mathewhe/aqua_rat huggingface dataset:
Question: the average of five no.s is 8.in this how much maximum no. can be negative.
(A) 4
(B) 3
(C) 2
(D) 1
(E) 0
Rationale: sum of five no. =8*5=40
it is very much possible that addition of four no. can be -a,in which all four are negative and fifth no. is a+40.
answer A
Answer: (A) 4
Question: All of the students of Music High School are in the band, the orchestra, or both. 40 percent of the students are in only one group. There are 100 students in the band. If 20 percent of the students are in the band only, how many students are in the orchestra only?
(A) 30
(B) 25
(C) 40
(D) 55
(E) 35
Rationale: % of students in one group only = 40%
% of students in both groups = 100 - 40 = 60%
% of students in the band only = 20%
Number of students who are in band = 100
60% + 20% = 80% = 100 Students
Finding total students:
x = (100 x 100)/80
x = 125
Students in orchestra only = 125 - 100 = 25
Answer:B
Answer: (B) 25
Question: Find the area of the square field if a train 800 metres long passes the field with a speed of 120 kmph in one minute.
(A) 1.44 sq. km
(B) 4 sq. km
(C) 2 sq. km
(D) 2.64 sq. km
(E) None of these
Rationale: Explanation:
120 km/hr = 120 * 5/18 = 33.33 m/s
v = d/t ; 33.33 = d/60
d = 2000 m
Hence, in one minute the train travels 2000 m. But, as the train is 800 m long and it passes the field, the length of the field is 2000 – 800 = 1200 m.
Area = 1200 * 1200 = 1.44 sq. km
ANSWER: A
Answer: (A) 1.44 sq. km
Question: The average of ten numbers is 210. The average of first five numbers is 40 and the average of last four numbers is 200. What is the middle number?
(A) A)200
(B) B)2000
(C) C)800
(D) D)2100
(E) E)1100
Rationale: The total of ten numbers = 10X210 = 2100
The total of first 5 and last 4 numbers is = 5 X 40+4 X 200 = 1000
So, the middle number is (2100 - 1000 ) = 1100
E
Answer: (E) E)1100
Question: A certain company plans to sell Product X for p dollars per unit, where p is randomly chosen from all possible positive values not greater than 100. The monthly manufacturing cost for Product X (in thousands of dollars) is 12 - p, and the projected monthly revenue from Product X (in thousands of dollars) is p(6 - p). If the projected revenue is realized, what is the probability that the company will NOT see a profit on sales of Product X in the first month of sales?
(A) 0
(B) 1/100
(C) 1/25
(D) 99/100
(E) 1
Rationale: Profit=Revenue-Cost=p(6 - p)-(12-p).
Let's see for which range of p company will see a profit on sales, so for which range of p the following holds true: p(6−p)−(12−p)>0 --> 6p−p2−12+p>0 --> p2−7p+12<0 --> (p−4)(p−3)<0 --> 3<p<4. So the probability that company will see a profit on sales is 1100 (1 unit range of p out of 100).
The probability that the company will NOT see a profit on sales is 1−1100=99100.
Answer: D.
Answer: (D) 99/100
Question: A bakery has 6 employees. It pays annual salaries of $18,000 to each of 2 employees, $20,000 to 1 employee, and $21,000 to each of the remaining 3 employees. Which number is closest to the average (arithmetic mean) annual salary of these employees?
(A) $19,200
(B) $19,500
(C) $19,800
(D) $20,000
(E) $20,400
Rationale: average = 2(18000)+(20000)+3(21000) / 6 = $19,833
The answer is C.
Answer: (C) $19,800
Question: Worker A takes 8 hours to do a job. Worker B takes 12 hours to do the same job. How long it take both A & B, working together but independently, to do the same job?
(A) 40 days
(B) 24/5 days
(C) 39/9 days
(D) 30/9 days
(E) 60/9 days
Rationale: A's one hour work = 1/8.
B's one hour work = 1/12.
(A+B)'s one hour work = 1/8+1/12 = 5/24.
