hectares
correct answer A
Answer: (A) 280
Question: What percent is 120 of 90?
(A) 133 1/3 %
(B) 132 1/3%
(C) 132 2/3%
(D) 132 2/5%
(E) 131 1/5%
Rationale: 120/90 = 4/3
4/3 × 100 = 400/3 = 133 1/3 %
A)
Answer: (A) 133 1/3 %
Question: The average age of students of a class is 15.8 years. The average age of boys in the class is 16.5 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) 2:5
(B) 2:3
(C) 2:4
(D) 2:1
(E) 4:7
Rationale: Let the ratio be k : 1. Then,
k * 16.5 + 1 * 15.4 = (k + 1) * 15.8
= (16.5 - 15.8)k = (15.8 - 15.4)
= k = 0.4/0.7 = 4/7
Required ratio = 4/7 : 1 = 4:7.
Answer:E
Answer: (E) 4:7
Question: A boy sells a horse for Rs.800 and loses something, if he had sold it for Rs.980, his gain would have been double the former loss. Find the cost price of the horse?
(A) 860
(B) 880
(C) 900
(D) 920
(E) 940
Rationale: CP = SP + 1CP = SP - g
800 + x = 980 - 2x
3x = 180 => x = 60
CP = 800 + 60 = 860
A
Answer: (A) 860
Question: If the cost price of 50 articles is equal to the selling price of 40 articles, then the gain or loss percent is?
(A) 27%
(B) 75%
(C) 95%
(D) 35%
(E) 25%
Rationale: Given that, cost price of 50 article is equal to selling price of 40 articles.
Let cost price of one article = Rs. 1
Selling price of 40 articles = Rs. 50
But Cost price of 40 articles = Rs. 40
Therefore, the trader made profit.\Percentage of profit = 10/40 * 100
= 25%
Answer: E
Answer: (E) 25%
Question: How many bricks each measuring 25cm x 11.25cm x 6cm, will be needed to build a wall 8m x 6m x 22.5m
(A) 5600
(B) 600
(C) 6400
(D) 7200
(E) None of these
Rationale: Explanation:
no. of bricks= volume of the wall/volume of 1 brick = (800 x 600 x 22.5) / (25 x 11.25 x 6) = 6400
Answer: C
Answer: (C) 6400
Question: 79 laboratories raise the bacterium, the laboratory have 48 culture dishes on average, which has about 25,070 bacteria each. How many bacteria are there approximately?
(A) 10^7
(B) 10^8
(C) 10^9
(D) 10^10
(E) 10^11
Rationale: 79 laboratories raise the bacterium, the laboratory have 48 culture dishes on average, which has about 25,070 bacteria each. How many bacteria are there approximately?
A. 10^7
B. 10^8
C. 10^9
D. 10^10
E. 10^11
-> Due to approximately, 79=80, 48=50, 25,070=25,000 are derived, which makes (79)(48)(25,075)=(80)(50)(25,000)=10^8. The answer is B.
Answer: (B) 10^8
Question: A and B can do a piece of work in 10 days, while B and C can do the same work in 15 days and C and A in 25 days. they started working together, after 4 days A left. After another 4 days B left. In how many days C can finish the remaining work?
(A) 16
(B) 32
(C) 64
(D) 96
(E) None of These
Rationale: Let the rates of A, B and C be a, b, and c respectively.
A and B can do a piece of work in 10 days: a + b = 1/10;
B and C can do the same work in 15 days: b + c = 1/15;
C and A can do the same work in 25 days: c + a = 1/25.
Sum the above 3 equations: 2(a + b + c) = 31/150 --> a + b + c = 31/300
Subtract a + b = 1/10 from above to get c = 1/300.
For 4 days all 3 worked and completed 4*(a + b + a) = 124/300 of the work.
For the next 4 days B and C worked and they completed 4(b + c) = 4/15 = 80/300 of the work.
So, by the time C is left alone 1 - (124/300 + 80/300) = 96/300 of the work is left to be completed by C alone.
Time = Job/Rate = (96/300)/(1/300) = 96 days.
Answer: D
Answer: (D) 96
Question: What is the smallest integer k for which 64^k > 4^16?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: 64^k > 4^16
4^(3k) > 4^16
3k > 16
k = 6
The answer is C.
Answer: (C) 6
Question: Find the average of all prime numbers between 30 and 50?
(A) 24.7
(B) 39.8
(C) 12.3
(D) 41.3
(E) 15.8
Rationale: There are five prime numbers between 30 and 50.
They are 31,37,41,43 and 47.
Therefore the required average=(31+37+41+43+47)/5 = 199/5 = 39.8.
