mathewhe/aqua_rat huggingface dataset:
Question: At 1:20 PM, Train X departed from Station A on the road to Station B. At 1:30 PM, Train Y departed Station B on the same road for Station A. If Station A and Station B are p miles apart, Train X’s speed is r miles per hour, and Train Y’s speed is s miles per hour, how many hours after 1:00 PM, in terms of p, r, and s, do the two trains pass each other?
(A) 0.5 + (p - 0.5s)/(r + s)
(B) (p - 0.5s)/(r + s)
(C) 0.5 + (p - 0.5r)/r
(D) (p - 0.5r)/(r + s)
(E) 0.5 + (p - 0.5r)/(r + s)
Rationale: The distance A is going to cover between 1:00 and 1:30
= .5r
now the distance between the two trains = (p-.5r)
the relative velocity = (r-(-s)) = r+s
From 1:30, time is going to take when they meet = (p-.5r)/(r+s)
so the ans is .5+((p-.5r)/(r+s)) [.5 is added for the time from 1:00 to 1:30]
ans is D
Answer: (D) (p - 0.5r)/(r + s)
Question: A painter intends to mixed two jars of paint to create a new color. He chooses one paint jar randomly from a display containing 2 red and 3 blue samples, and a second jar is chosen at random from a different display containing 3 red and 2 blue samples. If he plans on mixing the two chosen jars together, what is the probability that when mixed together, the result will be purple paint? (The color purple is created with 1 part red and 1 part blue.)
(A) 1/5
(B) 1/3
(C) 2/3
(D) 4/5
(E) 6/5
Rationale: Painter has two buckets he has to randomly pick from 2 different lists ... Let these Lists be A and B ... He has to choose the first bucket from List A , and the second bucket from List B
FOR THE FIRST BUCKET ...
Red color - 2
Blue color - 2
FOR THE SECOND BUCKET
Red color - 3
Blue color -2
In order to get Purple he has to mix red with blue .. Both the LISTS contain either blue or red , therefore we have two scenarios :
Scenario I - He picks Red color from List A and Blue color from List B
Scenario II - He picks Blue color from List A and Red color from List B
Scenario I - Odds for red color from List A are 1/2 .. and for Blue color from List B are 2 /5 .. Multiplying them (because we have to find the odds that both colors are selected from their respective lists together (this is a AND not an OR problem) we get 1/5
Scenario II - Odds for blue color from List A are 1/2 , and for Red color from List B are 3/5 ... Multiplying them we get 3/10 ...
Both the scenarios are equally possible therefore we must ADD the two (not multiply ) because both of them do not have to hold true together (have to independently) for our desired result to be achieved ...
We get 1/5 + 3/10 = 1/3 (B)
Answer: (B) 1/3
Question: How many three letter words are formed using the letters of the word TIME?
(A) 12
(B) 20
(C) 16
(D) 24
(E) 30
Rationale: Explanation:
The number of letters in the given word is four.
The number of three letter words that can be formed using these four letters is â´Pâ‚ƒ = 4 * 3 * 2 = 24.
ANSWER IS D
Answer: (D) 24
Question: In a office work is distribute between p persons. If 1/6 members are absent then work increased for each person is?
(A) 10%
(B) 14.28%
(C) 15%
(D) 16%
(E) 20%
Rationale: let total % of work is 100%
total person=p
1/6 person are absent of total person . so absent person is 1/6p ie p/6.
left person is, p-p/6=5p/6.
p person do the work 100%
1 person do the work 100*p%
5p/6 person do the work (100*p*6)/5p%=120.00%
work increased for each person is=(120-100)%=20%
ANSWER:E
Answer: (E) 20%
Question: The mean of 50 observations was 30. It was found later that an observation 48 was wrongly taken as 23. The corrected new mean is
(A) 35.2
(B) 36.1
(C) 30.5
(D) 39.1
(E) None
Rationale: Sol.
Therefore correct sum
= ( 30 × 50 + 48 – 23)
= 1525.