Both A & B can finish the work in 24/5 days
B
Answer: (B) 24/5 days
Question: Find the compound interest accrued on an amount of Rs.14,800 at 13.5% p.a at the end of two years. (Round off your answer to nearest integer)
(A) 4269
(B) 4267
(C) 4260
(D) 4266
(E) 4262
Rationale: CI = 14800{ [ 1 + 13.5/100]2 - 1 }
= 14800 { [1 + 27/200]2 - 1
= 14800 { 2 + 27/200}{27/200}
= (74)[2 + 27/200](27) =
1998[2 + 27/200] = 3996 + 269.73 = Rs.4266
Answer: D
Answer: (D) 4266
Question: A train 550 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
(A) 30
(B) 60
(C) 25
(D) 40
(E) 10
Rationale: Speed of train relative to man = (60 + 6) km/hr = 66 km/hr
[66 * 5/18] m/sec = [55/3] m/sec.
Time taken to pass the man = [550 * 3/55] sec = 30 sec
Answer: A
Answer: (A) 30
Question: The floor of a rectangular room is 18 m long and 12 m wide. The room is surrounded by a veranda of width 2 m on all its sides. The area of the veranda is :
(A) 124 m2
(B) 126 m2
(C) 136 m2
(D) 158 m2
(E) None of these
Rationale: Area of the outer rectangle = 22 Ã— 16 = 352 m2
Area of the inner rectangle = 18 Ã— 12 = 216 m2
Required area = (352 â€“ 216) = 136 m2
Answer C
Answer: (C) 136 m2
Question: A no. when divided by the sum of 555 and 445 gives 2times their difference as quotient & 10 as remainder. Find the no. is?
(A) 220010
(B) 145778
(C) 220110
(D) 235467
(E) 220001
Rationale: (555 + 445) * 2 * 110 + 10 = 220000 + 10 = 220010
A
Answer: (A) 220010
Question: A car traveled 281 miles in 4 hours 41 minutes. What was the average speed of the car in miles per hour?
(A) 30 miles / hour
(B) 90 miles / hour
(C) 60 miles / hour
(D) 80 miles / hour
(E) 70 miles / hour
Rationale: We first convert the time of 4 hours 41 minutes in minutes
4 hours 41 minutes = 4 ? 60 + 41 = 281 minutes
Average speed S is given by distance / time. Hence
S = 281 miles / 281 minutes = 1 mile / minute
= 60 miles / hour
correct answer C
Answer: (C) 60 miles / hour
Question: 4/x + 3x = 3(x+8)
(A) -9
(B) -1/3
(C) 1/6
(D) 1/9
(E) 9
Rationale: We can solve - expand the right side, multiply by x on both sides and then subtract away the 3x^2 terms:
(4/X) + 3x = 3(x+8)
(4/x) + 3x = 3x + 24
4 + 3x^2 = 3x^2 + 24x
4 = 24x
1/6 = x
and to confirm, you can plug that answer back into the original equation to see that it makes the left and right sides equal.
C
Answer: (C) 1/6
Question: xy=1 then what is (3^(x+y)^2) / (3^(x-y)^2)
(A) 2
(B) 4
(C) 81
(D) 16
(E) 32
Rationale: (x+y)^2 - (x-y)^2
(x+y+x-y)(x+y-x+y)
(2x)(2y)
4xy
4
3^4 = 81
Answer C
Answer: (C) 81
Question: Among the two clocks, clock A gains 20 seconds per minute. If clock A and B are set at 2 0'clock, when clock A is at 7:20, what does clock B show?
(A) 5:30
(B) 6:00
(C) 5:45
(D) 6:20
(E) 3:30
Rationale: Clock A gains 20 seconds per minute, 1200 seconds per hour or 20 minutes per hour.
The two clocks show 2:00 at 2 0'clock
At 3:00 -
Clock B is at 3:00
Clock A is at 3:20 (1 hour + gains 20 minutes)
AT 4:00 -
Clock B is at 4:00
Clock A is at 4:40 (2 hours + gains 40 minutes)
In 4 hours the clock A gains 4*20=80 minutes or 1 hour 20 minutes
If clock A is at 7:20 the clock B is at 6:00
Answer is B
Answer: (B) 6:00
Question: If eight machines working at the same rate can do 3/4 of a job in 30 minutes, how many minutes would it take two machines working at the same rate to do 3/5 of the job?
