mathewhe/aqua_rat huggingface dataset:
Question: Mr. Hernandez, who was a resident of State X for only 10 months last year, had a taxable income of $22,500 for the year. If the state tax rate were 4 percent of the year’s taxable income prorated for the proportion of the year during which the taxpayer was a resident, what would be the amount of Mr. Hernandez’s State X tax for last year?
(A)  $900
(B)  $750
(C)  $600
(D)  $300
(E)  $60
Rationale: Total tax for the year = 22,500 x 4% = 900
As stated Annual tax is prorated as per the duration of stay.
Prorated Tax = 900 (10/12) = 750
Answer B
Answer: (B)  $750
Question: Nicole cycles at a constant rate of 18 kilometers per hour, and is passed by Jessica, who cycles at a constant rate of 30 kilometers per hour. If Jessica cycles at her constant rate for x minutes after passing Nicole, then stops to wait for her, how many minutes will Jessica have to wait for Nicole to catch up to her?
(A) x/3
(B) 2x/3
(C) x
(D) 3x/2
(E) 2x
Rationale: In x minutes, Jessica travels (x/60)*30 = x/2 miles
The time it takes Nicole to travel x/2 miles is (x/2) / 18 = x/36 hours = 5x/3 minutes
Jessica needs to wait 5x/3 - x = 2x/3 minutes.
The answer is B.
Answer: (B) 2x/3
Question: For the past n days, the average (arithmetic mean) daily production at a company was 50 units. If today's production of 115 units raises the average to 55 units per day, what is the value of n?
(A) 8
(B) 10
(C) 12
(D) 14
(E) 16
Rationale: The daily production was raised by 5 units for n days, which has a weighting of 5n.
5n = 115-55 = 60
n = 12
The answer is C.
Answer: (C) 12
Question: What is the 23th digit to the right of the decimal point in the decimal form of 1/11?
(A) 1
(B) 6
(C) 3
(D) 5
(E) 0
Rationale: To solve ,we first have to use some long division.Long division allows us to get 1/11 in decimal form, which is 0.090909… where “09” is repeating.
We see that the 1st, 3rd, 5th digit to the right of the decimal point is a 0 and that the 2nd, 4th, 6th digit to the right of the decimal point is a 9. In other words, each odd-positioned digit is a 0, and each even-positioned digit is a 9.
Then the 23th digit to the right of the decimal point and we see that 23 is odd, then 23th digit is a 0.
Answer E.
Answer: (E) 0
Question: A certain company expects quarterly earnings of $0.80 per share of stock, half of which will be distributed as dividends to shareholders while the rest will be used for research and development. If earnings are greater than expected , shareholders will receive an additional $0.04 per share for each additional $0.10 of per share earnings. If quarterly earnings are $1.10 per share, what will be the dividend paid to a person who owns 100 shares of the company's stock?
(A) $92
(B) $96
(C) $52
(D) $120
(E) $240
Rationale: EPS Actual> EPS expected.
each gets and additional .12 per share.
Thus .52*100 --> $52
answer is C
Answer: (C) $52
Question: How many integers from 0 to 48, inclusive, have a remainder of 1 when divided by 3 ?
(A) 15
(B) 16
(C) 17
(D) 18
(E) 19
Rationale: My ans is also C.17.
Explanation:
1 also gives 1 remainder when divided by 3, another number is 4, then 7 and so on.
Hence we have an arithmetic progression: 1, 4, 7, 10,..... 46, which are in the form 3n+1.
Now we have to find out number of terms.
tn=a+(n-1)d, where tn is the nth term of an AP, a is the first term and d is the common difference.
so, 46 = 1+(n-1)3
or, (n-1)3 = 45
or, n-1 = 15
or, n = 16
B
Answer: (B) 16
Question: Of the five numbers in a sequence, the first term is 18,000, and each of the following terms is 20% of the previous term. What is the value range of the five numbers?
