mathewhe/aqua_rat huggingface dataset:
Question: A city council plans to renew its fleet of 60 police patrol cars by retiring 4 every month and buying 5 new cars. how many months will it take to replace the entire fleet of police cars?
(A) 15
(B) 16
(C) 10
(D) 18
(E) 13
Rationale: Total fleet--60
End of 1st month -- (retires 4 and buys 5) total fleet--61(56 old 5 new).
End of 2nd month -- (retires 4 and buys 5) total fleet--62(52 old 10 new).
End of 3rd month -- (retires 4 and buys 5) total fleet--63(48 old 15 new).
End of 4th month -- (retires 4 and buys 5) total fleet--64(44 old 20 new).
End of 5th month -- (retires 4 and buys 5) total fleet--65(40 old 25 new).
End of 6th month -- (retires 4 and buys 5) total fleet--66(36 old 30 new).
End of 7th month -- (retires 4 and buys 5) total fleet--67(32 old 35 new).
End of 8th month -- (retires 4 and buys 5) total fleet--68(28 old 40 new).
End of 9th month -- (retires 4 and buys 5) total fleet--69(24 old 45 new).
End of 10th month -- (retires 4 and buys 5) total fleet--70(20 old 50 new).
End of 11th month -- (retires 4 and buys 5) total fleet--71(16 old 55 new).
End of 12th month -- (retires 4 and buys 5) total fleet--72(12 old 60 new).
End of 13th month -- (retires 4 and buys 5) total fleet--73(8 old 65 new).
End of 14th month -- (retires 4 and buys 5) total fleet--74(4 old 70 new).
End of 15th month -- (retires 4 and buys 5) total fleet--75(0 old 75 new).
Answer is A--after 15 months the council has totally replaced its fleet .
Answer: (A) 15
Question: A man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is?
(A) 1 kmph
(B) 7 kmph
(C) 8 kmph
(D) 4 kmph
(E) 3 kmph
Rationale: DS = 6
US = 4
S = ?
S = (6 - 4)/2 = 1 kmph
\Answer:A
Answer: (A) 1 kmph
Question: Two varieties of wheat - A and B costing Rs. 9 per kg and Rs. 15 per kg were mixed in the ratio 3 : 7. If 5 kg of the mixture is sold at 25% profit, find the profit made?
(A) 16.5
(B) 12.5
(C) 14.5
(D) 12
(E) 13
Rationale: et the quantities of A and B mixed be 3x kg and 7x kg.
Cost of 3x kg of A = 9(3x) = Rs. 27x
Cost of 7x kg of B = 15(7x) = Rs. 105x
Cost of 10x kg of the mixture = 27x + 105x = Rs. 132x
Cost of 5 kg of the mixture = 132x/10x (5) = Rs. 66
Profit made in selling 5 kg of the mixture = 25/100 (cost of 5 kg of the mixture) = 25/100 * 66 = Rs. 16.50
ANSWER A
Answer: (A) 16.5
Question: Sonika deposited Rs.8000 which amounted to Rs.9200 after 3 years at simple interest. Had the interest been 2% more. She would get how much?
(A) 9680
(B) 2899
(C) 2893
(D) 2790
(E) 2702
Rationale: (8000*3*2)/100 = 480
9200
--------
9680
Answer: A
Answer: (A) 9680
Question: A train 600 m long can cross an electric pole in 20 sec and then find the speed of the train?
(A) 76 Kmph
(B) 54 Kmph
(C) 62 Kmph
(D) 72 Kmph
(E) 108 Kmph
Rationale: Length = Speed * time
Speed = L/T
S = 600/20
S = 30 M/Sec
Speed= 30*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 108 Kmph
Answer: E
Answer: (E) 108 Kmph
Question: (3 x 10^3) + (2 x 10^2) + (4 x 10) =
(A) 302400
(B) 32400
(C) 30240
(D) 3240
(E) 324
Rationale: When you multiply a number by 10 you just add a zero
=> 3 x 10^3 => add 3 zeros => 3 x 10^3 = 3000
=>2 x 10^2 = 200
=> 4 x 10 = 40
=>3 x 10^3 + 2 x 10^2 + 4 x 10 = 3000 + 200 + 40 = 3240
=> answer is D ( 3240)
Answer: (D) 3240
Question: The flow of water through a drainage pipe was monitored for a 3-hour period. In the second hour, the rate of flow was 30 gallons per hour, which was 50 percent faster than the rate of flow for the first hour. If 25 percent more water flowed through the pipe in the third hour than it did in the second, how many gallons of water flowed through the pipe during the entire three hours?
