mathewhe/aqua_rat huggingface dataset:
Question: In digging a pond 20 m * 10 m * 5 m the volumes of the soil extracted will be?
(A) 3387
(B) 1000
(C) 2866
(D) 2787
(E) 1121
Rationale: 20 * 10 * 5 = 1000
Answer: B
Answer: (B) 1000
Question: If b does not equal zero, and ab = b/5, what is the value of a?
(A) A)1/5
(B) B)1/4
(C) C)1/3
(D) D)1/2
(E) of the above
Rationale: Explanation:
To solve for a, divide both sides of the equation by b: ab = b/5
(ab)/b = (b/5)/b
a = (b/5)*1/b
a = 1/5
Answer: (A).
Answer: (A) A)1/5
Question: 476 ** 0 is divisible by both 3 and 11. The non-zero digits in the hundred's and ten's places are respectively
(A) 7 and 4
(B) 7 and 5
(C) 8 and 4
(D) 8 and 5
(E) None
Rationale: Let the given number be 476 xy 0.
Then (4 + 7 + 6 + x + y + 0) = (17 + x + y) must be divisible by 3.
And, (0 + x + 7) - (y + 6 + 4) = (x - y -3) must be either 0 or 11.
x - y - 3 = 0 y = x - 3
(17 + x + y) = (17 + x + x - 3) = (2x + 14)
x= 2 or x = 8.
x = 8 and y = 5.
Option D
Answer: (D) 8 and 5
Question: In a class of 69 students 41 are taking French, 22 are taking German. Of the students taking French or German, 9 are taking both courses. How many students are not enrolled in either course?
(A) 6
(B) 15
(C) 24
(D) 33
(E) 54
Rationale: Formula for calculating two overlapping sets:
A + B - both + NOT(A or B) = Total
so in our task we have equation:
41 (french) + 22 (german) - 9 (both) + NOT = 69
54 + NOT = 69
NOT = 69 - 54 = 15
So answer is B
Answer: (B) 15
Question: Find the simple interest on $3000 for 3 years at 10% per annum?
(A) $900
(B) $300
(C) $500
(D) $600
(E) $1000
Rationale: SI = PTR/100
= 3000*3*10/100 = $900
Answer is A
Answer: (A) $900
Question: How many different positive integers are factors of 36 ?
(A) 10
(B) 2
(C) 7
(D) 3
(E) 2
Rationale: 36=2*18
3*12
4*9
6*6
Answer : C
Answer: (C) 7
Question: A certain sum is invested at simple interest at 15% p.a. for two years instead of investing at 10% p.a. for the same time period. Therefore the interest received is more by Rs. 840. Find the sum?
(A) s. 8400
(B) s. 9000
(C) s. 14000
(D) s. 17000
(E) s. 27000
Rationale: Let the sum be Rs. x.
(x * 15 * 2)/100 - (x * 10 * 2)/100 = 840
=> 30x/100 - 20x/100 =840
=> 10x/100 = 840
=> x = 8400.
ANSWER:A
Answer: (A) s. 8400
Question: Car Z travels 48 miles per gallon of gasoline when driven at a constant rate of 45 miles per hour, but travels 20 percent fewer miles per gallon of gasoline when driven at a constant rate of 60 miles per hour. How many miles does car Z travel on 10 gallons of gasoline when driven at a constant rate of 60 miles per hour?
(A) 320
(B) 384
(C) 400
(D) 408.3
(E) 440
Rationale: The question stem asks us for the distance possible with 10 gallons of fuel at a constant speed of 60 miles per hour. We therefore first calculate the fuel efficiency at that speed.
The stem tells us that at 45 miles/hour, the car will run 48 miles/gallon and at 60 miles/hour, that distance decreases by 20%. We can therefore conclude that the car will travel 38.4 miles/gallon at a constant speed of 60 miles/gallon. With 10 gallons of fuel, the car can therefore travel 38.4 miles/gallon * 10 gallons = 384 miles.
Answer B.
Answer: (B) 384
Question: In a consumer survey, 85% of those surveyed liked at least one of three products: 1, 2, and 3. 50% of those asked liked product 1, 30% liked product 2, and 20% liked product 3. If 7% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products?