(A) 19,375.00
(B) 19,750.90
(C) 19,975.25
(D) 17,984.50
(E) 17,971.20
Rationale: 1st number= 18,000
2nd number = 20% of 18,000= 3600
3rd number= 20% of 3600= 720
4th number = 20% of 720= 144
5th number= 20% of 144= 28.8
Range = 18,000-28.8= 17971.20
E is the answer
Answer: (E) 17,971.20
Question: If x^2 + 1/x^2 = 9, what is the value of x^4 + 1/x^4 ?
(A) 10
(B) 72
(C) 79
(D) 16
(E) 18
Rationale: IMPORTANT: I notice that if we SQUARE x², we get x⁴, and if we SQUARE 1/x², we get 1/x⁴, so let's see what happens if we take the equation x² + 1/x² = 9 andSQUAREboth sides:
(x² + 1/x²)²= 81
So, (x² + 1/x²)(x² + 1/x²) = 81
Expand to get: x⁴ + 1 + 1 + 1/x⁴ = 81
Simplify: x⁴ + 1/x⁴ = 79
Answer: C
Answer: (C) 79
Question: Which of the following must be subtracted from 2^96 so that the resulting integer will be a multiple of 3?
(A) 2
(B) 5
(C) 3
(D) 1
(E) 4
Rationale: {4^1} / 3 =4/3 remainder 1
{4^2} / 3 = 16/3 remainder 1
{4^3} / 3 = 64/3 remainder 1
{4^4} / 3 = 256/3 remainder 1
Actually the same remainder keeps repeating .....
Try with a diff no, say 2
{2^1}/3 = remainder 2
{2^2}/3 = remainder 1
{2^3}/3 = remainder 2
{2^4}/3 = remainder 1
Answer : D
Answer: (D) 1
Question: list of salaries of 8 employees are listed below. What is the median salary?
$40,000, $29,000, $35,500, $31,000, $43,000, $30,000, $27,000, $34,000
(A) $28,000
(B) $28,500
(C) $32,500
(D) $30,800
(E) $31,500
Rationale: Ordering the data from least to greatest, we get:
$27,000, $29,000, $30,000, $31,000, $34,000, $35,500, $40,000, $43,000
Since there is an even number of items in the data set, we compute the median by taking the mean of the two middlemost numbers.
$31,000 + $34,000 = $65,000
The median salary is $32,500.
Answer : C
Answer: (C) $32,500
Question: A man saves a certain portion of his income during a year and spends the remaining portion on his personal expenses. Next year his income increases by 30% but his savings increase by 100%. If his total expenditure in 2 years is double his expenditure in 1st year, What %age of his income in the first year did he save?
(A) 21%
(B) 22.5%
(C) 25%
(D) 30%
(E) 40%
Rationale: 1st year Income= I
1st year savings= S
1st year Expense= E1
2nd year Income = 1.3I
2nd year savings= 2S (100% increase)
2nd Year expense= E2
E1+ E2= 2E1
E2=E1
That means Expenses are same during both years. With increase of 30% income the savings increased by 100%.
or S= .3I
or S= 30% of Income
D is the answer
Answer: (D) 30%
Question: A bag contains 6 white and 4 black balls .2 balls are drawn at random. Find the probability that they are of same color?
(A) 7/15
(B) 7/17
(C) 8
(D) 8/15
(E) 9
Rationale: Let S be the sample space
Then n(S) = no of ways of drawing 2 balls out of (6+4) = \inline {\color{Black}10C_{2}} = =45
Let E = event of getting both balls of same colour
Then,n(E) = no of ways (2 balls out of six) or (2 balls out of 4)
=\inline {\color{Black}6C_{2}+4C_{2}} = = 15+6 = 21
Therefore, P(E) = n(E)/n(S) = 21/45 = 7/15
A)
Answer: (A) 7/15
Question: The average of seven numbers is 22. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number?
(A) 27
(B) 55
(C) 31
(D) 34
(E) 35
Rationale: The total of seven numbers = 7X22 = 154
The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99
So, the middle number is (154 - 99 ) = 55
B
Answer: (B) 55
Question: Tough and Tricky questions: Absolute Values.
