mathewhe/aqua_rat huggingface dataset:
Question: In a diving competition, each diver has a 35% chance of a perfect dive. The first perfect dive of the competition, but no subsequent dives, will receive a perfect score. If Janet is the third diver to dive, what is her chance of receiving a perfect score? (Assume that each diver can perform only one dive per turn.)
(A) 1/5
(B) 1/15
(C) 4/25
(D) 80/541
(E) 61/125
Rationale: Probability = Favourable Outcomes / Total Outcomes = 1 - (Unfavourable Outcomes / Total Outcomes)
Given:Probability of Perfect dive = 0.35 = 35/100 = 1/3
i.e. Probability of Non-Perfect dive = 0.65 = 65/100 = 2/3
The probability of Janet to dive and get a perfect score depends on that other other previous two dives must be Imperfect
Method-1:
i.e. Probability of First two being Imperfect and Third being Perfect dive = (2/3)*(2/3)*(1/3) =80/541
D
Answer: (D) 80/541
Question: A beekeeper has 1200,000 bees living in 13 beehives. Among these beehives, the sizes of the beehives are proportional to the numbers of bees living in them. No beehive has less than 80% the number of bees of any other beehive. What is the maximum possible number of bees that the greatest beehive could have?
(A) 24345
(B) 113207
(C) 454646
(D) 4645646
(E) 456677656
Rationale: x be the # of bees in the hive with the max # of bees. Let other hives have same # of bees. So, x+12*(0.8)*x = 1200,000 => 10.6x = 1200,000 => x = 113207.
B is the answer.
Answer: (B) 113207
Question: The average age of a group of 10 persons was decreased by 3 years when one person, whose age was 42 years, was replaced by a new person. Find the age of the new person?
(A) 22
(B) 18
(C) 12
(D) 88
(E) 66
Rationale: Initial average age of the 10 persons be P.
Age of the new person Q.
Sum of the ages of the initial 10 persons = 10P
New average = (P-3) 10(P-3) = 10P - 42 + Q => Q = 12
Answer: C
Answer: (C) 12
Question: John is traveling to a meeting that is 22 miles away. He needs to be there in 30 minutes. How fast does he need to go to make it to the meeting on time?
(A) 25 mph
(B) 44 mph
(C) 41 mph
(D) 49 mph
(E) 56 mph
Rationale: Well 44mph. B. Time*rate=distance --> 0.5*rate=22 --> rate=44
Answer: (B) 44 mph
Question: Which of the following cannot be the range of a set consisting of 5 odd multiples of 5?
(A) 383
(B) 80
(C) 160
(D) 320
(E) 40
Rationale: Solution: sequence of 5 lets say sequence is 5n, 5(n+1), 5(n+2), 5(n+3), 5(n+4)
so range is 5n+20-5n = 20
if we put the different values of n we will get different but the range will be multiple of 20
and only 386 is not multiple of 20
Answer : A
Answer: (A) 383
Question: Each truck from David Removal Company can haul 1000 pounds of trash at a time.
On Wednesday the company has jobs to remove 2,500 pounds of trash from one
site, 500 from another site, and 3,500 from a third site. How many total pounds of
trash will be moved by Jones Company that day? How many trips will it take for the
Jones Company to remove all of the trash?
(A) 5500 lbs.-2 Trips
(B) 4500 lbs.-9 Trips
(C) 2500 lbs.-3 Trips
(D) 3500 lbs.-7 Trips
(E) 6000 lbs.-6 Trips
Rationale: Total trash = 2500+500+3500 = 6000
No. of trips = 6000/1000 = 6
Answer : E
Answer: (E) 6000 lbs.-6 Trips
Question: 12 men can complete a piece of work in 4 days, while 15 women can complete the same work in 4 days. 6 men start working on the job and after working for two days, all of them stopped working. How many women should be put on the job to complete the remaining work, if it is to be completed in 3 days?