(A) 81.25
(B) 82.5
(C) 83.75
(D) 85.0
(E) 87.5
Rationale: Rate of flow of water in second hour = 30 gallons per hour
Rate of flow of water in first hour = 30/(3/2) = 20 gallons per hour
Rate of flow of water in third hour = (125/100)* 30 = (5/4) * 30 = 37.5 gallons per hour
Number of gallons of water that flowed through the pipe during the entire 3 hours = 20+30+37.5 = 87.5 gallons
Answer E
Answer: (E) 87.5
Question: John and Karen begin running at opposite ends of a trail until they meet somewhere in between their starting points. They each run at their respective constant rates until John gets a cramp and stops. If Karen runs 50% faster than John, who is only able to cover 25% of the distance r before he stops, what percent longer would Karen have run than she would have had John been able to maintain his constant rate until they met.
(A) 25%
(B) 50%
(C) 75%
(D) 100%
(E) 200%
Rationale: John and Karen begin running at opposite ends of a trail until they meet somewhere in between their starting points. They each run at their respective constant rates until John gets a cramp and stops. If Karen runs 50% faster than John, who is only able to cover 25% of the distance r before he stops, what percent longer would Karen have run than she would have had John been able to maintain his constant rate until they met.
Lets say the distance of the trail is 100 miles. Lets also say that J rate = 10 miles/hour and K rate = 15 miles/hour.
If John stops at the 25% mark that means he travels 25 miles in 2.5 hours. It would take Karen t=d/r t=75/15 = 5 hours to reach john. If John had not stopped, their combined rate would 10+15 = 25 miles/hour meaning they would have met in 4 hours. Therefore, she ran one hour longer (25%) longer than she would have needed to if John ran for the entire time.
ANSWER: A) 25%
Answer: (A) 25%
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) 45
(B) 35
(C) 55
(D) 60
(E) 66
Rationale: Explanation :
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 : Option A
Answer: (A) 45
Question: A coin is tossed live times. What is the probability that there is at the least one tail?
(A) 31/32
(B) 15/11
(C) 14/15
(D) 48/11
(E) 99/18
Rationale: Let P(T) be the probability of getting least one tail when the coin is tossed five times.
= There is not even a single tail.
i.e. all the outcomes are heads.
= 1/32 ; P(T) = 1 - 1/32 = 31/32
Answer: A
Answer: (A) 31/32
Question: If a fair die is rolled four time, what is the probability that a 3 occurs on at least one roll?
(A) 25/36
(B) 125/216
(C) 91/216
(D) 11/36
(E) 248/479
Rationale: Questions such as these that talk about at least or maximum or minimum in probability questions should make sure realize that probability of any event (N) to occur = 1- P(Not N)
Thus, the probability of at least 1 roll = 1- Probability of NO 3s = 1-(5/6) (5/6)(5/6)(5/6) = 1-231/479 = 248/479.
5/6 is the probability of NOT getting a 3 in any 1 roll with 5 allowed numbers (=1,2,4,5,6) out of a total of 6 possibilities.
E is thus the correct answer.
Answer: (E) 248/479
Question: The ages of two persons differ by 28 years. If 5 years ago, the elder one be 5 times as old as the younger one, their present ages (in years) are respectively
(A) 40,12
(B) 20,10
(C) 25,15
(D) 30,10
(E) None of these
Rationale: Explanation:
Let their ages be x and (x + 28) years.