(A) 45
(B) 60
(C) 75
(D) 96
(E) 100
Rationale: using the std formula
m1d1h1/w1=m2d2h2/w2
substituting the values we have
8*1/2*4/3=2*5/3*x (converted 30 min into hours =1/2)
16/3=10/3*x
x=8/5 hour
so 96 minutes
ANSWER:D
Answer: (D) 96
Question: The profit obtained by selling an article for Rs. 56 is the same as the loss obtained by selling it for Rs. 42. What is the cost price of the article?
(A) Rs. 40
(B) Rs. 49
(C) Rs. 50
(D) Rs. 70
(E) None of these
Rationale: S.P 1- C.P = C.P – S.P 2
56 - C.P = C.P - 42
2 C.P = 56 + 42;
C.P = 98/2 = 49
ANSWER:B
Answer: (B) Rs. 49
Question: The value of ((x – y)³ + (y - z)³ + (z – x)³)/(12 (x – y) (y – z) (z – x))
is equal to :
(A) 0
(B) 1/12
(C) 1
(D) 1/4
(E) 1/3
Rationale: Since (x – y) + (y – z) + (z – x) = 0,
so (x – y)³ + (y – z)³ + (z – x)³= 3 (x – y) (y – z) (z – x).
(3 (x – y) (y – z) (z – x))/(12(x – y) (y – z) (z – x)) = 1/4.
ANSWER:D
Answer: (D) 1/4
Question: when n divided by 3, the remainder is 2.
when n divided by 4, the remainder is 1
what is the the remainder when divided by 16
(A) 1
(B) 3
(C) 4
(D) 5
(E) 2
Rationale: case1
N=5,8,11,14,17,20
case 2
M=5,9,13,17,21
Therefore n=17
Remainder of 17/16 will be 1
A
Answer: (A) 1
Question: If Sharon's weekly salary increased by 10 percent, she would earn $330 per week. If instead, her weekly salary were to increase by 8 percent, how much would she earn per week?
(A) Rs.424
(B) Rs.524
(C) Rs.324
(D) Rs.350
(E) Rs.354
Rationale: Soln:-
(330/110)108 =324
In this case long division does not take much time.
(330/110)108=324
ANSWER:C
Answer: (C) Rs.324
Question: A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 700 m long?
(A) 180 sec
(B) 190 sec
(C) 170 sec
(D) 175 sec
(E) 115 sec
Rationale: Answer: Option B
L = S*T
S= 1200/120
S= 10 m/Sec.
Total length (d)= 1900 m
T = d/S
T = 1900/10
T = 190 Sec
Answer: (B) 190 sec
Question: A certain tests consists 8 sections with 25 questions, numbered from 1 to 25, in each section. If a student answered all of the even-numbered questions correctly and 3/4 of the odd-numbered questions correctly, what was the total number of questions he answered correctly?
a. 150
b. 172
c. 174
d. 175
e. 176
(A) 174
(B) 150
(C) 180
(D) 175
(E) 190
Rationale: Each set has 12 even and 13 odd numbered questions leading to total 96 even and 104 odd questions.
96+3/4âˆ—104=96+78=17496+3/4âˆ—104=96+78=174
Answer: A
Answer: (A) 174
Question: There are 5 red balls, 10 blue balls, 8 green balls and 9 black balls in a bag. What is the minimum number of balls to be taken out of the bag to assure that you have all the balls of one color?
(A) 10
(B) 29
(C) 43
(D) 40
(E) 16
Rationale: The worst case scenario would be if we pick 4 red balls, 9 blue balls, 7 (?) balls and 8 black balls. In this case we'll have 4+9+7+8=28 balls and still won't have all the balls of one color. The next 29rd ball we pick, no matter which color it'll be, will guarantee that we have all the balls of one color.
Answer: B.
Answer: (B) 29
Question: If n is an integer, then the least possible value of |8 - 9n| is?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 11
Rationale: |8 - 9n| represents the distance between 8 and 9n on the number line. Now, the distance will be minimized when 9n, which is multiple of 9, is closest to 8. Multiple of 9 which is closest to 8 is 9 (for n = 1), so the least distance is 1: |8 - 9| = 1.