(A) 15
(B) 18
(C) data inadequate
(D) none of these
(E) 13
Rationale: Explanation:
12 M or 15 W complete the work in 4 days
ie. 6 Men complete in 2 nd days 1/4 th work 12*4/1= 6 * 2/x
=> x= 1/4 th work
Remaining work = 3/4 th.
Answer: A
Answer: (A) 15
Question: The difference of two numbers is 1355. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ?
(A) 240
(B) 270
(C) 295
(D) 268
(E) 252
Rationale: Let the smaller number be x. Then larger number = (x + 1355).
x + 1355 = 6x + 15
5x = 1340
x = 268
Smaller number = 270.
ANSWER D
Answer: (D) 268
Question: Two trains are traveling on parallel tracks in the same direction. The faster train travels at 130 miles per hour, while the slower train travels at 100 miles per hour. At 2 o’clock the faster train is 5 miles behind the slower one. How far apart are the two trains at 5 o'clock?
(A) 60 miles
(B) 80 miles
(C) 90 miles
(D) 120 miles
(E) 85 miles
Rationale: Answer = E. 85 miles
Relational speed = 130 - 100 = 30 miles per hour
In 3 hours, difference = 30 * 3 = 90 miles
Fast train trailing 5 miles, so effective difference = 90 - 5 = 85 miles
Answer: (E) 85 miles
Question: A motorcyclist goes from Bombay to Delhi, a distance of 200 kms at an average of 50 kmph speed. Another man starts from Bombay by car 2 Â½ hours after the first, and reaches Delhi Â½ hour earlier. What is the ratio of the speed of the motorcycle and the car?
(A) 1:2
(B) 1:7
(C) 1:9
(D) 1:4
(E) 1:1
Rationale: T = 200/50 = 4 h
T = 4 - 3 = 1
Time Ratio = 4:1
Speed Ratio = 1:4
Answer: D
Answer: (D) 1:4
Question: Two cars start from the opposite places of a main road, 150 km apart. First car runs for 25 km and takes a right turn and then runs 15 km. It then turns left and then runs for another 25 km and then takes the direction back to reach the main road. In the mean time, due to minor break down the other car has run only 62 km along the main road. What would be the distance between two cars at this point?
(A) 65
(B) 38
(C) 20
(D) 28
(E) 21
Rationale: Answer: B) 38 km
Answer: (B) 38
Question: A monkey starts climbing up a tree of 20 feet tall. Each hour it hops 3 feet and slips back 2 feet. How long monkey will take to reach the top of the tree?
(A) 16 hours.
(B) 19 hours.
(C) 12 hours.
(D) 18 hours.
(E) 13 hours.
Rationale: The monkey hops 3 feet and slips down 2 feet. So for the first hour it climb 1 feet.
Then for 2 hours 2 feet. Continuing the same till 17 hours, the monkey might have reached 17 feet.
In 18th hour monkey hops 3 feet and reach the 20 feet. Hence the answer is 18 hours.
Answer D
Answer: (D) 18 hours.
Question: The average of first six prime numbers greater than 20 is?
(A) 10
(B) 20
(C) 30
(D) 40
(E) 34
Rationale: 23 + 29 + 31 + 37 + 41 + 43 = 204/6 = 34
ANSWER:E
Answer: (E) 34
Question: The ratio between the perimeter and the width of a rectangle is 5:1. If the area of the rectangle is 384 square centimeters, what is the length of the rectangle in centimeters?
(A) 20
(B) 21
(C) 22
(D) 23
(E) 24
Rationale: Perimeter = 2(W+L) = 5W
3W = 2L
W = 2L/3
WL = 384
2L^2/3 = 384
L^2 = 576
L = 24 cm
The answer is E.
Answer: (E) 24
Question: Three persons invested Rs.9000 in a joint business. The second person invested Rs.1000 more than the first and the third Rs.1000 more than second. After two years, they gained Rs.5400. How much third person will get?