If |a| = 1/3 and |b| = 1/2, which of the following CANNOT be the result of a + b?
(A) -5/6
(B) -1/6
(C) 1/6
(D) 2/3
(E) 5/6
Rationale: |a| = 1/3
Absolute value of 'a' can have two values = 1/3 and -(1/3)
|b| = 1/2
Absolute value of 'b' can have two values = 1/2 and -(1/2)
Now different combinations of a + b are as follows:
a + b = (1/3) + (1/2) = 5/6
- a - b = -(1/3) - (1/2) = -5/6
a - b = (1/3) - (1/2) = -(1/6)
-a + b = -(1/3) + (1/2) = 1/6
Cross verifying with the given options, left over option is D.
Answer: (D) 2/3
Question: A boat goes 100 km downstream in 10 hours, and 200 Km upstream in 25 hours. The speed of the stream is?
(A) 1
(B) 22 1/7
(C) 2
(D) 22 1/2
(E) 3
Rationale: 100 --- 10 DS = 10
? ---- 1
200 ---- 30 US = 8
? ----- 1 S = (10 - 8)/2
= 1 kmph.
Answer:A
Answer: (A) 1
Question: The highest score in an inning was 3/11 of the total and the next highest was 3/11 of the reminder . If the score differ by 9, the total score was :
(A) 110
(B) 121
(C) 132
(D) 143
(E) None of these
Rationale: Explanation:
Let the score be x. Then the highest score = 3x/11.
Reminder = (x - 3x/11) = 8x/11 .Next the highest score = 3/11 of 8x/11 = 24x/121.
3x/11 - 24x/11 = 9 <=> 33x - 24x = 9 × 121 <=> x = 121..
Answer: B
Answer: (B) 121
Question: Avg cost of 6 pencils and 8 pens is Rs. 70.The avg cost of 8 pencils and 10 pens is Rs.90. Find the total cost of 25 pencils and 25 pens?
(A) 100
(B) 125
(C) 130
(D) 80
(E) 90
Rationale: Avg cost of 6 pencils and 8 pens is Rs. 70
(6 pencil + 8 pens) 14=70
therefore 1 pencil cost is 70/14=5, so 6 pencil cost is 6x5=30 and 8 pens cost is 8x5=40
Again, avg cost of 8 pencils and 10 pens is Rs.90
(8 pencil + 10 pens) 18=90
therefore 1 pencil cost is 90/18=5, so 8 pencil cost is 8x5=40 and 10 pens cost is 10x5=50
So 25 pencil cost is (25/a)=125 and 25 pens cost is (25x5)=125
ANSWER:B
Answer: (B) 125
Question: In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?
(A) 30%
(B) 70%
(C) 100%
(D) 250%
(E) 120%
Rationale: Let C.P. = Rs. 100. Then, profit = Rs. 320, S.P. = Rs. 420
New C.P. = 125% of Rs. 100 = Rs. 125.
New S.P. = Rs. 420
Profit = 420 - 125 = Rs. 295
Required percentage = 295/420 * 100 = 1475/21 = 70%
ANSWER:B
Answer: (B) 70%
Question: On the Richter scale, which measures the total amount of energy released during an earthquake, a reading of x-1 indicates one-tenth the released energy as is indicated by a reading of x. On that scale, the frequency corresponding to a reading of 7 is how many times as great as the frequency corresponding to a reading of 5?
(A) 10^2
(B) 10^3
(C) 10^4
(D) 10^5
(E) 10^6
Rationale: If Richter scale reading goes from X-1 to X it will be 10
if Richter scale reading goes from 5 to 6 it will be 10
Similarly if Richter scale reading goes from 6 to 7 it will be 10
so it will from 5 to 7 i.e 6,7 = 10*10 = 10^2
Answer is A
Answer: (A) 10^2
Question: In a group of 100 people,50 like reading books,20 like both reading books and listening songs. How many like listening songs?
(A) 40
(B) 50
(C) 70
(D) 60
(E) None
Rationale: Make a Venn diagram, and enter your data.