Ans: B
Answer: (B) 39.8
Question: The average of first six prime numbers greater than 3 is?
(A) 16
(B) 10
(C) 12
(D) 19
(E) 17.8
Rationale: 5 + 7 +11 + 13 + 17 + 19 = 72/6 = 12
Answer: C
Answer: (C) 12
Question: The average expenditure of a man for the first five months is Rs.60 and for the next seven months it is Rs.130. If he saves Rs.290 in that year, his monthly average income is :
(A) Rs.125
(B) Rs.150
(C) Rs.165
(D) Rs.170
(E) none
Rationale: Explanation:
Total income = Rs.(60Ã—5+130Ã—7+290)=Rs.1500
Average monthly income
= Rs. (1500/12)=Rs.125
Correct Option: A
Answer: (A) Rs.125
Question: A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 50 sq. feet, how many feet of fencing will be required?
(A) 34
(B) 40
(C) 25
(D) 88
(E) 78
Rationale: We have: l = 20 ft and lb = 50 sq. ft.
So, b = 2.5 ft.
Length of fencing = (l + 2b) = (20 + 5) ft = 25 ft.
ANSWER:C
Answer: (C) 25
Question: In how many different number of ways 4 boys and 3 girls can sit on a bench such that girls always sit together?
(A) 720
(B) 740
(C) 760
(D) 780
(E) 800
Rationale: Option 'A'
Answer: (A) 720
Question: A bag contains 3 red, 4 black and 2 white balls. What is the probability of drawing a red and a white ball in two successive draws, each ball being put back after it is drawn?
(A) 2/27
(B) 1/9
(C) 1/3
(D) 4/27
(E) 2/9
Rationale: P=2∗3/9∗2/9=4/27
We are multiplying by 2 as there are two possible wining scenarios RW and WR.
Answer: D.
Answer: (D) 4/27
Question: A car rental company charges for mileage as follows: 9 dollars per mile for the first n miles and 10 dollars per mile for each mile over n miles. How much will the mileage charge be, in dollars, for a journey of d miles, where d > n ?
(A) d-n
(B) 6d-n
(C) 10d-n
(D) 8d-n
(E) 12d-n
Rationale: Total Distance in miles = d
Millage Charge = 9n + (d-n) 10
9n --> For the first n Miles
(d-n)10--> Total no of miles after traveling the first n miles is d-n and the rate after n miles is 10 .
If we solve the equation , We will get 10d-n
Answer : C
Answer: (C) 10d-n
Question: The cost price of a radio is Rs.1500 and it was sold for Rs.1335, find the loss %?
(A) 18
(B) 16
(C) 26
(D) 17
(E) 11
Rationale: Explanation:
1500 ---- 165
100 ---- ? => 11%
Answer:E
Answer: (E) 11
Question: In the rectangular coordinate system, what is the x-intercept of a line passing through (10, 3) and (−10, −7)?
(A) 4
(B) 2
(C) 0
(D) −2
(E) −4
Rationale: slope = rise/run = 10/20 = 1/2
The equation of the line is y = (1/2)x + b
3 = (1/2)(10) + b
b = -2
The equation of the line is y = (1/2)x - 2
To find the x-intercept, let y = 0:
0 = (1/2)x - 2
x = 4
The answer is A.
Answer: (A) 4
Question: Find the 15th term of an arithmetic progression whose first term is 2 and the common difference is 3.
(A) 45
(B) 38
(C) 44
(D) 40
(E) 46
Rationale: n th term of A.P = a +(n-1) *d
= 2+(15-1)*3 , = 2 + 42 = 44.
ANSWER:C
Answer: (C) 44
Question: Ravi can do a piece of work in 20 days while Prakash can do it in 40 days. In how many days will they finish it together?
(A) 5 7/9 days
(B) 6 7/9 days
(C) 5 1/9 days
(D) 5 7/2 days
(E) 4 7/9 days
Rationale: 1/20 + 1/40 = 3/40
40/7 = 5 7/9 days
ANSWER:A
Answer: (A) 5 7/9 days
Question: In a dairy farm, 46 cows eat 46 bags of husk in 46 days. In how many days one cow will eat one bag of husk ?
(A) 34 days
(B) 40 days
(C) 46 days
(D) 50 days
(E) None of these
Rationale: Explanation:
Less Cows, More days (Indirect Proportion)
Less bags, Less days (Direct Proportion)
[Cows1 46
Bags 46 1]::46:x
=>x∗46∗1=46∗1∗46
=>x=46
Option C
Answer: (C) 46 days
Question: Tap A runs 3 liters of water per minute into a bucket that has a total volume of 36 liters. Tap B fills a third of the bucket in 20 mins.