5 (x - 5) = (x + 28 - 5) or 4x = 48 or x = 12.
Their present ages are 40 years and 12 years
Option A
Answer: (A) 40,12
Question: At what time, in minutes, between 3 o'clock and 4 o'clock, both the needles will coincide each other?
(A) 51/11
(B) 12 4/11
(C) 13 4/11
(D) 16 4/11
(E) None
Rationale: Explanation :
At 3 o'clock, the minute hand is 15 min. spaces apart from the hour hand.
To be coincident, it must gain 15 min. spaces.55 min. are gained in 60 min.
15 min. are gained in
= (60/55 x 15)min
=16x4/11
The hands are coincident at 16x4/11 min past 3.
Answer : D
Answer: (D) 16 4/11
Question: Predict the next number
2,20,10,100,50
(A) 200
(B) 300
(C) 400
(D) 500
(E) 600
Rationale: Look upon the series carefully
2,20,10,100,50...
2 * 10 = 20
20/ 2 = 10
10 * 10 = 100
100/2 = 50
similarly
50 * 10 = 500
ANSWER:D
Answer: (D) 500
Question: What will be the percentage increase in the area of the cube's surface if each of the cube's edges grows by 30%?
(A) 70%
(B) 69%
(C) 80%
(D) 82%
(E) 55%
Rationale: The question is very easy. My logic is the following:
A surface = 6*a^2
After 30% increase A surface = 6* ((1.3a)^2) = 6*1.69*a^2
The increase in the surface area = (6*1.69*a^2 - 6*a^2)/6*a^2 = (6*a^2(1.69-1))/(6*a^2) = 1.69-1=0.69 = 69%
Answer : B
Answer: (B) 69%
Question: Two numbers are in respectively 20% and 50% more than a third number. The ratio of the two numbers is?
(A) 2:5
(B) 1:2
(C) 4:5
(D) 3:7
(E) 5:6
Rationale: Let the 3rd number be x
Then, first number = 120% of x = 120x/100 = 6x/5
second number = 150% of x = 150x/100 = 3x/2
Ratio of first two numbers = 6x/5 : 3x/2 = 12x:15x = 4:5
Answer is C
Answer: (C) 4:5
Question: A basket contains 6 blue, 6 red and 6 yellow marbles. If 6 marbles are extracted from the basket at random, what is the probability that a marble of each color is among the extracted?
(A) 2/21
(B) 3/25
(C) 1/6
(D) 9/34
(E) 11/24
Rationale: 18/18*12/17*6/16 = 9/34
the answer is (D)
Answer: (D) 9/34
Question: A is thrice as good a workman as B and takes 10 days less to do a piece of work than B takes. B alone can do the whole work in
(A) 15days
(B) 10days
(C) 9days
(D) 8days
(E) 7days
Rationale: Explanation:
Ratio of times taken by A and B = 1:3
Means B will take 3 times which A will do in 1 time
If difference of time is 2 days, B takes 3 days
If difference of time is 10 days, B takes (3/2) * 10 =15 days
Option A
Answer: (A) 15days
Question: If the figure 5286.142 is rounded off to the nearest thousand, hundred, ten and one and the result is represented using d,e,f,g respectively, which of the following statements would be accurate?
(A) f>e>g>d
(B) e>f>g>d
(C) g>f>e>d
(D) e>d>g>f
(E) e>g>f>d
Rationale: 5286.142..
Nearest thousand 5000..d
Nearest hundred 5300..e
Nearest ten 5290..f
Nearest one 5286..g
e>f>g>d
The correct option is B
Answer: (B) e>f>g>d
Question: The product of two successive numbers is 462. Which is the smaller of the two numbers?
(A) 21
(B) 23
(C) 26
(D) 27
(E) 29
Rationale: A
21
From the given alternatives,
21 × 22 = 462
∴ Smaller number = 21
Answer: (A) 21
Question: A boat can move upstream at 30 kmph and downstream at 15 kmph, then the speed of the current is?