Therefore correct mean
= 1525 / 50
= 30.5.
Answer C
Answer: (C) 30.5
Question: A man can row 8 kmph in still water. When the river is running at 1.8 kmph, it takes him 2 hour to row to a place and back. What is the total distance traveled by the man?
(A) 8.2 km
(B) 6.7 km
(C) 7.6 km
(D) 7.4 km
(E) 6.3 km
Rationale: M = 8
S = 1.8
DS = 9.8
US = 6.2
x/9.8 + x/6.2 = 1
x = 3.8
D = 2.88 * 2 = 7.6
Answer:C
Answer: (C) 7.6 km
Question: Two stations A and B are 110 km apart on a straight line. One train starts from A at 8 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
(A) 11
(B) 10
(C) 8
(D) 12
(E) 15
Rationale: Suppose they meet x hours after 8 a.m.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x - 1) hours = 25(x - 1) km.
Therefore 20x + 25(x - 1) = 110
45x = 135
x = 3.
So, they meet at 11 a.m.
Answer: A
Answer: (A) 11
Question: The H.C.F. of two numbers is 10 and the other two factors of their L.C.M. are 11 and 15. The larger of the two numbers is:
(A) 150
(B) 300
(C) 299
(D) 322
(E) 345
Rationale: the numbers are (10 x 11) and (10 x 15).
Larger number = (10 x 15) = 150.
ANSWER :A
Answer: (A) 150
Question: In the first week of the Year, Mancy saved $1. In each of the next 51 weeks, she saved $1 more than she had saved in the previous week. What was the total amount that Mancy saved during the 52 weeks?
(A) $1,326
(B) $1,352
(C) $1,378
(D) $2,652
(E) $2,756
Rationale: In the first week of the Year, Mancy saved $1.If you don't recall the formula, there is one method:
1 + 2 + 3 + 4 + 5 ........ + 26 + 27 + ............ + 48 + 50 + 51 + 52
Sum of 1stlast digit = 1 + 52 = 53
Sum of 2nd2nd last digit = 2 + 51 = 53
Sum of 3rd3rd last digit = 3 + 50 = 53
.
.
.
.
This is repeated 26 times
So, 26 * 53 = 1378
Answer = C
Answer: (C) $1,378
Question: A, B, C rent a pasture. If A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing and the rent of the pasture is Rs. 175, then how much amount should C pay as his share of rent?
(A) 23
(B) 45
(C) 15
(D) 28
(E) 18
Rationale: A : B: C = 10*7 : 12*5 : 15*3 = 2*7 : 12*1 : 3*3 = 14 : 12 : 9
amount that C should pay = 175 * (9/35) = 5*9 = 45
Answer is B
Answer: (B) 45
Question: A circle graph shows how the budget of a certain company was spent: 61 percent for salaries, 10 percent for research and development, 6 percent for utilities, 5 percent for equipment, 3 percent for supplies, and the remainder for transportation. If the area of each sector of the graph is proportional to the percent of the budget it represents, how many degrees of the circle are used to represent transportation?
(A) 18°
(B) 36°
(C) 54°
(D) 72°
(E) 90°
Rationale: The percent of the budget for transportation is 100 - (61+10+6+5+3)= 15%
100% of the circle is 360 degrees.
Then (15%/100%)*360 = 54 degrees
The answer is C.
Answer: (C) 54°
Question: If |x – 9/2| = 5/2, and if y is the median of a set of p consecutive integers, where p is odd, which of the following must be true?
I. xyp is odd
II. xy(p^2 + p) is even
III. x^2y^2p^2 is even
(A) II only
(B) III only
(C) I and III
(D) II and III
(E) I, II, and III
Rationale: x is in range of 2 and 7 so it can be even or odd
y is median of set of odd integers so it can be even or odd
p is given as odd
using above information only II for sure can be inferred as even.
other two, either can be even or odd
correct response is A.
Answer: (A) II only
Question: Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Two years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand's present age in years?