Let the number of people who like Listening Songs be x
x + 20 + 30 = 100
x = 50
so number who like Listening Songs = 20+50 = 70
Answer C
Answer: (C) 70
Question: There are 6 baskets numbered from 1 to 6 and filled with apples . 10 children are asked to pick apples one by one from each basket such that the number of apples picked by each child from each basket is equal to the number marked on the basket. If there were 1000 apples in total and the baskets were filled in such a way that none of the basket became empty in the process, how many apples were left in the end?
(A) 90
(B) 91
(C) 210
(D) 790
(E) 910
Rationale: Total number of apples in the basket initially = 1000
Each child picks up = 1+2+3+4+5+6 = 6*7/2 = 21
Total number of apples picked up by 10 children = 21*10 = 210
Number of apples left in the end = 1000-210 =790
Answer is D
Answer: (D) 790
Question: A man whose bowling average is 12.4, takes 3 wickets for 26 runs and there by decreases his average by 0.4. the number of wickets taken by him before his last match is?
(A) 23
(B) 24
(C) 25
(D) 26
(E) 27
Rationale: 12.4*x+26=(3+x)12
solve equation x=25
ANSWER:C
Answer: (C) 25
Question: Vishal invested 10% more than Trishul. Trishul invested 10% less than Raghu. If the total sum of their investments is Rs. 6358, how much amount did Raghu invest ?
(A) 1287
(B) 2200
(C) 2000
(D) 1129
(E) 1192
Rationale: Let money invested by Raghu = Rs. x
Money invested by Trishul = 9/10 x = 0.9x
Money invested by Vishal = 9/10x * 110/100 = 0.99x
Also, x+0.9x+0.99x = 6358
= x= 6358/2.89 = 2200
Therefore, amount invested by Raghu is Rs. 2200.
Answer: B
Answer: (B) 2200
Question: For any integer p, *p is equal to the product of all the integers between 1 and p, inclusive. How many prime numbers are there between *7 + 3 and *7 + 7, inclusive?
(A) None
(B) One
(C) Two
(D) Three
(E) Four
Rationale: 7! = 720 * 7 = 5040
# in question = 5043, 5044, 5045, 5046, 5047
none of these are prime
Answer - A
Answer: (A) None
Question: What is the ratio of 6/7 to the product 3*(7/3)?
(A) 3:7
(B) 1:3
(C) 3:21
(D) 6:49
(E) 3:49
Rationale: 6/7 / 21/3 = 6/49...
IMO option D.
Answer: (D) 6:49
Question: Mars travels around the Sun at an approximate speed of 14.4 miles per second. This speed is how many kilometers per hour? (1 km = 0.6 miles)
(A) 64,200
(B) 75,300
(C) 86,400
(D) 97,500
(E) 108,600
Rationale: The speed is 14.4 miles/s. Then 14.4/0.6 = 24 km/s
24*3600 = 86,400 kph
The answer is C.
Answer: (C) 86,400
Question: If -1 < h < 2, which of the following has the greatest value?
(A) a) 1-h
(B) b) 1+h
(C) c) 1+h^2
(D) d) 1-1/h
(E) e) 1-1/(h^2)
Rationale: easiest way of solving this would be to substitute a value.
lets say h= - 1/2
a) 3/2
b) 1/2
c) 5/4
d) 3
e) - 3
the value you chose is wrong . h cannot be 0.9 as -1<h<0. if you chose -0.9 answer will still be D.
Answer is C.
Answer: (C) c) 1+h^2
Question: Nine men and nine women have to sit around a circular table so that no 2 women are together. In how many ways can that be done?
(A) 5!*6!
(B) 6!*6!
(C) 5!*7!
(D) 6!*7!
(E) 8!*9!
Rationale: The number of arrangements of n distinct objects in a row is given by n!.
The number of arrangements of n distinct objects in a circle is given by (n-1)!.
The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have: n!/n=(n-1)!
Now, 9 men in a circle can be arranged in (9-1)! ways and if we place 9 women in empty slots between them then no two women will be together. The # of arrangement of these 9 women will be 9! and not 8! because if we shift them by one position we'll get different arrangement because of the neighboring men.