(A) 5
(B) 8
(C) 15
(D) 20
(E) 25
Rationale: Use the forumla ;
Total = Group1 + Group2 + Group3 - (sum of 2-group overlaps) - 2*(all three) + Neither
100 = 50 + 30 + 20 - ( sum of 2) -2(7) +15
100 = 101-( sum of 2)
1 = sum of 2
so more than 1 = 8
B
Answer: (B) 8
Question: The ratio of the volumes of two cubes is 729 : 1331. What is the ratio of their total surface areas?
(A) 81:121
(B) 81:128
(C) 81:126
(D) 81:124
(E) 81:122
Rationale: Ratio of the sides = ³√729 : ³√1331
= 9 : 11
Ratio of surface areas = 92 : 112
= 81:121
Answer: A
Answer: (A) 81:121
Question: Which of the following points is closest to line y=x
(A) (2, -1)
(B) (2, 4)
(C) (1, 1)
(D) (2, -1)
(E) (-2, 0)
Rationale: Attachment:
m12-20.pngAs you can see point (1, 1) is the closest to line y=x.
Answer: C.
Answer: (C) (1, 1)
Question: x and y are positive integers. If x is a prime factor of y^2 , which of the following MUST be true?
(A) x is even
(B) x=y^2
(C) y/x is even
(D) x/y <=1
(E) x+1 is also the prime factor of y^2
Rationale: A. x is even --> not necessarily true: x=3=odd and y=3
B. x=y2--> never true, as x=primex=prime then it can not equal to square of another integer;
C. yx is even --> not necessarily true: if x=3x=3 and y=3y=3 then yx=1=odd
D. xy≤1 is less than or equal to 1 --> always true as shown above or by POE;
E. x+1 is also a prime factor of y2--> not necessarily true: if x=2 and y=2 then x+1=3 and 3 is not a factor of y2=4
Answer: D.
Answer: (D) x/y <=1
Question: How many numbers with 2 different digits can be formed using only the odd digits?
(A) 10
(B) 20
(C) 40
(D) 60
(E) 120
Rationale: Odd digits are 1, 3, 5, 7, 9.
We want 3 different digits.
First digit can be chosen in 5 ways.
Second digit can be chosen in 4 ways.
Total ways = 5*4
= 20
Hence option (B).
Answer: (B) 20
Question: What is the least number of digits (including repetitions) needed to express 10^600 in decimal notation?
(A) a) 4
(B) b) 601
(C) c) 101
(D) d) 1000
(E) e) 1001
Rationale: 10^n is a decimal number with a 1 followed by n zeros.
So 10^600 will include 600 0's + 1 digit for 1 = 601
So the answer is B
Answer: (B) b) 601
Question: In a 2000 m race, A beats B by 100 meters or 40 seconds. Find the speed of B?
(A) 10m/s
(B) 2.5m/s
(C) 5m/s
(D) 7m/s
(E) 3m/s
Rationale: Since A beats B by 100 m or 40 seconds,
it implies that B covers 100 m in 40 seconds.
Hence speed of B = 100/40 = 2.5 m/s.
Answer: B
Answer: (B) 2.5m/s
Question: It takes 2 tons of copper ore and 4 tons of iron ore to make one ton of alloy A. How many tons of alloy A can be made from 60 tons of copper ore and 90 tons of iron ore?
(A)  18
(B)  18 3/4
(C)  20
(D)  22 1/2
(E)  50
Rationale: Yes, you need copper ore:iron ore in the ratio 2:4. Total 6 tons of the mix in this ratio will give 1 ton of alloy A.
If you have 60 tons of copper ore, it is enough for 60/2 = 30 tons of alloy A.
If you have 90 tons of iron ore, it is enough for 90/4 = 22 1/2 tons of alloy A.
Since iron ore is available for only 22 1/2 tons of alloy A, you can make only 22 1/2 tons of alloy A.
The leftover copper ore alone cannot make any alloy A and hence will be leftover only.
Answer must be 22 1/2.
(D)
Answer: (D)  22 1/2
Question: If a fair coin is flipped seven times in a row, what is the probability that there will be at least one head and one tail?