(A) A)24
(B) B)89
(C) C)67
(D) D)56
(E) E)16
Rationale: Let the present ages of Sameer and Anand be 5x years and 4x years respectively.
Then,	(5x + 2/4x + 2)=11/9
9(5x + 2) = 11(4x + 2)
45x + 18 = 44x + 22
45x - 44x = 22 - 18
x = 4.
Anand's present age = 4x = 16 years.
Answer:E
Answer: (E) E)16
Question: The difference of 2 digit number & the number obtained by interchanging the digits is 36. What is the difference the sum and the number if the ratio between the digits of the number is 1:2?
(A) 3
(B) 8
(C) 9
(D) 11
(E) 12
Rationale: Let the number be xy.
Given xy – yx = 36.
This means the number is greater is than the number got on reversing the digits.
This shows that the ten’s digit x > unit digit y.
Also given ratio between digits is 1 : 2 => x = 2y
(10x + y) – (10y +x) = 36 => x – y = 4 => 2y – y =4.
Hence, (x + y) – (x – y) = 3y – y = 2y = 8
B
Answer: (B) 8
Question: A particular store purchased a stock of turtleneck sweaters and marked up its cost by 20%. During the New Year season, it further marked up its prices by 25% of the original retail price. In February, the store then offered a discount of 18%. What was its profit on the items sold in February?
(A) 27.5%
(B) 30%
(C) 35%
(D) 23%
(E) 40%
Rationale: Assume the total price = 100x
Price after 20% markup = 120x
Price after 25%further markup = 1.25*120x = 150x
Price after the discount = 0.82*150x = 123x
Hence total profit = 23%
Option D
Answer: (D) 23%
Question: By investing Rs. 1620 in 8% stock, Michael earns Rs. 135. The stock is then quoted at:
(A) Rs 96
(B) Rs 100
(C) Rs 150
(D) Rs 160
(E) Rs 200
Rationale: to earn Rs 135 investment = Rs 1620
to earn Rs 8 investment =>1620/135*8=96
ANSWER A
Answer: (A) Rs 96
Question: The average of five numbers id 28. If one number is excluded, the average becomes 25. What is the excluded number?
(A) 30
(B) 40
(C) 32.5
(D) 35
(E) 37
Rationale: Explanation:
Sum of 5 numbers = 5 × 28
Sum of 4 numbers after excluding one number = 4 × 25
Excluded number
= 5 × 28 - 4 × 25
= 140 - 100 = 40
Answer: Option B
Answer: (B) 40
Question: Find the average (arithmetic mean) of x and y if the average of x, y, and 10 is 20 greater than the average of x, y, 10, and 20.
(A) 115
(B) 130
(C) 145
(D) 160
(E) 175
Rationale: consider the statement 30 is 20 greater than 10: 30 = 10 + 20
similarly
the average of x, y, and 10 = (the average of x, y, 10, and 20) + 20
(x+y+10)/3 = (x+y+10+20)/4 + 20
(x+y+10)/3 = (x+y+30)/4 + 80/4
(x+y+10)/3 = (x+y+30+80)/4
(x+y+10)/3 = (x+y+110)/4
cross multiply
4(x+y+10) = 3(x+y+110)
4x+4y+40 = 3x+3y+330
4x-3x + 4y-3y = 330 - 40
x + y = 290
thus
(x+y)/2 = 290/2
(x+y)/2 = 145
thus the average of x and y is 145
C
Answer: (C) 145
Question: The sum of two numbers is 16. The difference is 10. What are the two numbers?
(A) 10-6
(B) 8-8
(C) 9-7
(D) 11-5
(E) 13-3
Rationale: 13+3 = 16
13 - 3 = 10
The Answer is E
Answer: (E) 13-3
Question: During a car trip, Maria stopped to rest after she traveled 1/2 of the total distance to her destination. she stopped again after she traveled 1/4 of the distance remaining between her first stop and her destination, and then she drove the remaining 210 miles to her detination. What was the total distance, in miles from Maria's starting point to her destination?
(A) 280
(B) 320
(C) 360
(D) 420
(E) 560
Rationale: Easy 560 is the answer.