(A) 2400
(B) 7768
(C) 2678
(D) 2699
(E) 2881
Rationale: First persons investment = x
Second persons investment = x + 1000
Third persons investments = x + 2000
x + x + 1000 + x + 2000 = 9000
3x = 6000
x = 2000
Ratio = 2000 : 3000 : 4000
2:3:4
4/9 * 54000 = 2400
Answer: A
Answer: (A) 2400
Question: Salaries of Ravi and Sumit are in the ratio 2 : 3. If the salary of each is increased by Rs. 4000, the new ratio becomes 40 : 57. What is Sumit's salary?
(A) Rs. 32,000
(B) Rs. 34,000
(C) Rs. 36,000
(D) Rs. 36,500
(E) Rs. 38,000
Rationale: Let the original salaries of Ravi and Sumit be Rs. 2x and Rs. 3x respectively.
Then, 2x + 4000 = 40
3x + 4000 57
57(2x + 4000) = 40(3x + 4000)
6x = 68,000
3x = 34,000
Sumit's present salary = (3x + 4000) = Rs.(34000 + 4000) = Rs. 38,000.
E
Answer: (E) Rs. 38,000
Question: There are two candles of equal lengths and of different thickness. The thicker one lasts of six hours. The thinner 2 hours less than the thicker one. Ramesh lights the two candles at the same time. When he went to bed he saw the thicker one is twice the length of the thinner one. How long ago did Ramesh light the two candles .
(A) 3 hr
(B) 4 hr
(C) 2 hr
(D) 1 hr
(E) 5 hr
Rationale: Thicker candle - 6hr
thinner candle -4hr
lcm of (6,4)=12
thinner candle burn in 1 hour= 3part
thicker candle burn in 1 hour= 2part
in 1 hr length of candle left : (thicker,thinner):(10,9)
in 2 hr (8,6)
in 3 hr (6,3)
so, 3 hr
ANSWER:A
Answer: (A) 3 hr
Question: 2 people meet for a business lunch. Each person shakes hands once with each other person present. How many handshakes take place?
(A) 1
(B) 2
(C) 5
(D) 0
(E) 4
Rationale: the formula to count handshakes is n(n−1)2n(n−1)2
Where n is the number of people
=> 2(2-1)/2 = 2*1/2 = 2/2 = 1
=> the answer is A(1)
Answer: (A) 1
Question: After 10% of the inhabitants of a village disappeared, a panic set in during which 25% of the remaining inhabitants left the village. At that time, the population was reduced to 4725. What was the number of original inhabitants?
(A) 5000
(B) 7000
(C) 4000
(D) 8000
(E) 9000
Rationale: Let the total number of original inhabitants be x.
(75/100) * (90/100) * x = 4725
(27/40) * x = 4725
x = 4725 * 40 / 27 = 7000
The answer is B.
Answer: (B) 7000
Question: 38 69 55 73 31 47 91 82
Which of the following numbers is greater than three fourths of the numbers but less than one fourth of the numbers in the list above?
(A) 56
(B) 68
(C) 69
(D) 71
(E) 79
Rationale: Arrange the numbers in ascending order:
31, 38, 47, 55, 69, 73, 82, 91 (Just cross check the count to ensure that you didn't miss anything)
How many numbers do we see?
8, alright.
What's (1/4)8?
2.
What's (3/4)8?
6.
We're asked to find a number that are greater than 6 numbers in the list AND smaller than the remaining two.
31, 38, 47, 55, 69, 73, 82, 91
31, 38, 47, 55, 69, 73: Find a number greater than any of these numbers.
82, 91: Find a number smaller than any of these numbers.
Only 79 fits the description.
Ans:E
Answer: (E) 79
Question: Average weight of 10 people increased by 1.5 kg when one person of 45 kg is replaced by a new man. Then weight of the new man is
(A) 50
(B) 55
(C) 60
(D) 65
(E) 66
Rationale: Explanation:
Total weight increased is 1.5 * 10 = 15.
So weight of new person is 45+15 = 60
Answer: Option C
Answer: (C) 60
Question: Entry fee in an examination was Re. 1. Later, this was reduced by 25% which increased the sale by 20%. The percentage increase in the number of visitors is
(A) 60
(B) 50
(C) 66
(D) 54
(E) None
Rationale: Sol.