Answer: B.
Answer: (B) 1
Question: If the simple interest on a sum of money at thirteen percent per annum for two years is Rs.22400, compound interest on the same sum for the same period at the same rate of interest is
(A) 28,356.00
(B) 25,638.00
(C) 23,856.00
(D) 23,685.00
(E) 25,865.00
Rationale: S I for 2 years = 22400 ie for one year =11200
The compound interest for Rs.11200 for the second year = 11200*13/100 = 1456
The CI for two years 22400+1456 = 23,856.00
ANSWER:C
Answer: (C) 23,856.00
Question: The cash difference between the selling prices of an article at a profit of 4% and 6% is Rs. 3. The ratio of the two selling prices is:
(A) 51:52
(B) 52:53
(C) 51:53
(D) 52:55
(E) 55:50
Rationale: Explanation:
Let C.P. of the article be Rs. x.
Then, required ratio = 104% of x / 106% of x
= 104/106 = 52/53 = 52:53
ANSWER IS B
Answer: (B) 52:53
Question: How many 3 digit numbers can be made from the numbers 1,2,3,4,5,6,7,8,9,0
(A) 1000
(B) 720
(C) 648
(D) 500
(E) 100
Rationale: A3 digit number is made from (First Digit , Second digit, Third digit) ABC
For the first digit of the 3 digit numbers we have to choose from numbers 1,2,3,4,5,6,7,8,9 we cannot take 0 since it is a 3 digit number that we have to make
So the first digit can have 9 entries.
For the second digit we can have all numbers including 0 except one number which we used for first digit. So we have 9 choices (including 0)
For the third digit we have all numbers minus two digits which we used for A and B
So we have 8 choices.
Total ways by which we can form a 3 digit number are 9 * 9 * 8 = 648
Answer: C
Answer: (C) 648
Question: If p^2 – 6p + 8 = q, and p is a positive integer between 1 and 10, inclusive, what is the probability that q < 0?
(A) 1/5
(B) 1/10
(C) 2/5
(D) 3/5
(E) 3/10
Rationale: (p-2)(p-4) = q
p = 3 for this to be true, so
1/10
Ans :B
Answer: (B) 1/10
Question: Total dinning bill for 10 people was $211.00.If they add 15% tip and divided the bill evenly ,approximate.What was each persons find share
(A) $30.14
(B) 45.14
(C) 34.66
(D) 32.29
(E) 24.26
Rationale: 211*15=3165/100=31.65
211+31.65=242.65
242.65/10=24.26
ANSWER:E
Answer: (E) 24.26
Question: If a coin is tossed twice what is the probability that it will land either heads both times or tails both times?
(A) A)1/8
(B) B)1/6
(C) C)1/4
(D) D)1/2
(E) E)1
Rationale: Prob to get 2 heads = 1/2*1/2 = 1/4
Prob to get 2 tails = 1/2*1/2 = 1/4
So, Prob to get either 2 heads or 2 tails = 1/4+1/4 = 1/2
Answer will be D.
Answer: (D) D)1/2
Question: A merchant marks his goods up in such a way that the profit made on selling 30 articles is equal to the cost price of 20 articles. What is the % profit made by the merchant?
(A) 66.67 %
(B) 50 %
(C) 200 %
(D) 100 %
(E) 33.33 %
Rationale: Let Selling Price be x and Cost Price be y of each article;
now, 30x - 30y = the profit earned on selling 30 articles
it is known that the profit earned on 30 articles i.e 30x - 30y = 20y (Cost price of 20 articles)
we get, 30x = 50y
that means x/y = 50/30
Selling Price/Cost price = 5/3
Something that costs $3 is being sold at $5 which is at 66.67% profit.
ANSWER:A
Answer: (A) 66.67 %
Question: You roll two six sided dices together.
Can you calculate the probability that the first dice gives the number 2 while the second dice gives the number 5?
(A) 2/23
(B) 1/33
(C) 1/36
(D) 3/54
(E) 6/35
Rationale: C
1/36
The number of possibilities for the first as well as the second dice are 6 and 6 respectively. Therefore the total possibilities or outcome are 6 * 6 = 36.