(A) 5
(B) 7.5
(C) 32.5
(D) 9.2
(E) 5.8
Rationale: US = 30
DS = 15
M = (30 - 15)/2 = 7.5
Answer: B
Answer: (B) 7.5
Question: A tank is 25m long 12m wide and 6m deep. The cost of plastering its walls and bottom at 25 paise per sq m is
(A) Rs. 186
(B) Rs. 258
(C) Rs. 486
(D) Rs. 586
(E) None of these
Rationale: Explanation:
Area to be plastered = [2(l + b) Ã— h] + (l Ã— b)
= [2(25 + 12) Ã— 6] + (25 Ã— 12) = 744 sq m
Cost of plastering = 744 Ã— (25/100) = Rs.186 Answer: A
Answer: (A) Rs. 186
Question: If A = {17, 27, 31, 53, 61}, what is the sum of mean and median of the numbers in A?
(A) 69
(B) 75
(C) 82
(D) 91
(E) 56
Rationale: Mean = (17 + 27 +31 + 53 + 62 )/5 = 38
Median = 31
sum = 38+31 = 69
Option A
Answer: (A) 69
Question: A train passes a station platform in 39 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 285 m
(B) 240 m
(C) 277 m
(D) 765 m
(E) 176 m
Rationale: Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/39 = 15 ==> x + 300 = 585 ==> x
= 285 m.
Answer: A
Answer: (A) 285 m
Question: If â€œ*â€ is called â€œ+â€, â€œ/â€ is called â€œ*â€, â€œ-â€ is called â€œ/â€, â€œ+â€ is called â€œ-â€. 80/40 â€“ 10 * 20 + 10 = ?
(A) 185
(B) 160
(C) 170
(D) 145
(E) 225
Rationale: Explanation:
Given : 80/40 â€“ 10 * 20 + 10 = ?
Substituting the coded symbols for mathematical operations, we get,
80 * 40/20 +20 â€“ 10 = ?
80 * 2 + 20 â€“ 10 = ?
160 + 20 â€“ 10 = ?
180 â€“ 10 = 170
ANSWER : C
Answer: (C) 170
Question: If the sum of the interior angles of a regular polygon is 1080 degrees, how many sides does the polygon have?
(A) 4
(B) 3
(C) 6
(D) 8
(E) None of these
Rationale: 8 sides...answer is D
Answer: (D) 8
Question: For all positive integers n and m, the function A(n) equals the following product:
(1 + 1/2 + 1/2^2)(1 + 1/3 + 3^2)(1 + 1/5 + 5^2)…(1 + 1/p_n + 1/p_n^2), where p_n is the nth smallest prime number, while B(m) equals the sum of the reciprocals of all the positive integers from 1 through m, inclusive. The largest reciprocal of an integer in the sum that B(25) represents that is NOT present in the distributed expansion of A(5) is
(A) 1/4
(B) 1/5
(C) 1/6
(D) 1/7
(E) 1/8
Rationale: For all positive integers n and m,
A(n) = (1 + 1/2 + 1/2^2)(1 + 1/3 + 3^2)(1 + 1/5 + 5^2)…(1 + 1/p_n + 1/p_n^2), where p_n is the nth smallest prime number,
note: i think there's a typo in the above function, A(n) could be (1 + 1/2 + 1/2^2)(1 + 1/3 + 1/3^2)(1 + 1/5 + 1/5^2)…(1 + 1/p_n + 1/p_n^2)
B(m) = sum of the reciprocals of all the positive integers from 1 through m, inclusive.
A(5), here 5 represents the 5th smallest prime number; the 5th smallest prime number is 11 {2, 3, 5, 7, 11, ...}
A(5) = (1 + 1/2 + 1/2^2)(1 + 1/3 + 3^2)(1 + 1/5 + 5^2)(1 + 1/7 + 1/7^2)(1 + 1/11 + 11^2)
The distributed expansion of A(5) = 1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/9 + 1/10 + 1/11 + 1/12 + 1/14 + ...
missing numbers are 1/8, 1/13, 1/16, ....