Working together how long will it take both taps to fill the bucket ?
(A) 10 minutes
(B) 1.5 hours
(C) 9 hours and 12 minutes
(D) 15 hours
(E) 1 hour and 48 minutes.
Rationale: Pipe A has a rate of 3 liters per minute which equals a rate of 180 liters per hour.
Pipe B has a rate of 36 liters per hour.
180 + 36 (A+B) = Together they have a rate of 2000 liters per hour.
36 (The bucket) / 216 = 1/6 = 10 minutes
Answer -A
Answer: (A) 10 minutes
Question: A person can row upstream 20 kmph and downstream 30 kmph. Find the person rate in still water and rate of the stream.
(A) 25,5
(B) 10,5
(C) 5,5
(D) 10,5
(E) 1,5
Rationale: Explanation:
Please remember,
If a is rate downstream and b is rate upstream
Rate in still water = 1/2(a+b)
Rate of current = 1/2(a-b)
=> Rate in still water = 1/2(30+20) = 25 kmph
=> Rate of current = 1/2(30-20) = 5 kmph
Option A
Answer: (A) 25,5
Question: The cost price of 18 articles is equal to the selling price of 11 articles. Find the profit percent?
(A) 68 2/91%
(B) 63 7/11
(C) 68 9/11%
(D) 68 2/91%
(E) 62 2/11%
Rationale: 18 CP = 11 SP
11 --- 2 CP
100 --- ? =>63 7/11%
Answer:B
Answer: (B) 63 7/11
Question: Anand and Deepak started a business investing Rs. 12,500 and Rs. 35,000 respectively. Out of a total profit of Rs. 10,800, Deepak's share is?
(A) Rs. 9400
(B) Rs. 8900
(C) Rs. 8400
(D) Rs. 3400
(E) Rs. 7957.9
Rationale: Ratio of their shares = 12500 : 35000 = 5:14
Deepak's share = 10800 * 14/19 = Rs. 7957.9
Answer:E
Answer: (E) Rs. 7957.9
Question: A fruit vendor purchased 20 dozens of bananas at Rs. 15 per dozen. But one-fourth of the bananas were rotten and had to be thrown away. He sold two-third of the remaining bananas at Rs. 22.50 per dozen. At what price per dozen should he sell the remaining bananas to make neither a profit nor a loss?
(A) Rs.18
(B) Rs.15
(C) Rs.11
(D) Rs.19
(E) Rs.12
Rationale: CP of 20 dozen of bananas = 15 * 20 = Rs. 300
Number of bananas which are rotten = 1/4 * 20 = 5 dozen.
SP of two-third of remaining bananas = (2/3 * 15) * 22.5 = Rs. 225
SP of remaining 5 dozens of bananas to make no profit and no loss =(300 - 225) = Rs. 75.
SP of 1 dozen bananas = 75/5 = Rs.15.
Answer:B
Answer: (B) Rs.15
Question: The diagonals of a rhombus are 14 cm and 18 cm. Find its area?
(A) 176
(B) 190
(C) 150
(D) 126
(E) 292
Rationale: 1/2 * 14 * 18
= 126
Answer:D
Answer: (D) 126
Question: Mr. Yutaro’s class contains 4 boys and 12 girls. If two students are chosen, one at a time, from the class, what is the probability that a boy and a girl are chosen?
(A) 9/48
(B) 2/15
(C) 11/24
(D) 27/48
(E) 13/16
Rationale: Probability of a boy being chosen first, then a girl:
4/16 * 12/15
Probability of a girl being chosen first, then a boy:
12/16 * 4/15
Probability of a boy and a girl being chosen:
(4*12+12*4) / (15*16)
=2/15
Answer:B
Answer: (B) 2/15
Question: A tour group of 25 people paid a total of $600 for entrance to a museum. If this price included a 5% sales tax, and all the tickets cost the same amount, what was the face value of each ticket price without the sales tax?
Choices
(A) $22.8
(B) $23.94
(C) $24
(D) $25.20
(E) $30
Rationale: A.
Answer: (A) $22.8
Question: Find the missing figures :
?% of 50 = 2.125
(A) 8.55
(B) 6.55
(C) 8.75
(D) 7.75
(E) 4.25
Rationale: (i)	Let x% of 50 = 2.125. Then , (x/100)*50 = 2.125
X = (2.125 * 2) = 4.25
Answer is E.