Out of 36 outcomes, we need only one case i.e. the first gives 2 and the second gives 5.
Therefore, the probability will be 1 on 36 or 1/36.
Answer: (C) 1/36
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) 5
(B) 2
(C) 10
(D) 12
(E) 15
Rationale: 4/12+X/15=1
x=10
ANSWER C
Answer: (C) 10
Question: Round off the given number to nearest hundreds
7456
(A) 7400
(B) 7500
(C) 7000
(D) 8000
(E) 7450
Rationale: the given number is 7456
its tens digit is 5. so replace each of the tens and ones digit by 0 and increase the hundreds digit by 1 to get the rounded off number to the nearest hundred.
correct answer (B)
Answer: (B) 7500
Question: A trader sells 40 metres of cloth for Rs.8200 at a profit of Rs.55 per metre of cloth. How much profit will the trder earn on 40 metres of cloth?
(A) Rs.950
(B) Rs.1500
(C) Rs.1000
(D) Rs.2200
(E) None of these
Rationale: Explanation:
SP of 1 metre cloth = 8200/40 = Rs.205.
CP of 1 metre cloth = Rs.205 – 55 = Rs.150
CP on 40 metres = 150 x 40 = Rs.6000
Profit earned on 40 metres cloth = Rs.8200 – Rs.6000 = Rs.2200.
Answer: Option D
Answer: (D) Rs.2200
Question: How many times will the digit 7 be written when listing the integers from 1 to 1000?
(A) 110
(B) 111
(C) 271
(D) 300
(E) 304
Rationale: Another approach:
In the range 0-100:
7 as units digit - 10 times (7, 17, 27, ..., 97);
7 as tens digit - 10 time (71, 72, 73, ..., 79);
So in first one hundred numbers 7 is written 10+10=20 times.
In 10 hundreds 7 as units or tens digit will be written 10*20=200 times. Plus 100 times when 7 is written as hundreds digit (700, 701, 702, ..., 799).
Total 200+100=300.
Answer: D.
Answer: (D) 300
Question: Arrange the following in a logical order:
1. Birth
2. College
3. Marriage
4. School
5. Employment
(A) 1, 4, 2, 5, 3
(B) 1, 4, 2, 5, 4
(C) 1, 4, 7, 5, 3
(D) 1, 9, 2, 5, 3
(E) 6, 4, 2, 5, 3
Rationale: Explanation:
The given words when arranged in the order of various events as they occur in man's life, the sequence is : Birth, School, College, Employment, Marriage.
Sequence is : 1, 4, 2, 5, 3.
ANSWER: A
Answer: (A) 1, 4, 2, 5, 3
Question: A retailer bought a shirt at wholesale and marked it up 80% to its initial price of $36. By how many more dollars does he need to increase the price to achieve a 100% markup?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Rationale: Let x be the wholesale price.
Then 1.8x= 36 and x = 36/1.8 = 20.
To achieve a 100% markup, the price needs to be $40.
The retailer needs to increase the price by $4 more.
The answer is B.
Answer: (B) 4
Question: Two pipes X and Y can separately fill a cistern in 18 and 24 hours respectively. If they are turned on alternately for one hour each, how long will it take to fill the cistern?
(A) 20 1/2 hours
(B) 20 1/7 hours
(C) 20 1/3 hours
(D) 20 3/2 hours
(E) 20 1/4 hours
Rationale: 1/18 + 1/24 = 7/72
72/7 = 10 2/7
7/72 * 10 = 35/36 ----- 20 hours
WR = 1 – 35/36 = 1/36
1 h ----- 1/18
? ----- 1/36 = 1/2 hours
=> 20 1/2 hours
Answer: A
Answer: (A) 20 1/2 hours
Question: The area of a rectangular field is equal to 300 square meters. Its perimeter is equal to 70 meters. Find the length of this rectangle.
(A) L = 60
(B) L = 20
(C) L = 40
(D) L = 30
(E) L =50
Rationale: L * W = 300 : area , L is the length and W is the width.
2 L + 2 W = 70 : perimeter
L = 35 - w : solve for L
(35 - W) * W = 300 : substitute in the area equation
W = 15 and L = 20 : solve for W and find L using L = 35 - w.
correct answer B
Answer: (B) L = 20
Question: A and B together have Rs. 1210. If of A's amount is equal to of B's amount, how much amount does B have?