(A) 3/4
(B) 11/12
(C) 15/16
(D) 31/32
(E) 63/64
Rationale: The number of possible outcomes is 2^7 = 128
There is one way to get no heads and one way to get no tails.
Thus there are 126 outcomes with at least one head and one tail.
P(at least one head and one tail) = 126/128 = 63/64
The answer is E.
Answer: (E) 63/64
Question: A watch was sold at a loss of 10%. If it was sold for Rs.196 more, there would have been a gain of 4%. What is the cost price?
(A) s:1000
(B) s:1067
(C) s:1278
(D) s:1028
(E) s:1400
Rationale: 90%
104%
--------
14% ---- 196
100% ---- ? =>
Rs:1400
Answer: E
Answer: (E) s:1400
Question: A WORKS TWICE AS FAST AS B. IF B CAN COMPLETE A WORK IN 12 DAYS INDEPENDENTLY, THE NUMBER OF DAYS IN WHICH A AND B CAN TOGETHER FINISH THE WORK IS:
(A) 4 DAYS
(B) 6 DAYS
(C) 8 DAYS
(D) 18 DAYS
(E) NONE OF THESE
Rationale: RATIO OF RATES OF WORKING OF A AND B = 2:1. SO, RATIO OF TIME TAKEN = 1:2
A'S 1 DAY'S WORK = 1/6, B'S 1 DAY'S WORK = 1/12
(A+B)'S 1 DAY'S WORK = (1/6+1/12)=3/12=1/4
SO, A AND B TOGETHER CAN FINISH THE WORK IN 4 DAYS.
CORRECT OPTION: A
Answer: (A) 4 DAYS
Question: John traveled 80% of the way from Yellow-town to Green-fields by train at an average speed of 80 miles per hour. The rest of the way John traveled by car at an average speed of v miles per hour. If the average speed for the entire trip was 70 miles per hour, what is v in miles per hour?
(A) 30
(B) 40
(C) 50
(D) 55
(E) 60
Rationale: HiBunuel
THe question seems incorrect. it should not be 80% at the speed of 80. However if it's 20% at the speed of 80, Answer comes out 55.
The question is correct. Here's the explanation:
Let distance be D. We can find the total timeequate it, which comes as:
0.8D / 80 + 0.2D / v = D / 70 => v = 60 (Option E).
Answer: (E) 60
Question: An amount of money is to be divided between P, Q and R in the ratio of 3:7:12. If the difference between the shares of P and Q is Rs.4000, what will be the difference between Q and R's share?
(A) 2788
(B) 5000
(C) 7282
(D) 2782
(E) 2729
Rationale: 4 --- 4000
5 --- ? => 5000
Answer:B
Answer: (B) 5000
Question: In the next Worldcup of cricket there will be 12 teams, divided equally in 2groups. Teams of eachgroup will play a match against each other. From each group 3 top teams will qualify for the next round. In this round each team will play against each others once. 4top teams of this round will qualify for the semifinal round, where they play the best of 3matches. The Minimum number of matches in the next World cup will be
(A) 48
(B) 49
(C) 53
(D) 55
(E) 58
Rationale: The number of matches in first round,
= 6C2 +6C2;
Number of matches in next round,
= 6C2;
Number of matches in semifinals,
= 4C2;
Total number of matches,
= 6C2 +6C2+6C2+4C2+2.
= 53.
C
Answer: (C) 53
Question: find the number, difference between number and its 3/5 is 62.
(A) 150
(B) 153
(C) 154
(D) 155
(E) 156
Rationale: Explanation:
Let the number = x,
Then, x-(3/5)x = 62,
=> (2/5)x = 62 => 2x = 62*5,
=> x = 155
Answer: Option D
Answer: (D) 155
Question: A team bought a total of 198 balls. If each player on the team bought at least 17 balls, then what is the greatest possible number of players on the team?
(A) 21
(B) 11
(C) 23
(D) 24
(E) 25
Rationale: 198/17=11 plus remainder.
The answer is B.
Answer: (B) 11
Question: Every month Rani gives 65% of her salary to her mother. She spends 15% of her salary and saves the remainder. She saves $130 more than what she spends. What is her monthly salary?