Answer: (E) 4.25
Question: A diet contains 400 grams of a mixture of two foods, food X and food Y. Food X contains 10 percent protein and food Y contains 15 percent protein. If a diet provides exactly 46 grams of protein daily, how many grams of food X are in the mixture?
(A) 280
(B) 300
(C) 320
(D) 340
(E) 360
Rationale: Let x be the number of grams of food X in the mixture.
0.1x + 0.15(400-x) = 46
0.05x = 14
x = 280
The answer is A.
Answer: (A) 280
Question: How many odd factors does 270 have?
(A)  3
(B)  4
(C)  5
(D)  6
(E)  8
Rationale: Start with the prime factorization: 270 = 2*3*5
For odd factors, we put aside the factor of two, and look at the other prime factors.
set of exponents = {1, 1}
plus 1 to each = {2, 2}
product = 2*2 = 4
Therefore, there are 4 odd factors of 270.
Answer: B.
Answer: (B)  4
Question: There are 99 people that own pets. 15 people own only dogs, 10 people own only cats, 5 people own only cats and dogs, 3 people own cats, dogs and snakes. How many total snakes are there?
(A) 2
(B) 4
(C) 8
(D) 69
(E) 32
Rationale: lets assign variables to all the areas in Venn Diagram of Three.
three different Units are DOG, Cat, Snake= Total = 99
Only Dog= d=15
Only Cat = c=10
Only Snake = s
Exactly Dog and Cat= 5
Exactly Dog and Snake = x
Exactly Cat and Snake = y
all three= 3
so 99=15+10+5+3+x+y+s
we need to know total snakes= x+y+s+3 = 69
answer:D
Answer: (D) 69
Question: A garrison of 400 men had a provision for 31 days. After 28 days 280 persons re-enforcement leave the garrison. Find the number of days for which the remaining ration will be sufficient?
(A) 227
(B) 66
(C) 10
(D) 99
(E) 77
Rationale: 400 --- 31
400 --- 3
120 --- ?
400*3 = 120*x => x =10 days
Answer: C
Answer: (C) 10
Question: What is the probability of rolling two six-sided dice, and getting a different number on each die?
(A) 5/6
(B) 1/3
(C) 4/9
(D) 5/9
(E) 7/18
Rationale: MAGOOSHOFFICIAL SOLUTION
For the first die, we can roll any one of six numbers. For the second die, we can roll any number save for the number we rolled on the first die, giving us 5 possibilities. For the third die, we can roll four different numbers (we can’t roll the number we rolled on the first or second die.
6 x 5 = 30 possibilities out of 36 total possibilities. (For total possibilities we get 6 x 6 = 36).
30/36 = 5/6
Answer: A.
Answer: (A) 5/6
Question: A box contain Red, Blue and Green colored balls. The number of Red balls is 80 and the number of Blue balls is 60.
The number of Green balls subtracted from the number of Red balls is the same as the number of Green balls added with the number of Blue balls. Then the number of Green balls is?
(A) 80
(B) green balls = 70
(C) 60
(D) 85
(E) 140
Rationale: Answer
Let the number of Green balls be x.
Then, x - 60= 80 - x
â‡’ 2x = 80+ 60= 140
â‡’ 2x = 140
âˆ´ x = 70
Correct Option: B
Answer: (B) green balls = 70
Question: The total age of A and B is 20 years more than the total age of B and C. C is how many years younger than A.?
(A) 20
(B) 12
(C) 15
(D) 16
(E) 10
Rationale: (A+B)-(B-C)=20
A-C=20
Answer is A
Answer: (A) 20
Question: A man can row with a speed of 40 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?
(A) 29
(B) 378
(C) 20
(D) 27
(E) 45
Rationale: M = 40
S = 5
DS = 40 + 5 = 45
Answer: E
Answer: (E) 45
Question: There are 6 ladies and 3 gents to dine at a round table. In how many ways can they seat themselves so that no two gents are seated together.
(A) 8540
(B) 2880
(C) 8640
(D) 6560
(E) 8860
Rationale: First arrange the ladies. This is a circular arrangment. 6 Gents can be arranged in 5! ways.
Now there are 4 spaces (space in between two ladies) and we have to seat 3 gents there.
First select 3 places out of 4 available places. can be done in 4C3 ways. Then arrange 3 gents there in 3! ways.
Total: 5!*4C3*3! = 2880
B is the answer.
Answer: (B) 2880
Question: A butler stole wine from a butt of sherry which contained
40% of spirit and he replaced,what he had stolen by wine
containing only 16% spirit. The butt was then of 24%
strength only. How much of the butt did he steal?