B(25) = (1 + 1/2 + 1/3 + 1/4 + ... + 1/16 + 1/17 + ... + 1/25)
here the largest reciprocal is 1 and the reciprocals are arranged in descending order based on their values
The largest reciprocal that present in B(25) but not in A(5) is 1/8
Answer E
Answer: (E) 1/8
Question: A focus group is currently made up of x men and y women. If 3 men and 7 women are added to the group, and if one person is selected at random from the larger focus group, then what is the probability that a woman is selected?
(A) x/(x + 7)
(B) y/(x + y)
(C) (y + 3)/(x + y + 7)
(D) (y + 7)/(x + y + 10)
(E) (x + 3)/(x + y + 10)
Rationale: x men
y women
x+3+y+7 is the total
=x+y+10
y+7 is the number of men
so (y + 7)/(x + y + 10)
D. (y + 7)/(x + y + 10)
Answer: (D) (y + 7)/(x + y + 10)
Question: How many times in a day, are the hands of a clock in straight line but opposite in direction?
(A) 20
(B) 22
(C) 24
(D) 48
(E) 52
Rationale: The hands of a clock point in opposite directions (in the same straight line) 11 times in every 12 hours. (Because between 5 and 7 they point in opposite directions at 6 o'clcok only).
So, in a day, the hands point in the opposite directions 22 times.
Answer: Option B
Answer: (B) 22
Question: The dimensions of a room are 10m x 7m x 5m. There are 2 doors and 3 windows in the room. The dimensions of the doors are 1m x 3m. One window is of size 2m x 1.5m and the other 2 windows are of size 1m x 1.5m. The cost of painting the walls at Rs. 3 per sq m is?
(A) Rs.229
(B) Rs.429
(C) Rs.129
(D) Rs.474
(E) Rs.111
Rationale: Area of 4 walls = 2(l+b)h
=2(10+7) x 5 = 170 sq m
Area of 2 doors and 3 windows = 2(1x3)+(2x1.5)+2(1x1.5) = 12 sq m
area to be planted = 170 -12 = 158 sq m
Cost of painting = Rs. 158 x 3 = Rs. 474
Answer: D
Answer: (D) Rs.474
Question: I travel 20 miles towards north and then travel 25 miles eastward. I then travel 40 miles rightwards, then travel 30 miles towards left and then travels 12 miles to the left and finally 20 miles northwards. How far am i pproximately from my original destination and in what direction ?
(A) 20 miles towards south
(B) 13 miles towards south-west
(C) 12 miles towards east
(D) 13 miles towards north-east
(E) None of these
Rationale: Explanation:
Using pythagorus rule,
x2=(12)2+(5)2
x=13
ANSWER IS B
Answer: (B) 13 miles towards south-west
Question: A number is 101102103104...150. As 101 102 103 103.... 150. What is reminder when divided by 3?
(A) 2
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: Divisibility rule for 3 also same as 9. so from the above discussion sum of the digits = 380 and remainder = 380/3 = 2.
Answer:A
Answer: (A) 2
Question: A bowl was half full of water. 4 cups of water were then added to the bowl, filling the bowl to 70% of its capacity. How many cups of water are now in the bowl?
(A) 14
(B) 15
(C) 16
(D) 17
(E) 18
Rationale: lets say total volume of the container = V
Initial water content is half of total volume = V/2
Then 4 cups of water were added.
Current water content = (V/2) + 4 cups = (70/100)V
=> V = 20 cups
=> current water content is equivalent to = V/2+ 4 cups = 20/2 + 4 = 14 cups; ANSWER:A
Answer: (A) 14
Question: There are eight boxes of chocolates, each box containing distinct number of chocolates from 1 to 8. In how many ways four of these boxes can be given to four persons (one boxes to each) such that the first person gets more chocolates than each of the three, the second person gets more chocolates than the third as well as the fourth persons and the third person gets more chocolates than fourth person?
(A) 35
(B) 70
(C) 105
(D) 210
(E) None
Rationale: Solution:
All the boxes contain distinct number of chocolates.