So the answer is indeed 8!*9!.
E
Answer: (E) 8!*9!
Question: x =2.5 3.5 1.5
y= 25 49 9 then what is the relation between x and y
(A) Y=(2*X)^2
(B) Y=(2*X)^3
(C) Y=(2*X)^4
(D) Y=(3*X)^2
(E) Y=(4*X)^2
Rationale: Y=(2*X)^2
25=(2*2.5)^2
ANSWER:A
Answer: (A) Y=(2*X)^2
Question: A question paper has 2parts, A & B, each containing 10 questions. If a student has to choose 8 from part A &5 from part B, in how many ways can he choose the questions?
(A) 1020
(B) 1100
(C) 1140
(D) 1150
(E) 1140
Rationale: There 10 questions in part A out of which 8 question can be chosen as = 10C8.
Similarly, 5 questions can be chosen from 10 questions of Part B as = 10C5.
Hence, total number of ways,
=10C8*10C5
=[10!/(2!8!)]*[10!/(5!*5)]
= {10*9/2}*{10*9*8*7*6/(5*4*3*2*1)}
= 1140.
E
Answer: (E) 1140
Question: A certain manufacturer of cake, muffin, and bread mixes has 100 buyers, of whom 50 purchases cake mix, 40 purchase muffin mix, and 17 purchase both cake mix and muffin mix. If a buyer is to be selected at random from the 100 buyers, what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix?
(A) 1/10
(B) 3/10
(C) 1/2
(D) 27/100
(E) 9/100
Rationale: C+M+B-CM-MB-CB-2CMB = 100
C - cake buyers, M - muffin and B - Bread buyers. CM,MB,CB and CMB are intersecting regions.
the question asks for people who have bought only bread mixes = B-CB-MB-2CMB has to be found out.
50 + 40 + B-CB-MB-17-2CMB = 100
B-CB-MB-2CMB = 27
hence the probability = 27/100
D
Answer: (D) 27/100
Question: How many paying stones, each measuring 2 1/2 m * 2 m are required to pave a rectangular court yard 30 m long and 16 1/2 m board?
(A) 99
(B) 18
(C) 16
(D) 10
(E) 15
Rationale: 30 * 33/2 = 5/2 * 2 * x => x
= 99
Answer:A
Answer: (A) 99
Question: A toy store sells small, medium, large, and super-large toy trucks in each of the colors red, blue, black, green, orange, and yellow. The store has an equal number of trucks of each possible color-size combination. If Paul wants a medium, red truck and his mother will randomly select one the trucks in the store, what is the probability that the truck she selects will have at least one of the two features Paul wants?
(A) 1/3
(B) 2/5
(C) 3/5
(D) 3/8
(E) 11/24
Rationale: Probability of NOT selecting medium out of 4 sizes = 3/4
Probability of NOT selecting red out of 6 colours = 5/6
Total probability of NOT selecting red and medium = (3/4)*(5/6) = 5/8
Required probability = 1 - 5/8 (this will select at least one of red and medium)
= 3/8
The answer is D.
Answer: (D) 3/8
Question: In honor of the year 2012, a donor has purchased 2016 books to be distributed evenly among the elementary schools in a certain school district. If each school must receive the same number of books, and there are to be no books remaining, which of the following is NOT a number of books that each school could receive?
(A) 18
(B) 36
(C) 42
(D) 51
(E) 56
Rationale: All options other than 'D' are factors of 2012. Hence, 'D' is the answer
Answer: (D) 51
Question: Find the number of square tiles to cover the floor of a room measuring 3.5 m * 9 m leaving 0.25 m space around the room. A side of square tile is given to be 25 cms?
(A) 408
(B) 476
(C) 472
(D) 471
(E) 445
Rationale: 3 * 8 1/2 = 1/4 * 1/4 * x => x
= 408
Answer:A
Answer: (A) 408
Question: 7 people average age is 30. youngest person age is 3. find average of the people when youngest was born.