(A) 1/3 OF THE BUTT
(B) 2/3 OF THE BUTT
(C) 1/4 OF THE BUTT
(D) 1/8 OF THE BUTT
(E) 1/9 OF THE BUTT
Rationale: Wine containing 40%spirit Wine containing 16% spirit
Wine containing 24% spirit
8 16
They must be mixed in the ratio of =1:2.
Thus 1/3 of the butt of sherry was left
hence the butler drew out 2/3 of the butt.
ANSWER B
Answer: (B) 2/3 OF THE BUTT
Question: If (0.2)x = 2 and log 2 = 0.3010, then the value of x to the nearest tenth is:
(A) -10.0
(B) -0.5
(C) -0.4
(D) -0.2
(E) 10.0
Rationale: (0.2)x = 2.
Taking log on both sides
log (0.2)x = log 2.
x log (0.2) = 0.3010, [since log 2 = 0.3010].
x log (2/10) = 0.3010.
x [log 2 - log 10] = 0.3010.
x [log 2 - 1] = 0.3010,[since log 10=1].
x [0.3010 -1] = 0.3010, [since log 2 = 0.3010].
x[-0.699] = 0.3010.
x = 0.3010/-0.699.
x = -0.4306….
x = -0.4 (nearest tenth)
correct answer C
Answer: (C) -0.4
Question: Rahul went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
(A) 19
(B) 19.7
(C) 20
(D) 21.1
(E) 23
Rationale: Total cost of the items he purchased = Rs.25
Given that out of this Rs.25, 30 Paise is given as tax
=> Total tax incurred = 30 Paise = Rs.30/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (25−30/100−x)6/100 = 30/100
⇒ 6(25 −0.3 −x) = 30
⇒ (25 − 0.3 − x) = 5
⇒ x = 25 − 0.3 − 5 = 19.7
B)
Answer: (B) 19.7
Question: Calculate the different number of ways 5 boys and 3 girls can sit on a bench?
(A) 40120
(B) 40220
(C) 40420
(D) 40320
(E) 40325
Rationale: npn = n!
8p8 = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 40320
D
Answer: (D) 40320
Question: A vessel contains 20 liters of a mixture of milk and water in the ratio 3:2. 10 liters of the mixture are removed and replaced with an equal quantity of pure milk. If the process is repeated once more, find the ratio of milk and water in the final mixture obtained?
(A) 9:1
(B) 9:6
(C) 9:3
(D) 9:2
(E) 9:9
Rationale: Milk = 3/5 * 20 = 12 liters, water = 8 liters
If 10 liters of mixture are removed, amount of milk removed = 6 liters and amount of water removed = 4 liters.
Remaining milk = 12 - 6 = 6 liters
Remaining water = 8 - 4 = 4 liters
10 liters of pure milk are added, therefore total milk = (6 + 10) = 16 liters.
The ratio of milk and water in the new mixture = 16:4 = 4:1
If the process is repeated one more time and 10 liters of the mixture are removed, then amount of milk removed = 4/5 * 10 = 8 liters.
Amount of water removed = 2 liters.
Remaining milk = (16 - 8) = 8 liters.
Remaining water = (4 -2) = 2 liters.
The required ratio of milk and water in the final mixture obtained = (8 + 10):2 = 18:2 = 9:1.Answer: A
Answer: (A) 9:1
Question: The radius of the wheel of a bus is 140 cms and the speed of the bus is 66 km/h, then the r.p.m. (revolutions per minutes)of the wheel is
(A) 125
(B) 250
(C) 300
(D) 330
(E) None of these
Rationale: Radius of the wheel of bus = 140 cm. Then,
circumference of wheel = 2Ï€r = 280Ï€ = 880 cm
Distance covered by bus in 1 minute
= 66â„60 Ã— 1000 Ã— 100 cms
Distance covered by one revolution of wheel
= circumference of wheel
= 880 cm
âˆ´ Revolutions per minute = 6600000/60Ã—880 = 125
Answer A
Answer: (A) 125
Question: The number of boys in a class is four times the number of girls. Which one of the following numbers cannot represent the total number of children in the class ?
(A) A)48
(B) B)44
(C) C)42
(D) D)40
(E) E)38
Rationale: Explanation:
Let number of girls = x and number of boys = 4x.
Then, 4x + x = 5x = total number of students.
Thus, to find exact value of x, the total number of students must be divisible by 5.
Answer: D
Answer: (D) D)40
Question: A tradesman by means of his false balance defrauds to the extent of 30%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?
(A) 37
(B) 69
(C) 65
(D) 78
(E) 56
Rationale: Explanation:
g% = 30 + 30 + (30*30)/100
= 69%
Answer: B
Answer: (B) 69