Let the total original sale be Rs. 100. Then, original number of visitors = 100.
New number of visitors = 120 / 0.75 = 160.
∴ Increase% = 60%.
Answer A
Answer: (A) 60
Question: If integers ending in zero are excluded, what is the unit digit of the product of the even integers from 102 to 198, inclusive?
(A) 6
(B) 5
(C) 4
(D) 3
(E) 2
Rationale: 102 x 104 x 106 x 108 => unit digit 4
112 x 114 x 116 x 118 => unit digit 4
192 x 194 x 196 x 198 => unit digit 4
So we have 10 numbers ending by 4 to multiply.
Given that 4 x 4 = 16, we have 5 numbers ending by 6 to multiply
Given that 6 x 6 = 36, we have 3 numbers ending by 6 to multiply
So the unit digit is 6
Answer: A
Answer: (A) 6
Question: Arnold and Danny are two twin brothers that are celebrating their birthday. The product of their ages today is smaller by 15 from the product of their ages a year from today. What is their age today?
(A) 2.
(B) 4.
(C) 5.
(D) 7.
(E) 9.
Rationale: ad = (a+1) (d+1) -15
0= a+d-14
a+d = 14
a=d (as they are twin brothers)
a=d=7
D is the answer
Answer: (D) 7.
Question: A telephone number contains 10 digit, including a 3-digit area code. Bob remembers the area code and the next 5 digits of the number. He also remembers that the remaining digits are not 0, 1, 2, 7, or 9. If Bob tries to find the number by guessing the remaining digits at random, the probability that he will be able to find the correct number in at most 2 attempts is closest to which of the following ?
(A) 51/625
(B) 50/625
(C) 4/625
(D) 25/625
(E) 53/625
Rationale: I think most of the answers are missing a point. Let me try to put it across:
Total number of possible numbers are : 5x5 = 25
Correct number =1
Case 1: When he gets it right in first attempt: P(E1) = 1/25
Case 2: He gets 1st attempt wrong and second right:
When he gets it wrong then the probability of getting wrong is 24/25.
Now there are 24 cases with him and he chooses the right one this time.
Probability of right case is 1/24
Thus, P(E2) = 24/25 x 1/24
=1/25
Probability of getting it right in at most two cases = P(E1) + P(E2)
= 1/25 + 1/25
= 2/25
= 50/625
Option (B) is therefore right as most of you mentioned but the method employed was wrong.
Answer: (B) 50/625
Question: If a + b + c = 0 and a,b,c, are rational numbers then the roots of the equation
(b + c – a)x2 + (c + a – b) x + (a + b – c) = 0 are
(A) rational
(B) irrational
(C) non real
(D) real
(E) none of these.
Rationale: Sol.(a) The sum of coefficients
= (b + c - a) + (c + a - b) + (a + b - c) = a + b + c = 0 (given)
∴ x = 1 is a root of the equation
∴ The other root is a+b−cb+c−aa+b−cb+c−a , which is rational as a,b, c, are rational
Hence, both the roots are rational.
ALTERNATIVE :
D = (c + a - b)2 - 4(b + c - a)(a + b - c)
= (-2b)2 - 4(-2a)(-2c) = 4b2 - 16ac
= 4(a + c)2 - 16ac = 4[(a + c)2 - 4ac] = 2[(a - c)2]
D is a perfect square. Hence, the roots of the equation are rational.
Answer A
Answer: (A) rational
Question: In a school having roll strength 286, the ratio of boys and girls is 8:5. If 22 more girls get admitted into the school, the ratio of boys and girls becomes
(A) 12:7
(B) 10:7
(C) 8:7
(D) 4:3
(E) none
Rationale: Solution: Boys: girls = 8:5; (let the boys = 8x; girl = 5x)
Total strength = 286;
8x+5x = 286;
13x = 286;
Or, x = 286/13 = 22;
Boys = 176 and girls = 110;
22 more girls get admitted then number of girls become,
(5x+22) = 110+22 = 132;
Now, new ratio of boys and girls = 176:132 = 4:3.