3/4 ( x/2) = 210
x = 210 * 8 /3 = 560.
Answer E
Answer: (E) 560
Question: All of the bonds on a certain exchange are designated by a 3-letter, a 4-letter, or a 5-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different bonds that can be designate with these codes?
(A) 26(26^3 + 26^4)
(B) 26(26^3 + 26^5)
(C) 27(26^3 + 26^5)
(D) 27(26^3) + 26^5
(E) 26^3 + 27(26^5)
Rationale: 3-letter codes = 26^3;
4-letter codes = 26^4;
5-letter codes = 26^5;
Total = 26^3 + 26^4 + 26^5 = 26^3(1+26) + 26^5 = 26^3*27 + 26^5.
Answer: D.
Answer: (D) 27(26^3) + 26^5
Question: I buy coffee from 3 different shops at Rs.150,Rs.140,Rs.130 per kg and mix them in proportion 8:5:3.At what price per kg must I sell the mixture to make a profit of 25%?
(A) 168.906
(B) 178.906
(C) 188.906
(D) 198.906
(E) 158.906
Rationale: total=16x kg, tot cp=2290x
sp should be=2862.5x
so sp/kg=178.906
ANSWER:B
Answer: (B) 178.906
Question: In a game, a person is declared winner, if he gets 4 consecutive tails in five throws of a coin. What is the probability of A to win if he has got a tail in the first throw?
(A) 1/5
(B) 1/4
(C) 1/8
(D) 1/16
(E) 1/6
Rationale: First throw = Tails
For a person to win, the next 3 throws must be tails and the 5th throw can be heads or tails. i.e. TTTTH or TTTTT
So the person can win in 2 ways if the first throw is Tails.
Total number of outcomes for the next 4 throws = 2^4 = 16
Probability = 2/16 = 1/8
Answer: C
Answer: (C) 1/8
Question: For any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum of all the even integers between 99 and 171?
(A) 2820
(B) 3440
(C) 4860
(D) 5560
(E) 6720
Rationale: 100 + 102 + ... + 170 =
100*36 + (2+4+...+70) =
100*36 + 2*(1+2+...+35) =
100*36 + 2(35)(36)/2 =
100*36 + 35*36 = 135(36) = 4860
The answer is C.
Answer: (C) 4860
Question: A girl has 8 dolls out of which a pair of is to be selected to take with her. At most, how many different pairs are possible?
(A) 100
(B) 90
(C) 50
(D) 45
(E) 28
Rationale: N=8C2=8!/(6!2!)=8*7/2=28
Correct Option: E
Answer: (E) 28
Question: The average age of a class of 39 students is 15 years. If the age of the teacher be included, then the average increases by 3 months. Find the age of the teacher.
(A) 22
(B) 25
(C) 97
(D) 27
(E) 91
Rationale: Answer: 25 y
Explanation:
Average age of 39 students = 15 yrs
Total age of 39 students = 39 × 15 = 585 yrs
Avg age of 39 students + teacher =15+ (3/12) =15.25 years
So the total age of (39 student + 1 teacher) or 40 persons = 40 × 15.25 = 610 years
So age of teacher = 610 – 585 = 25 years
Answer:B
Answer: (B) 25
Question: Bert and Rebecca were looking at the price of a condominium. The price of the condominium was 50% more than Bert had in savings, and separately, the same price was also 25% more than Rebecca had in savings. What is the ratio of what Bert has in savings to what Rebecca has in savings.
(A) 1:6
(B) 1:3
(C) 1:2
(D) 3:4
(E) 5:6
Rationale: Suppose bert had 100 so price becomes 150 , this 150 = 1.25 times R's saving .. so R's saving becomes 120
So required ratio is 100:120=5:6
ANSWER:E
Answer: (E) 5:6
Question: At a bank, the service charges for transactions were US Dollar 1 for every 5 transactions. The bank recently revised the charges to US Dollar 0.75 for every 3 transactions. By approximately what percent did the ratio of price to transactions increase from the previous charge?