(A) 2200
(B) 2400
(C) 2600
(D) 2800
(E) 3000
Rationale: Total Salary given+Spent+Saving= 100%
65%+15%+Savings =100%
80%+Savings=100%
Savings=100%-80%=20%
Savings%-Spent%=$130
20-15=5%
5%of Salary =$130
5/100 * Salary = 130
Salary =130*100/5 =$2600
answer : C
Answer: (C) 2600
Question: If you select two cards from a pile of cards numbered 1 to 10, what is the probability that the sum of the numbers is less than 4?
(A) 1/45
(B) 4/45
(C) 1/15
(D) 1/10
(E) 1/5
Rationale: The number of ways to choose two cards is 10C2=45.
There is only one way to get a sum less than 4.
P(sum less than 4)=1/45
The answer is A.
Answer: (A) 1/45
Question: The difference between a discount of 35% and two successive discounts of 20% and 20% on a certain bill was 22. Find the amount of the bill.
(A) 1,100
(B) 200
(C) 2,200
(D) Data inadequate
(E) None of these
Rationale: Successive discount = 20%+20×80/100
= 20 + 16 = 36%
Difference in discount = 36 – 35 = 1%
\ Bill amount = 22 × 100 = 2200
Answer C
Answer: (C) 2,200
Question: A boy goes to his school 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. The distance between his house and school is?
(A) 3 km
(B) 2 km
(C) 8 km
(D) 6 km
(E) 9 km
Rationale: D
Average speed = (2 * 3 * 2) / (3 + 2) = 12/5 km/hr.
Distance traveled = 12/5 * 5 = 12 km.
Distance between house and school = 12/2 = 6 km.
Answer: (D) 6 km
Question: Rahim bought 27 books for Rs.581 from one shop and 20 books for Rs.594 from another. What is the average price he paid per book ?
(A) 28
(B) 18
(C) 27
(D) 25
(E) 21
Rationale: Average price per book
= (581+ 594) / (27 + 20)
= 1175 / 47
= Rs.25
Answer:D
Answer: (D) 25
Question: Two pipes A and B can separately fill a tank in 2 minutes and 15 minutes respectively. Both the pipes are opened together but 4 minutes after the start the pipe A is turned off. How much time will it take to fill the tank?
(A) 22
(B) 10
(C) 88
(D) 566
(E) 222
Rationale: 4/12 + x/15 = 1
x = 10.Answer: B
Answer: (B) 10
Question: In a race of length L metres, Johnson beats Lewis by M metres and Greene by N metres, By how many metres does Lewis beat Greene in the same race ? (M<N)
(A) L(L-N) / L-M
(B) L(N-M) / L-M
(C) L-N
(D) M-N
(E) M+
Rationale: the ans is quite simple N-M but since the ans is not given, the best way to 'find' the correct option is to plug in the numbers. For my work, i took the following numbers:
L = 300
M = 10
N =20.
So basically, L beat G by 10 meters. Now whatever options comes close to the figure 10 is the right ans..
looking the the opion C to E, one can make out that they are incorrect, leaving us with just ..A
Out of which, i choose A.
Answer: (A) L(L-N) / L-M
Question: By selling 16 pencils for a rupee a man loses 5%. How many for a rupee should he sell in order to gain 15%?
(A) 12.95
(B) 19
(C) 17.56
(D) 16.56
(E) 15
Rationale: 85% --- 16
105% --- ?
85/105 * 16 = 8
Answer: A
Answer: (A) 12.95
Question: Four friends go to see a movie at the local movie theater and sit in a row together. If there are two friends who refuse to sit next to each other, how many 4-person seating arrangements are possible?
(A) 6
(B) 8
(C) 10
(D) 12
(E) 24
Rationale: The number of ways to arrange 4 people in a row is 4!
From this we want to subtract all the arrangements where the two friends are next to each other. If we consider them as one unit, then the number of arrangements of this 2-person unit and the 2 other friends is 3! And the number of arrangements of the two friends within this unit are 2 because the two friends can switch places. So the total number of arrangements of the 4 friends with the 2-person unit together is 3!*2
The total number of permutations where these two friends are not seated next to each other is 4! - 3!*2 = 24-12 = 12
The answer is D.