(A) 568
(B) 484
(C) 456
(D) 258
(E) 125
Rationale: 4/5A=2/5B
A=(2/5*15/4)B
A=3/2B
A/B=3/2
B's share=Rs(1210*2/5)=484
Answer: (B) 484
Question: Each night before he goes to bed, Jordan likes to pick out an outfit to wear the next day. He has 12 different shirts, 10 different pairs of jeans, and 6 pairs of sneakers. If an outfit consists of 1 shirt, 1 pair of jeans, and 1 pair of sneakers, how many different outfits does Jordan have?
(A) 720
(B) 90
(C) 240
(D) 480
(E) 960
Rationale: Total # of outfits = 12 * 10 * 6 = 720
Answer - A
Answer: (A) 720
Question: Sekar started a business investing Rs.25,000 in 1999. In 2000, he invested an additional amount of Rs.10,000 and Rajeev joined him with an amount of Rs.35,000. In 2001, Sekar invested another additional amount of Rs.10,000 and Jatin joined them with an amount of Rs.35,000. What will be Rajeev's share in the profit of Rs.1,50,000 earned at the end of 3 years from the start of the business in 1999?
(A) Rs.45,000
(B) Rs.50,000
(C) Rs.70,000
(D) Rs.75,000
(E) none
Rationale: Solution
Sekar:Rajeev:Jatin=	(25000×12+35000×12+45000×12):(35000×24) : (35000×12)
= 1260000 : 840000 : 420000
= 3 : 2 : 1.
Rajeev's share	=Rs.(150000×2/6)
= Rs.50000.
Answer B
Answer: (B) Rs.50,000
Question: The average of ten numbers is 7. If each number is multiplied by 10, then what is the average of the new set of numbers?
(A) 7
(B) 17
(C) 70
(D) 100
(E) 107
Rationale: The sum of the ten numbers is 7*10 = 70
If each number is multiplied by 10, the new sum is 10*(70).
The average is then 10*7 = 70
The answer is C.
Answer: (C) 70
Question: If f(x) = 3x^4 - 4x^3 - 3x^2 + 6x , then f(-1) =
(A) -2
(B) -1
(C) 0
(D) 1
(E) 2
Rationale: f(-1) = 3(-1)^4 - 4(-1)^3 - 3(-1)^2 + 6(-1) = 3+4-3-6 = -2
The answer is A.
Answer: (A) -2
Question: If k is an integer and 2 < k < 7, for how many different values of k is there a triangle with sides of lengths 2, 6, and k?
(A) one
(B) two
(C) three
(D) four
(E) five
Rationale: (6-2) < k < (6+2)
4 < k < 8
Thus k = 5, 6, 7
Since 2 < k < 7, then k can be 5 or 6.
The answer is B.
Answer: (B) two
Question: At their respective rates, pump A, B, and C can fulfill an empty tank, or pump-out the full tank in 2, 3, and 6 hours. If A and B are used to pump-out water from the half-full tank, while C is used to fill water into the tank, in how many hours, the tank will be empty?
(A) 2/3
(B) 1
(C) 3/4
(D) 3/2
(E) 2
Rationale: Rate of A = 1/2 tank/hour;
Rate of B = 1/3 tank/hour;
Rate of C = 1/6 tank/hour.
Combined rate when A and B are used to pump-out water, while C is used to fill water into the tank is 1/2+1/3-1/6=2/3 tank hour.
So, to empty the full tank 3/2 hours (reciprocal of rate) are needed. To empty the half-full tank half of that time would be needed: 1/2*3/2=3/4 hours.
Answer: C.
Answer: (C) 3/4
Question: At what price must an Book costing $47.50 be marked in order that after deducting 12% from the list price. It may be sold at a profit of 25% on the cost price?
(A) 72.5
(B) 55.5
(C) 67.5
(D) 82.5
(E) 60.5
Rationale: C
$62.50
CP = 47.50
SP = 47.50*(125/100) = 59.375
MP*(88/100) = 59.375
MP = 67.5
C
Answer: (C) 67.5
Question: A die is drawed, find the probability that an odd number is draw?