For each combination of 4 out of 8 boxes, the box with the greatest number has to be given to the first person, the box with the second highest to the second person and so on.
The number of ways of giving 4 boxes to the 4 person is,
8C4 = 70.
Answer: Option B
Answer: (B) 70
Question: In right triangle ABC, AC is the hypotenuse. If AC is 20 and AB + BC = 50, what is the area of the triangle ABC?
(A) 225
(B) 525
(C) 25√2
(D) 200
(E) 200√2
Rationale: Square AB + BC = 50:
(AB)^2 + 2*AB*BC + (BC)^2 = 2500. Since (AC)^2 = (AB)^2 + (BC)^2 = 20^2 = 400, then (AB)^2 + 2*AB*BC + (BC)^2 = 400 + 2*AB*BC = 2500.
400 + 2*AB*BC = 2500.
AB*BC = 1050.
The area = 1/2*AB*BC = 525.
Answer: B.
Answer: (B) 525
Question: Michael completes a piece of work in 6 days, Madan completes the same work in 18 days. If both of them work together, then the number of days required to complete the work is?
(A) 4.5 days
(B) 8 days
(C) 10 days
(D) 12 days
(E) 14 days
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days.
That is, the required No. of days = 6 × 18/24 = 4.5 days
Answer : A
Answer: (A) 4.5 days
Question: Mysoon collects glass ornaments. Ten more than 1/6 of the ornaments in her collection are handmade, and 1/2 of the handmade ornaments are antiques. If 1/8 of the ornaments in her collection are handmade antiques, how many ornaments are in her collection?
(A) 36
(B) 60
(C) 120
(D) 144
(E) 180
Rationale: The number of ornaments = a
Ten more than 1/6 of the ornaments in her collection are handmade => Handmade = 10+a/6
1/2 of the handmade ornaments are antiques => Handmade ornaments = 1/2*(10+a/6) = 5 + a/12
1/8 of the ornaments in her collection are handmade antiques => Handmade ornaments = a/8
=> 5 + a/12 = a/8 => a = 120
Ans: C
Answer: (C) 120
Question: A and B’s salaries together amount to Rs. 3,000. A spends 95% of his salary and B spends 85% of his. If now their savings are the same, what is B’s salary?
(A) 777
(B) 750
(C) 789
(D) 776
(E) 881
Rationale: (5/100) A = (15/100) B
A = 3B
A + B =3000
4B = 3000 => B = 750
Answer B
Answer: (B) 750
Question: If n divided by 5 has a remainder of 4, what is the remainder when 3 times n is divided by 5?
(A) 1
(B) 4
(C) 3
(D) 2
(E) 0
Rationale: As per question => N=5P+4 for some integer p
hence 3N => 15Q + 12
But again, 12 can be divided by 5 to get remainder 2 for some integer Q
hence D
Answer: (D) 2
Question: How many natural numbers that are less than 10,000 can be formed using the digits 0, 1, 2, 3, 4, 6, 78?
(A) 5000
(B) 4096
(C) 6560
(D) 4095
(E) 8000
Rationale: According to what i have read - it is always better to assume natural numbers beginning from 01 onward (for the gmat) unless otherwise stated. Assuming that to be the case we can sub divide the problem into :
A) Four digit Numbers : _ _ _ _ , The ones place - hundreds place can be filled by any one of the 8 numbers given (the problem speaks nothing about NOT REPEATING the numbers so we have to assume that they can be repeated) the thousands place can be filled by any number except0.. This gives us 7 x 8 x 8 x 8 = 3584
B) Three digit Numbers : _ _ _ , The ones place - tens Place can be filled by any one of the 8 numbers given ( the problem speaks nothing about NOT REPEATING the numbers so we have to assume that they can be repeated) , the hundreds place can be filled by only 7 of the given 8 numbers (If we use0we will end up with a two digit number ). This gives us 7 x 8 x 8 = 448
C) Two digit numbers : _ _ , The ones place can be filled up by any one of the 8 numbers given , and the tens place by any 7 of the 8 ... This gives us 7 x 8 = 56
D) Assuming that zero is not a natural number , we have seven different possibilities for the one digit numbers . 7
Add A + B + C + D , This gives us 3584 + 448 + 56 + 7 = 4095 (D)
Now let us assume that ZERO is a NATURAL number (as some mathematicians do) ... A thru C is not effected by this assumption as the resultant would have meant that a four number digit with a zero at the beginning would have effectively made it a three digit no. , and a 0 to begin a three digit number would make it a two digit number etc ... The only difference including ZERO to be a natural number would have made for D , in that it would have given it 8 possibilities instead of 7 ... Which would have added 1 to our total making it 4096. Simply by looking at the answer choices we can determine that the test maker wanted natural numbers to begin from 1 and not from 0 ( as per the answer choices) ..