Answer: (D) 12
Question: Tough and Tricky questions: Exponents.
If 2^(3x+2)*3^(2y-3) = 32^x*9^y, then x + y =
(A) -3
(B) -1
(C) 0
(D) -5
(E) -2
Rationale: Here is my solution.
2^(3x+2)*3^(y-3) = 32^x*9^y
Here RHS 32^x*9^y= 2^(5x)*3^(2y)
Equating powers on both sides-->
3x+2=5x , thus x=1 and
y-3=2y giving y=-3
So, x+y=-2
Option: E
Answer: (E) -2
Question: Let us say that a table tennis tournament was going on with knock out terms which means the one who loses the match is out of the tournament. 120 players took part in that tournament.
How many matches were played?
(A) 99 matches.
(B) 88 matches.
(C) 77 matches.
(D) 66 matches.
(E) 119 matches.
Rationale: Solution:
119 matches.
The number of matches will always sum up to one less than the number of players in a knock out tournament. You may calculate it in any manner. Thus 119 matches were played.
Answer E
Answer: (E) 119 matches.
Question: A, B and C invests Rs.2000, Rs.3000 and Rs.4000 in a business. After 2 year A removed his money; B and C continued the business for two more year. If the net profit after 3 years be Rs.4000, then A's share in the profit is?
(A) 460
(B) 289
(C) 220
(D) 400
(E) 640
Rationale: 2*24 : 3*36 : 4*36
4: 9: 12
4/25 * 4000 = 640
Answer: E
Answer: (E) 640
Question: What is the probability of rolling a total of 8 with a single roll of two fair six-sided dice, each with the distinct numbers 1 through 6 on each side?
(A) 1/12
(B) 1/6
(C) 2/7
(D) 5/36
(E) 1/2
Rationale: Totalsample spacefrom two fair six-sided dice is 36.
There are six possible ways to be 8 i.e. (2+6), (3+5), (4+4), (5+3), (6+2)
So, total probability is 5/36.
Answer is D.
Answer: (D) 5/36
Question: What is the smallest positive integer K such that the product of 2205 x K is a perfect square?
(A) 5
(B) 9
(C) 15
(D) 25
(E) 63
Rationale: A perfect square, is just an integer that can be written as the square of some other integer. For example 16=4^2, is a perfect square.
Now, 2205 = 3^2 * 7^7 * 5, so if k=5 then 2205 k = (3 * 7 * 5)^2, which is a perfect square (basically the least positive value of k must complete only the power of 7 to even power as powers of other primes are already even).
Answer: A.
Answer: (A) 5
Question: Which of the following will divide evenly into 347,456,520?
(A) 3
(B) 9
(C) 11
(D) 13
(E) none of these
Rationale: Rule:
3: Sum of the digits should be divisible by 3
Given number : 3+4+7+4+5+6+5+2+0 =36 which is divisible by 3
Answer: A
Answer: (A) 3
Question: a, b, c, d, and e are positive consecutive odd integers and a < b < c < d < e.
If the sum of a+c+e is four less than the square of b, what is the product of de?
(A) 25
(B) 35
(C) 53
(D) 99
(E) 143
Rationale: a+c+e = bb - 4
Because we know the numbers are consecutive odd integers, we can rewrite the list as versions of the first number:
b = a+2
c = a+4
d = a+6
e = a+8
Therefore we can rewrite the original problem: a+(a+4)+(a+8) = (a+2)(a+2) - 4
Simplify: 3a + 4 + 8 = (aa + 4a + 4) - 4
Simplify: 3a + 12 = aa + 4a
Swap (just switch the sides in their entirety): aa + 4a = 3a + 12
Separate the number from the variables: aa + 4a - 3a = 12
Simplify: aa + a = 12
So the square of a, plus another a, equals 12. We can try out a few numbers quickly:
1x1 = 1, +1 = not 12
5x5 = 25, +5 = not 12
3x3 = 9, +3 = there we go!
So a = 3, and the sequence of consecutive odd numbers is 3, 5, 7, 9, 11.
The answer is the product of the last two numbers: 9x11 = 99 (option D).