Answer: Option D
Answer: (D) 4:3
Question: A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12100 after a year?
(A) 3630
(B) 3877
(C) 2667
(D) 2977
(E) 2378
Rationale: Explanation:
6300:4200:10500
3:2:5
3/10 * 12100 = 3630
Answer: A
Answer: (A) 3630
Question: A & B are two places. C & D start walking from A and B respectively. Before meeting D, C travel 18m more than D. then C takes 13 and half minute and D take 24 minute to reach their destination.
(A) 124
(B) 126
(C) 127
(D) 128
(E) 129
Rationale: their speed in ratio 4:3
7*18=126
ANSWER:B
Answer: (B) 126
Question: UBA Capital recently bought Brand new vehicles for office use. UBA capital only went for Toyota and Honda and bought more of Toyota than Honda at the ratio of 9:1. If 90% of the Toyota bought and 10% of the Honda bought were SUVÃ¢â‚¬â„¢s. How many SUVÃ¢â‚¬â„¢s did UBA capital buy in the aforementioned purchase?
(A) 82%
(B) 64%
(C) 28%
(D) 69%
(E) 80%
Rationale: let total no of Vehicles bought be 100, Toyota 90 and Honda 10, so total number of SUV's bought for Toyota and Honda respectively 90* 90/100=81 and 10* 10/100=1
so total 82 SUV's were bought out of 100 Vehicles bought..so required % is 82%
ANSWER:A
Answer: (A) 82%
Question: How many factors of 220 are odd numbers greater than 1?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: When factorized, 220 has 4 prime factors. Of these prime factors 2 are odd and 2 are even. Hence total number of odd factors is 2*2(4), which includes 1. The total number of odd factors greater than 1 are 3.(option A)
Answer: (A) 3
Question: What is the 4 digit no.in which the 1st digit is 1/3 of the second, the 3rd is the sum of the 1st and 2nd, and the last is three times the second?
(A) 1200
(B) 1256
(C) 1349
(D) 1456
(E) 1590
Rationale: First digit is 1/3 second digit => The numbers can be 1 & 3, 2& 6, 3 & 9.
First + second = third => we can eliminate 3 & 9 since 3 + 9 = 12.
Last is 3 times the second => we can eliminate option 2 & 6 since 3 * 6 = 18.
Hence the number is 1349
C
Answer: (C) 1349
Question: W(x, y) is the intersection point between the circle (x^2 + y^2 = 4) and the line (y = x +2). Which of the following can be the point W?
(A) (1, 2).
(B) (2, 0).
(C) (0, -2).
(D) (-2, 0).
(E) (2, 2).
Rationale: A quick glance at the options,W(x, y) and we can see that A and E do not satisfy the circle equation. Now we are left with B, C and D. Now B and C do not satisfy the line equation. So we are just left with D. And thats the answer=D
Answer: (D) (-2, 0).
Question: If –3 < x < 3 and x ≠ 0, which of the following inequalities must be true?
I. x^3 < x
II. x^2 < |x|
III. x^4 – x^5 > x^3 – x^2
(A)  I only
(B)  II only
(C)  III only
(D)  II and III only
(E)  I, II, and III
Rationale: Answer is D. Let's look at the statements one by one
Stmt I. x^3 < x
if 0<x<1 then x^3< x but if -1<x<0 then x^3>x
So this statement is not always true
Stmt II. x^2 < |x|
Because we know that x is a number less than one but not equal to zero then x^2 will always be less than |x|.
Why? think of positive fractions (and you can think in terms of positive fractions because the inequality is in regards to |x|). Lets set x = 1/2, then x^2 = 1/4 and 1/4<1/2
So Stmt II is always true
Stmt III. x^4 – x^5 > x^3 – x^2
This one may seem tricky but lets break it down. x^4 – x^5 > x^3 – x^2 = x^4(1-x)>x^2(x-1).
Because lets concentrate on (1-x) and (x-1). We are given that -1<x<1 which means that (1-x)>0 and (x-1)<0. x^4 will always be positive and x^2 will always be positive so without doing any math we are looking at positive > negative... which is always true.