(A) 23
(B) 24
(C) 25
(D) 26
(E) 27
Rationale: average age of people =30
so have total age =210
before 7 years we have to deduct each person age by seven years 210-21=189
so average age would be 189/7=27
ANSWER:E
Answer: (E) 27
Question: A man covered a certain distance at some speed. Had he moved 3 kmph faster, he would have taken 40 minutes less. If he had moved 2 kmph slower, he would have taken 40 minutes more. The distance (in km) is
(A) 27
(B) 87
(C) 40
(D) 18
(E) 17
Rationale: Explanation:
Let distance = x km and usual rate = y kmph.
Then, x/y - x/(y+3) = 40/60 --> 2y (y+3) = 9x ----- (i)
Also, x/(y-2) - x/y = 40/60 --> y(y-2) = 3x -------- (ii)
On dividing (i) by (ii), we get:
x = 40 km.
Answer: C
Answer: (C) 40
Question: The function F(n) is defined as the product of all the consecutive positive integers between 3 and n^2, inclusive, whereas the function G(n) is defined as the product of the squares of all the consecutive positive integers between 1 and n, inclusive. The exponent on 2 in the prime factorization of F(3)/G(3) is
(A) 	1
(B) 	2
(C) 	3
(D) 	4
(E) 	5
Rationale: F(3)/G(3)
=product(1 to 3 ^2) / 1.2^2.3^2
=1.2.3.4.5.6.7.8.9/1.4.9
=1.2.3.(2^2).5.(2.3).7.(2^3).9/1.(2^2).9
=1.(2^7).3.5.7.9/1.(2^2).9
Loof for 2^7/2^2=2^5 ----Exponent 3
Answer: C
Answer: (C) 	3
Question: The average of 7 consecutive numbers is 20. The largest of these numbers is
(A) 12
(B) 27
(C) 23
(D) 28
(E) 11
Rationale: Let the numbers be x, x + 1, x + 2, x + 3, x + 4, x + 5 and x + 6,
Then (x + (x + 1) + (x + 2) + (x + 3) + (x + 4) + (x + 5) + (x + 6)) / 7 = 20.
or 7x + 21 = 140 or 7x = 119 or x =17.
Latest number = x + 6 = 23.
Answer: C
Answer: (C) 23
Question: On the xy co-ordinate plane, point C is (5,-1) and point D is (-1,2.5). The point on line segment CD that is twice as far from C as from D is:
(A) (1,-1)
(B) (1,1)
(C) (2,0.25)
(D) (3,0.5)
(E) (3,1)
Rationale: We want the point on the line that is twice as far from C as it is from D. We can examine the x and y coordinates separately since they are independent.
*It should be noted that there are two solutions to this problem, one point between C and D, and another point with D in the middle of C and the point. We can quickly look at the answer choices and see that all the points are between C and D, therefore we can search for that point using the following method:
Taking the x-coordinate first, the distance between C and D is |(x-coordinate of C) - (x-coordinate of D)|= |5 - (-1)| = 6
The x-coordinate that is twice as far from C as it is from D (and in between C and D) will be 4 units from C and 2 units from D. So the x coordinate of the point we're looking for is 5-4 = 1, or (-1)+2 = 1.
Now looking at the y-coordinate, we do the same thing. The distance between C and D is |(-2) - 2.5| = 4.5
The y-coordinate that is twice as far from C as it is from D (and in between C and D) will be 3 units from C and 1.5 units from D. So the y coordinate of the point we're looking for is (-2)+3 = 1, or 2.5-1.5 = 1.
So now we have our coordinates of the point on the line that is twice as far from C as it is from D: (2,0.25)
Answer: C
Answer: (C) (2,0.25)
Question: A ladies hostel had provision of food for 120 women for 35 days. After 10 days, 25 women left the hostel. The number of days for which the remaining food will last is:
(A) 39.47
(B) 39
(C) 39.23
(D) 39.74
(E) 39.64
Rationale: Explanation :
After 10 days : 120 women had food for 25 days.
Suppose 95 women had food for x days.