Answer: (D) 99
Question: The Average of 11 results is 16, if the average of the 1st 6 results is 58 & that of the last 63. Find the 6th result.
(A) 66
(B) 55
(C) 44
(D) 77
(E) 88
Rationale: 6th result = (58*6+63*6-60*11)
=66
Answer is A.
Answer: (A) 66
Question: Andrew started saving at the beginning of the year and had saved $200 by the end of the year. He continued to save and by the end of 2 years had saved a total of $540. Which of the following is closest to the percent increase in the amount Andrew saved during the second year compared to the amount he saved during the first year?
(A) 11%
(B) 25%
(C) 44%
(D) 56%
(E) 70%
Rationale: Percent increase in the amount Andrew saved during the second year compared to the amount he saved during the first year.
Percentage Change = ( Change in value / Original value ) * 100
Percentage Change = [ (Saving in 2nd year - Saving in 1st year ) / Saving in 1st year ] * 100
Saving in 2nd year + Saving in 1st year = 540
Saving in 2nd year + 200 = 540
Saving in 2nd year = 540 - 200 = 340
Change in Value = 340 - 200 =140
Original Value = 200
Percentage Increase = (140 / 200 ) * 100 = 70% ..... Answer E......
Answer: (E) 70%
Question: Find the number of different ways in which 7^11 can be expressed as the product of three factors
(A) 13
(B) 14
(C) 15
(D) 16
(E) 17
Rationale: let 7^11=7^x*7^y*7^z
then possible triplets of (x,y,z)
(0,0,11)(0,1,10)(0,2,9)(0,3,8)(0,4,7)(0,5,6)
(1,1,9)(1,2,8)(1,3,7)(1,4,6)(1,5,5)
(2,2,7)(2,3,6)(2,4,5)
(3,3,5)(3,4,4)
so number of different ways=16
ANSWER:D
Answer: (D) 16
Question: 144 candies are distributed to children with the same number. What can’t be the range including the number of children?
(A) 1~10
(B) 10~20
(C) 20~30
(D) 50~60
(E) 70~80
Rationale: -> In 144=1*144=2*72=4*36=6*24=8*18=9*16, you can come up with 4 cases. One is distributing 77 candies to 2 children each. Another is distributing 2 candies to 77 children each. Also, you can distribute 22 candies to 7 children. The other is distributing 7 candies to 22 children. Amongst these cases, what is not included is D. 50~60. Therefore, the answer is D.
Answer: (D) 50~60
Question: For dinner, Sandy ate 200 grams of corn which was five times as much corn as she ate for lunch, and twice as much corn as she ate for breakfast. How much corn did Sandy eat in total?
(A) 300
(B) 320
(C) 340
(D) 360
(E) 380
Rationale: For breakfast, Sandy ate 200 / 2 = 100 grams.
For lunch, Sandy ate 200 / 5 = 40 grams.
For dinner, Sandy ate 200 grams.
The total is 100 + 40 + 200 = 340 grams.
The answer is C.
Answer: (C) 340
Question: Alice worked for three straight hours on her homework questions. If she solved 90 questions in the third hour, which was five times as many as she solved in the second hour, and three times as many questions as she solved in the first hour, how many questions did she solve in total?
(A) 134
(B) 138
(C) 142
(D) 146
(E) 150
Rationale: In the first hour, Alice solved 90/3 = 30 questions.
In the second hour, Alice solved 90/5 = 18 questions.
In the third hour, Alice solved 90 questions.
The total is 30 + 18 + 90 = 138.
The answer is B.
Answer: (B) 138
Question: Julie put half of her savings in a savings account that pays an annual simple interest and half in a savings account that pays an annual compound interest. After two years she earned $120 and $122 from the simple interest account and the compound interest account respectively. If the interest rates for both accounts were the same, what was the amount of Julie's initial savings?
(A) 600
(B) 720
(C) 1080
(D) 2200
(E) 3600
Rationale: $120 for 2 years = $60 per year.
Extra $2 yearned with the compound interest is the percent yearned on percent. So, $2 is yearned on $60, which means that the interest = 30%.
This on the other hand means that half of the savings = 60*30 = $1800. Twice of that = $3,600.