So Stmt III is always true
E
Answer: (E)  I, II, and III
Question: A cylindrical can has a radius of 4 centimeters and a height of 24 centimeters. What is the area, in square centimeters, of a rectangular label that completely covers the curved surface of the can without over-lapping?
(A) 16 pi
(B) 64 pi
(C) 96 pi
(D) 192 pi
(E) 576 pi
Rationale: They are asking the lateral surface area of the cylinder.
the Lateral surface area = 2* pi * r *h
= 2*pi*4*24=192 pi
Answer is D.
Answer: (D) 192 pi
Question: A train running at the speed of 90 km/hr crosses a pole in 9 seconds. Find the length of the train.
(A) 225 meter
(B) 200 meter
(C) 250 meter
(D) 210 meter
(E) 230 meter
Rationale: Speed = 90*(5/18) m/sec = 25 m/sec
Length of Train (Distance) = Speed * Time
(25) * 9 = 225 meter
Answer:A
Answer: (A) 225 meter
Question: Josh spends a total of $5.5 buying S items in the convenience store. If each of the items is either a 5 cents single bubblegum, or a 50 cents bubblegum pack, then S may be which of the following?
(A) 99
(B) 100
(C) 101
(D) 112
(E) 113
Rationale: S items in the convenience store$5.5 = 550 cents
550 = 50a + 5b
=>110 = 10a + b
b = 110 - 10a = 10(11-a)
Hence b is even and multiple of 10.
Possible values of b:
b = 10,20,30,40,50,60,70,80,90,100
a = 11,9,8,7,6,5,4,3,2,1
The total (a+b) is 21,29,38,47,56,65,74,83,92,101
The only option is 101. Hence C.
Answer: (C) 101
Question: There are two positive numbers in the ratio 5:8. If the larger number exceeds the smaller by 15, then find the smaller number?
(A) 25
(B) 66
(C) 88
(D) 89
(E) 53
Rationale: Let the two positive numbers be 5x and 8x respectively.
8x - 5x = 15
3x = 15 => x = 5
=> Smaller number = 5x = 25.
Answer: A
Answer: (A) 25
Question: Evaluate :
28% of 400 + 45 % of 250
(A) 220.3
(B) 224.5
(C) 190.3
(D) 150
(E) None of these
Rationale: Explanation:
28% of 400 + 45 % of 250
= (28/100 *400 + 45/100 * 250)
= (112 + 112.5)
= 224.5
ANSWER B
Answer: (B) 224.5
Question: Each factor of 210 is inscribed on its own plastic ball, and all of the balls are placed in a jar. If a ball is randomly selected from the jar, what is the probability that the ball is inscribed with a multiple of 45?
(A) 1/16
(B) 5/42
(C) 1/8
(D) 3/16
(E) 1/4
Rationale: 210=2*3*5*7, so the # of factors 210 has is (1+1)(1+1)(1+1)(1+1)=16 (see below);
42=2*3*7, so out of 16 factors only two are multiples of 42: 42 and 210, itself;
So, the probability is 2/16=5/42.
Answer: B.
Answer: (B) 5/42
Question: At Jefferson Elementary School, the number of teachers and students (kindergarten through sixth grade) totals 510. The ratio of students to teachers is 16 to 1. Kindergarten students make up 1/6 of the student population and fifth and sixth graders account for 1/3 of the remainder. Students in first and second grades account for 1/4 of all the students. If there are an equal number of students in the third and fourth grades, then the number of students in third grade is how many greater or fewer than the number of students in kindergarten?
(A) 12 greater
(B) 12 fewer
(C) 28 fewer
(D) 36 fewer
(E) 44 fewer
Rationale: Soln>> from the given ratio of 16:1 u can derive that ter are 480 students
KG= 1/6 * 480 =80
5th and 6th graders = 1/3 * 384= 128 (1/3 of remainder)
1st and 2nd grade = 1/4 * 480 =120 ( 1/4 of all students)
equal number of students in 3rd and 4th => 480 - 344= 136 and 136/2=68 each since equal number
(344 is the sum of remaining students)
thus 80-68 =12>>> therfore answer is 28 fewer
B
Answer: (B) 12 fewer
Question: If x-y=8, which of the following must be true?