(A) 28
(B) 24
(C) 23
(D) 22
(E) 25
Rationale: Initial charge/transaction ratio = 1/5 = 3/15
Revised charge/transaction ratio = .75/3 = 3.75/15
Answer: E
Answer: (E) 25
Question: A, B and C enter into partnership. A invests some money at the beginning, B invests double the amount after 6 months, and C invests thrice the amount after 8 months. If the annual gain be Rs.18600. A's share is?
(A) 8876
(B) 2765
(C) 6000
(D) 6200
(E) 1261
Rationale: x* 12 : 2x* 6: 3x* 4
1:1:1
1/3 * 18600 = 6200
Answer:D
Answer: (D) 6200
Question: If 7^q is a factor of the product of the integers from 1 to 100, inclusive, what is the largest value of q?
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Rationale: So the question just means that we have to find all the multiples q of 7 between 1 to 100
So there are 14 multiples of 7 ( 7 - 98)
But 49 and 98 contain two 7's as factors
so we have to add 14 + 2 = 16
E
Answer: (E) 16
Question: At a dinner party, 5 people are to be seated around a circular table. 2 seating arrangements are considered different only when the positions of the people are different relative to each other. what is the total number R of different possible seating arrangements for the group?
(A) 5
(B) 10
(C) 24
(D) 32
(E) 120
Rationale: Circular arrangements= (n-1)!
Hence (4!) = 24=R
Answer is C
Answer: (C) 24
Question: At what price must an article costing Rs.47.50 be marked in order that after deducting 10% from the list price. It may be sold at a profit of 25% on the cost price?
(A) 65.97
(B) 62.6
(C) 62.1
(D) 62.7
(E) 62.2
Rationale: CP = 47.50
SP = 47.50*(125/100) = 59.375
MP*(90/100) = 59.375
MP = 65.97
Answer: A
Answer: (A) 65.97
Question: Susan, Daisy and Tim need to be seated in 3 identical chairs in straight line so that Susan is seated always left to Tim. How many such arrangements are possible ?
(A) 3
(B) 12
(C) 80
(D) 240
(E) 60
Rationale: Total # of arrangement of 3 people is 3!.
In half of the cases Susan will be seated left to Tim and in half of the cases Susan will be seated right to Tim (why should one seating arrangement have more ways to occur than another?).
So, # of arrangements to satisfy the given condition is 3!/2=3.
Answer: A.
Answer: (A) 3
Question: The area of a square is 4096 sq cm. Find the ratio of the breadth and the length of a rectangle whose length is twice the side of the square and breadth is 24 cm less than the side of the square.
(A) 5:28
(B) 5:19
(C) 5:12
(D) 5:13
(E) 5:16
Rationale: Let the length and the breadth of the rectangle be l cm and b cm respectively. Let the side of the square be a cm.
a2 = 4096 = 212
a = (212)1/2 = 26 = 64
L = 2a and b = a - 24
b : l = a - 24 : 2a = 40 : 128
= 5:16
Answer:E
Answer: (E) 5:16
Question: Machine A can make 350 widgets in 1 hour, and machine B can make 250 widgets in 1 hour. If both machines work together, how much time will it take them to make a total of 900 widgets?
(A) 1 hour and 20 minutes
(B) 1 hour and 24 minutes
(C) 1 hour and 30 minutes
(D) 1 hour and 36 minutes
(E) 1 hour and 40 minutes
Rationale: (350+250)t=900
600t=900
t=3/2
t=1 hour and 30 minutes
Answer: C
Answer: (C) 1 hour and 30 minutes
Question: A, B and C are partners. A receives 2/3 of profits, B and C dividing the remainder equally. A's income is increased by Rs.600 when the rate to profit rises from 5 to 7 percent. Find the Capital of B?