Answer: (D) 4095
Question: Efrida and Frazer who live 13 miles apart, meet at a restaurant that is directly north of Efrida's home and directly east of Frazer's home. If the restaurant is two miles closer to Efrida's home, than to Frazer's home, how many miles is the restaurant from Frazer's home?
(A) 6
(B) 7
(C) 8
(D) 10
(E) 11
Rationale: It's a simple geometry problem. Look at the diagram below:
Answer: E.
Answer: (E) 11
Question: which of the following is odd, if r is even and t is odd?
(A) rt
(B) 5rt
(C) 6r + 5t
(D) 5r + 6t
(E) 6(r^2)t
Rationale: Just checking options (In case you have difficulty then choose values of r=2 and t=1)
r = even
t= Odd
A. rt = Even*Odd = EvenINCORRECT
B. 5rt = Odd*Even*Odd = EvenINCORRECT
E. 6(r^2)t = 6*(Even^2)*Odd = EvenINCORRECT
D. 5r + 6t = 5*Even + 6*Odd = Even+Even = EvenINCORRECT
C. 6r + 5t = 6*Even + 5*Odd = Even+Odd = OddCORRECT
Answer: option C
Answer: (C) 6r + 5t
Question: In triangle PQR, the angle Q = 90 degree, PQ = 5 cm, QR = 8 cm. X is a variable point on PQ. The line through X parallel to QR, intersects PR at Y and the line through Y, parallel to PQ, intersects QR at Z. Find the least possible length of XZ
(A) 3.6 cm
(B) 2.4 cm
(C) 4.0 cm
(D) 2.16 cm
(E) 3.2 cm
Rationale: Look at the diagram below:
Now, in case when QY is perpendicular to PR, two right triangles PQR and PQY are similar: QY:QP=QR:PR --> QY:5=8:10 --> QY=4.0.
Answer: C.
Answer: (C) 4.0 cm
Question: A football coach must choose 5 freshers from a team of 12players. How many different ways can the coach choose the freshers?
(A) 652
(B) 634
(C) 729
(D) 850
(E) 870
Rationale: Choose 5 starters from a team of 12 players. Order is not important.
\inline {\color{Black} 12C_{5}}= 729
C
Answer: (C) 729
Question: A salesperson receives a base salary of $1100 per month and a commission of 7.5% of the selling price of each item sold above the first 50 item. If this month she sold 210 items for $150 each, what will her monthly salary be?
(A) $1,500
(B) $1,800
(C) $2,100
(D) $2,500
(E) $2,900
Rationale: Ans : 1100+ 7.5 % * 150 * (210-50) = $ 2900
Answer E
Answer: (E) $2,900
Question: A year ago, the ratio of Betty's and Chi's age was 6:7 respectively. Four years hence, this ratio would become 7:8. How old is Betty?
(A) 34 years
(B) 29 yeras
(C) 25 years
(D) 30 years
(E) 40 years
Rationale: (b-1)/(c-1)=6/7;
(b-1+4)/(c-1+4)=7/8;
by solving them we get
8b-7c=-3
7b-6c=1
then solving these eq we get
c=29
b=25
ANSWER:C
Answer: (C) 25 years