Now, Less women, More days (Indirect Proportion)
95 : 150 :: 25 : x
=> 95 x x = 150 x 25
=> x = 150 x 25 / 95
=> x = 39.47
Answer : A
Answer: (A) 39.47
Question: A basket contains 10 bananas and 20 mangoes out of which 3 bananas and 5 mangoes are spoiled. If we choose two fruits at random, what is the probability that either both are mangoes or both are non spoiled?
(A) 309/435
(B) 311/433
(C) 316/401
(D) 314/501
(E) 316/435
Rationale: Let A be the event of getting two oranges and
B be the event of getting two non-defective fruits.
and be the event of getting two non-defective oranges
= 316/435
E
Answer: (E) 316/435
Question: With out any halt a train travels a certain distance with an average speed of 75 km ph , and with halts it covers the same distance at an average speed of 60 kmph. When it is traveling with halts, how many
minutes/per hour does the train halt on an average ?
(A) 48 min
(B) 12min.
(C) 15min.
(D) 18min.
(E) 20min
Rationale: With halt in 1 hour the train travels 60km
With out halt for traveling same distance it take 60/75 = 4/5 = 48 minutes
:. 12 minutes is the halting time per hour
Answer: B
Answer: (B) 12min.
Question: How many two-element subsets of {1,2,3,4} are there that do not contain the pair of elements 2 and 4?
(A) One
(B) Two
(C) Four
(D) Five
(E) Six
Rationale: {1,2}, {1,3}, {1,4}, {2,3}, {3,4}.
Or: C24−1=5
Answer: D.
Answer: (D) Five
Question: 8 man's increases average weight by 2.5 kg when a new man comes in place of one of them weighing 65 kg. What might be the weight of the new man?
(A) 85 kg
(B) 70 kg
(C) 75 kg
(D) 90 kg
(E) 79 kg
Rationale: Total weight = (8 x 2.5) kg = 20 kg.
Weight - new man = (65 + 20) kg = 85 kg
ANSWER A
Answer: (A) 85 kg
Question: During 2001, a stock lost 60 percent of its value. During the following year, the stock's value increased by 200 percent. Which of the following is the percent change in the stock's value during those two years?
(A) 60 percent decrease
(B) 40 percent decrease
(C) 20 percent increase
(D) 60 percent increase
(E) 140 percent increase
Rationale: Let the value of the stock in 2000 be 100, then in 2001 its value would be 100*(1-60/100)=100*0.4=40 and in 2002 its value would be 40*(1+200/100)=120. Hence during those two years the value of the stock increased from 100 to 120, so by 20%.
Answer: C.
Answer: (C) 20 percent increase
Question: Two pipes can fill a tank in 18 minutes and 15 minutes. An outlet pipe can empty the tank in 45 minutes. If all the pipes are opened when the tank is empty, then how many minutes will it take to fill the tank?
(A) 1/15
(B) 1/16
(C) 1/11
(D) 1/10
(E) 1/12
Rationale: Part of the filled by all the three pipes in one minute
= 1/18 + 1/15 - 1/45 = (5 + 6 - 2)/90 = 9/90 = 1/10
So, the tank becomes full in 10 minutes.
Answer:D
Answer: (D) 1/10
Question: 6,61,212,507,_?
(A) 974
(B) 994
(C) 954
(D) 845
(E) 754
Rationale: (2)3-2=6
(4)^3-3=61
(6)^3-4=212
(8)^3-5=507
(10)^3-6=994
ANSWER:B
Answer: (B) 994
Question: John bought a 1-year, $20,000 certificate of deposit that paid interest at an annual rate of 8 percent compounded semiannually. What was the total amount of interest paid on this certificate at maturity?
(A) $1650
(B) $1660
(C) $2632
(D) $1632
(E) $2750
Rationale: 8 percent compounded semiannually --> 4% in 6 moths.
For the first 6 moths interest was 4% of $20,000, so $800;
For the next 6 moths interest was 4% of $20,800, so $832
Total interest for 1 year was $800+$832=$1632
Answer : D
Answer: (D) $1632