(A) 3999
(B) 7799
(C) 2500
(D) 7500
(E) 2912
Rationale: A:B:C = 2/3:1/6:1/6 = 4:1:1
x * 2/100 * 2/3 = 600
B capital = 45000*1/6 = 7500.Answer: D
Answer: (D) 7500
Question: A man can row upstream at 25 kmph and downstream at 35 kmph, and then find the speed of the man in still water?
(A) 22
(B) 27
(C) 30
(D) 82
(E) 21
Rationale: US = 25
DS = 35
M = (35 + 25)/2 = 30
Answer: C
Answer: (C) 30
Question: Look at this series: 49, 46, 51, 48, 53, 50, ... What number should come next?
(A) 54
(B) 58
(C) 45
(D) 55
(E) 58
Rationale: Explanation:
In this simple alternating subtraction and addition series; 3 is subtracted, then 5 is added, and so on.
Answer: Option D
Answer: (D) 55
Question: What number should replace the question mark?
105, ?, 70, 52, 35
(A) 49
(B) 37
(C) 70
(D) 55
(E) 87
Rationale: E
87
The sequence progresses -18, -17, -18, -17.
Answer: (E) 87
Question: The data A and B are equal to the data subtracted C; The data B is three times the data A; If the data A is equal to 12 What is the sum of the data A, B and C?
(A) 86
(B) 92
(C) 84
(D) 102
(E) 96
Rationale: The equations raised.
A + B = C
B = 3A
A = 12 then
B = 36 and C = 48
A + B + C = 96
Answer: E
Answer: (E) 96
Question: P can finish a work in 18 days. Q can finish the same work in 15 days. Q worked for 10 days and left the job. how many days does P alone need to finish the remaining work?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: Work done by P in 1 day = 1/18
Work done by Q in 1 day = 1/15
Work done by Q in 10 days = 10/15 = 2/3
Remaining work = 1 – 2/3 = 1/3
Number of days in which P can finish the remaining work = (1/3) / (1/18) = 6
Answer is E.
Answer: (E) 6
Question: Which of the following leads to the correct mathematical solution for the number of ways that the letters of the word DATA could be arranged to create a four-letter code?
(A) 4!/2!
(B) 6! − (3! + 2!)
(C) 6! − (3! × 2!)
(D) 6!/(3! + 2!)
(E) 6!/(3! × 2!)
Rationale: Number of letters in word 'DATA' = 4.
The letters 'A' appear 2 times in the word 'DATA'.
Therefore the mathematical solution for number of ways that the letters of the word DATA can be arranged to create four-letter code
= 4!/2!
Answer:A
Answer: (A) 4!/2!
Question: If each of 4 digit code is formed of integers from 1 to 10, inclusively, and each of the digits are different, how many possible codes are there?
(A) 6,040
(B) 6,840
(C) 6,240
(D) 5,040
(E) 4,069
Rationale: Code consists of 4 digits and no digit is repeated.
First digit of the code can have 10 possibilities
Second digit can have 9 possibilities
Third digit can have 8 possibilities
Total number of possible codes = 10*9*8*7 = 5040
Answer: D
Answer: (D) 5,040
Question: If * stands for /, / stands for -, + stands for * and - stands for +, then
9/15*9+2-9 = ?
(A) 14.7
(B) 15.3
(C) 14.1
(D) 16.2
(E) 17.2
Rationale: 9/15*9+2-9 is changed to 9-15/9*2+9
resolve it like (9)-(15*2)/9+(9)
=> 18-30/9
=>18-10/3 => (54-10)/3
=> 44/3=14.6666666666666666666
implies 14.7
ANSWER:A
Answer: (A) 14.7
Question: Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. The sum placed on simple interest is:
(A) Rs.1550
(B) Rs.1650
(C) Rs.1750
(D) Rs.2000
(E) Rs.3000
Rationale: C.I = 4000 * (1+10/100)2 –4000
= 4000 *11/10 + 11/10 –4000 = Rs.840
:. Sum = Rs.(420 * 100)/ (3 *8) = Rs.1750
ANSWER:C
Answer: (C) Rs.1750
Question: Find the compound interest on $500 in 5years at 5% per annum, the interest being compounded yearly?