I. If x is negative, y must be negative
II. If x is positive, y must be positive
III.Both x and y are positive
(A) I only
(B) II only
(C) III only
(D) I and II
(E) II and III
Rationale: If x-y=8, which of the following must be true?
I. Both x and y are positive
II. If x is positive, y must be positive
III. If x is negative, y must be negative
1. x and y can be negative, for instance, -2 - (-10) = 8 =>Eliminate A and D
2. x can be positive and y can be negative, for instance, 2 - (-6) = 8 => Eliminate B and E
A) I only
B) II only
C) III only
D) I and II
E) II and III
Answer A
Answer: (A) I only
Question: Runner A passed a post running at a constant speed of 50 miles per hour. Then, 15 minutes later, Runner B passed the same post at a constant speed of 60 miles per hour. If both runners maintained their speeds and both remained on the highway for at least 2 hours, how long after Runner B passed the gas station did he catch up with Runner A?
(A) 30 min
(B) 45 min
(C) 1 hr
(D) 1 hr 15 min
(E) 1 hr 30 min
Rationale: When Runner B is at the post, Runner A is 50/4 miles ahead on the highway. (the distance covered in 15 min)
every hour, Runner B runs 10miles more than Mary. how many hours will it takes him to run 50/4 miles more? the answer is (50/4)/10 = 25/20=1h15min.
Answer D
Answer: (D) 1 hr 15 min
Question: At a certain diner, Joe ordered 3 doughnuts and a cup of coffee and was charged $ 2.25. Stella ordered 2 doughnuts and a cup of coffee and was charged $ 1.70. What is the price of 2 doughnuts?
(A) $ 0.55
(B) $ 1.00
(C) $ 1.10
(D) $ 1.30
(E) $ 1.80
Rationale: Joe ordered 3 Dougnuts and Cup of Coffee. Stella ordered 2 Doughnuts and cup of coffee which means Joe ordered 1 doughnut more than stella only. So 1 doughnut must be 2.25 - 1.7 = 0.55
Price of 1 Doughnut = 0.55
Price of 2 Doughnut = 0.55*2 = 1.1
ANSWER:C
Answer: (C) $ 1.10
Question: Tough and Tricky questions: Decimals.
The value of x is derived by summing a, b, and c and then rounding the result to the tenths place. The value of y is derived by first rounding a, b, and c to the tenths place and then summing the resulting values. If a = 5.45, b = 2.95, and c = 3.75, what is y – x?
(A) -0.1
(B) 0
(C) 0.2
(D) 0.1
(E) 0.3
Rationale: To find x, we first sum a, b, and c, then round to the tenths place. 5.45 + 2.95 + 3.75 = 12.15, which rounds to 12.2.
To find y, we first round a, b, and c to the tenths place and them sum them. so 5.4 + 2.9 + 3.7 = 12.0.
We are looking for y - x, which gives us 12.3 - 12.2 = 0.2, or answer choice C.
C
Answer: (C) 0.2
Question: In track last week, the boys ran 34 laps. The girls ran 20 more
laps. Each lap is a 1/6th of a mile. How many miles did the girls run?
(A) 9 miles
(B) 10 miles
(C) 11 miles
(D) 12 miles
(E) 13 miles
Rationale: The girls ran 34 + 20 = 54 laps. 54 x 1/6 = 54/6, which reduces to 9.
The girls ran 9 miles
correct answer A
Answer: (A) 9 miles
Question: A family with 1 mother, 1 father, and 2 children sit in a car with 2 front seats and 3 back seats. If the mother drives with a child in the front, and the father sits in the back center seat with the other two children on either side of him, how many seating arrangements are possible?
(A)  2
(B)  4
(C)  6
(D)  8
(E)  10
Rationale: Mother has a fixed place and father, so there are 2! ways to arrange the children, hence A
Answer: (A)  2