(A) 1/2
(B) 2/4
(C) 3/2
(D) 1/5
(E) 2/5
Rationale: Let us first write the sample space S of the experiment.
S = {1,2,3,4,5,6}
Let E be the event "an odd number is obtained" and write it down.
E = {1,3,5}
P(E) = n(E) / n(S) = 3 / 6 = 1/2
A
Answer: (A) 1/2
Question: A bucket full of nuts was discovered by the crow living in the basement. The crow eats a fifth of the total number of nuts in 4 hours. How many hours in total will it take the crow to finish a quarter of the nuts?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: In one hour, the crow eats 1/20 of the nuts.
(1/4) / (1/20) = 5 hours
The answer is B.
Answer: (B) 5
Question: If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 56, what is the compound interest on the same sum at the rate and for the same time?
(A) s. 57.40
(B) s. 57.22
(C) s. 51.219
(D) s. 56.18
(E) s. 53.11
Rationale: Explanation:
Sum = (56 * 100) / (2 * 5) = Rs. 560
Amount = [560 * (1 + 5/100)2] = Rs. 617.4
C.I. = (617.4- 560) = Rs. 57.4.
Answer:A
Answer: (A) s. 57.40
Question: A rectangular pig farm has a fence along three sides and a wall along the fourth side. The fenced side opposite the wall is twice the length of each of the other two fenced sides. If the area of the rectangular region is 1250 square feet, what is the total length of the fence, in feet?
(A) 25
(B) 50
(C) 100
(D) 150
(E) 200
Rationale: two sides EACH = x the third = 2x and the wall length is thus 2x too
x*2x = 2x^2 = 1250 ie x^2 = 625 ie x = 25
L = 50 W= 25
TOTAL LENGTH OF FENCE = 2*25 + 50 = 100
MY ANSWER IS C
Answer: (D) 150
Question: If a:b=1:3 and b:c=2:4 find a:b:c?
(A) 1:6:3
(B) 1:3:6
(C) 6:1:3
(D) 6:3:1
(E) 3:6:1
Rationale: a:b = 1:3, b:c = 2:4
1:3
2:4
(a = a × b, b = b × b and c = b × c)
a:b:c = 1:3:6
B
Answer: (B) 1:3:6
Question: In a bag containing 3balls, a white ball was placed & then 1ball was taken out atrandom. What is the probability that the extracted ball would turn on to be white, if all possible hypothesis concerning the color of theballs that initiallyin the bag were equally possible ?
(A) 3
(B) 5/8
(C) 27
(D) 54
(E) 81
Rationale: Since, all possible hypothesis regarding the colour of the balls are equally likely, therefore these could be 3 white balls, initially in the bag.
∴ Required probability = 1/4 [1 + 3/4 + 1/2 + 1/4]
= 1/4 [(4 + 3 + 2 + 1)/4] = 5/8
B
Answer: (B) 5/8
Question: What ratio must a shopkeepermix Peas and Soybean of Rs.16 and Rs. 25/kg, As to obtain a mixture of Rs.20 ?
(A) 10 : 7
(B) 9 : 8
(C) 5 : 4
(D) 13 : 11
(E) 14 : 8
Rationale: Correct option: (C)
Use rule of alligation, to determine the ratio
The required ratio of Soybean and Peas = 5 : 4
Answer: (C) 5 : 4
Question: Which is better investment?
(I) 7(1/2) % stock at 105 or
(II) 6(1/2) % at 94.
(A) I
(B) II
(C) Both
(D) Cannot Determine
(E) Data Insufficient
Rationale: Let the investment in each case be $ (105*94).
Case I : 7(1/2) 5 stock at 105:
On investing $ 105, income = $ (15/2).
On investing $ (105*94), income = $ [(15/2)*(1/105)*105*94]
= $705.
Case II : 6(1/2) % stock at 94:
On investing $ 94, income = $ (13/2).
On investing $ (105*94), income = $ [(13/2)*(1/94)*105*94]
= $ 682.5.
Clearly, the income from 7(1/2) % stock at 105 is more.
Hence, the investment in 7(1/2) % stock at 105 is better.
Answer A.
Answer: (A) I