(A) $138.14
(B) $150.12
(C) $142.65
(D) $152
(E) $164.12
Rationale: Principle = $500
Rate = 5% yearly
Amount = 500*(1 + 5/100)^5 = 500 * 21/20 * 21/20 * 21/20 * 21/20 * 21/20
= $638.14
C.I. = 638.14-500 = $138.14
Answer is A
Answer: (A) $138.14
Question: A case of 12 rolls of paper towels sells for $9. The cost of one roll sold individually is $1.What is the percent T of savings per roll for the 12-roll package over the cost of 12 rolls purchased individually?
(A) 9%
(B) 11%
(C) 15%
(D) 25%
(E) 90%
Rationale: Cost of 12 paper towels individually = 1*12=12
Cost of a set of 12 paper towels = 9
Cost of one roll = 9/12 = 3/4 = 0.75
Savings per roll = 1-.75 = 0.25
% of savings is T = .25/ 1 *100 = 25% D is the answer.
Answer: (D) 25%
Question: A man can row a boat at 20 kmph in still water. If the speed of the stream is 4 kmph, what is the time taken to row a distance of 60 km downstream?
(A) 30/18
(B) 30/29
(C) 30/12
(D) 30/13
(E) 30/12
Rationale: Speed downstream = 20 + 4 = 24 kmph.
Time required to cover 60 km downstream = d/s = 60/24
= 30/12 hours.
Answer:E
Answer: (E) 30/12
Question: What is the place value of 3 in the numeral 3259
(A) 2700
(B) 2800
(C) 2900
(D) 2980
(E) 3000
Rationale: 3 * 1000 = 3000
E
Answer: (E) 3000
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) 40
(B) 70
(C) 20
(D) 80
(E) 60
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 C
Answer: (C) 20
Question: If T = 5/9 * (K - 32), and if T = 50, then what is the value of K?
(A) 116
(B) 119
(C) 122
(D) 125
(E) 128
Rationale: K-32=9T/5
K=9T/5 + 32
K=9(50)/5 + 32 = 122
The answer is C.
Answer: (C) 122
Question: What is the sum of the integers from -190 to 192 inclusive?
(A) 0
(B) 5
(C) 383
(D) 875
(E) 965
Rationale: sum/n= average.
sum=(average)(n)
average=a+b/2=190+192/2=1
number of items(n)=B-A+1=192-(-190)+1=192+191=383.
sum=average*n=1*383=383.
answer is C
Answer: (C) 383
Question: What is the units digit of (147^25)^49 ?
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
Rationale: The units digit of the exponents of 7 repeat in a cycle of four, which is {7,9,3,1}. The number 25 has the form 4n+1 so the units digit is 7 inside the bracket. The exponent 49 has the form 4n+1, so the units digit is 7. The answer is D.
Answer: (D) 7
Question: A certain cube floating in a bucket of water has between 60 and 85 percent of its volume below the surface of the water. If between 9 and 26 cubic centimeters of the cube's volume is above the surface of the water, then the length of a side of the cube is approximately
(A) 4
(B) 5
(C) 7
(D) 8
(E) 9
Rationale: If sides are 7, vol=7^3=343
60%= 205.8, 85%=291.55
so vol above water, between 137.2 and 51.45 -->too big
If side are 4, vol = 64
60%=38.4, 85%=54.4
vol above water between 25.6 and 9.6
So 4 should be the answer.
Check option C,
If sides are 5, vol = 125
60%= 75, .85%=106.25
vol above water between 18.75-50
(Sides are 4 cubic centimeters)
A
Answer: (A) 4
Question: In a kilometer race, A beats B by 80 meters or 10 seconds. What time does A take to complete the race?
(A) 167 sec
(B) 190 sec
(C) 176 sec
(D) 115 sec
(E) 123 sec
Rationale: Time taken by B run 1000 meters
= (1000 * 10)/80 = 125 sec.
Time taken by A = 125 - 10
= 115 sec.
Answer:D
Answer: (D) 115 sec