Answer: E.
Answer: (E) 3600
Question: If the diameter of circle R is 80% of the diameter of circle S, the area of circle R is what percent of the area of circle S?
(A) 74%
(B) 64%
(C) 84%
(D) 94%
(E) 34%
Rationale: Let diameter of circle R , dr = 80
and diameter of circle S , ds = 100
Radius of circle R , Rr = 40
Radius of circle S , Rs = 50
Area of circle R/ Area of circle S = (pi * Rr ^2 ) /( pi * Rs^2 )
= (40/50)^2 = (8/10)^2
=64%
Answer :B
Answer: (B) 64%
Question: Five men and nine women can do a piece of work in 10 days. Six men and twelve women can do the same work in 8 days. In how many days can three men and three women do the work?
(A) 80 days
(B) 70 days
(C) 20 days
(D) 10 days
(E) 30 days
Rationale: C
20 days
(5m + 9w)10 = (6m + 12w)8
=> 50m + 90w = 48w + 96 w => 2m = 6w => 1m = 3w 5m + 9w = 5m + 3m = 8m
8 men can do the work in 10 days.
3m +3w = 3m + 1w = 4m
So, 4 men can do the work in (10 * 8)/4 = 20 days.
Answer: (C) 20 days
Question: If a fair coin is tossed five times, what is the probability of getting exactly three heads in a row?
(A) 3/16
(B) 5/16
(C) 3/32
(D) 5/32
(E) 7/32
Rationale: Let X represent either H or T (it doesn't matter which).
P(HHHTX) = 1/16
P(THHHT) = 1/32
P(XTHHH) = 1/16
The sum of these probabilities is 5/32
The answer is D.
Answer: (D) 5/32
Question: There are two men aged 30 and 36 years. The probability to live 35 years more is 0.67 for 30 -years pld man and 0.60 for 36 year old man. Find the probability that at least one of these men will be alive 35 years hence.
(A) 0.35
(B) 0.868
(C) 0.43
(D) 0.44
(E) 0.47
Rationale: Explanation :
Let, A ≡ event that 30 year-old man will live 35 years more.
B ≡ event that 36 year-old man will live 35 years more.
[ A and B are independent events ]
To find at least one of the men will be alive it easier to calculate the complementary of the event (i.e none will be alive) first. Since
P(at least one) = 1 - P(none).
P(none will be alive)
= P(~A~B)
= P(~A) x P(~B)
= [1 - P(A)] x [1 - P(B)]
= (1- 0.67)(1-0.6)
= 0.33 x 0.40
= 0.132
P ( at least one of them will be alive)
= 1 - 0.132
= 0.868.
Answer : B
Answer: (B) 0.868
Question: Saleem bought 4 baskets with the average cost of $4. If Saleem also buys the fifth basket with the price of $ 8, what is the average (arithmetic mean) price of those 5 baskets?
(A) $4.50
(B) $6.00
(C) $4.00
(D) $5.50
(E) $4.80
Rationale: 4 baskets -> Total cost = 4 * Avg cost = 4*4 = 16
Fifth basket cost = 8
Total cost for 5 baskets = 16+8 = 24
AM = 24/5 = 4.80
ANSWER:E
Answer: (E) $4.80
Question: A person covered one-fourth of the total distance at 26 kmph and remaining distance at 24 kmph. What is the average speed for the total distance?
(A) 21 (1/36)kmph
(B) 21 (1/3)kmph
(C) 21 (8/3)kmph
(D) 27 (1/3)kmph
(E) 25 (1/3)kmph
Rationale: Let the total distance be x km
total time taken = (x/4)/16 + (3x/4)/24
= x/64 + x/32 = 3x/64
Average speed = x/(3x/64)
= 64/3kmph
= 21 (1/3)kmph.
Answer: B
Answer: (B) 21 (1/3)kmph
Question: At what rate will Rs.1400 fetch an interest of Rs.210 in 5 years?
(A) 2%
(B) 6%
(C) 5%
(D) 4%
(E) 3%
Rationale: 70 = (P*4*7/2)/100
R =( 210x100)/(1400x5)=3% p/a
Answer: E
Answer: (E) 3%