mathewhe/aqua_rat huggingface dataset:
Question: In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together?
(A) 109620
(B) 106920
(C) 109260
(D) 102960
(E) 120960
Rationale: In the word 'MATHEMATICS', we treat the vowels AEAI as one letter.
Thus, we have MTHMTCS (AEAI).
Now, we have to arrange 8 letters, out of which M occurs twice, T occurs twice and the rest are different.
Number of ways of arranging these letters = 8!/(2!)(2!)= 10080.
Now, AEAI has 4 letters in which A occurs 2 times and the rest are different.
Number of ways of arranging these letters =4!/2!	= 12.
Therefore, Required number of words = (10080 x 12) = 120960.
Answer is E.
Answer: (E) 120960
Question: The probability of a lottery ticket being a prized ticket is 0.2. When 4 tickets are purchased, the probability of winning a prize on atleast one ticket is
(A) 0.8904
(B) 0.5904
(C) 0.5909
(D) 0.8904
(E) 0.5984
Rationale: Explanation:
P(winning prize atleast on one ticket)
= 1 - P("Losing on all tickets")
= 1 - (0.8)4 = (1 + (0.8)2)(1 - (0.8)2)
= (1.64)(0.36) = 0.5904
Answer: Option B
Answer: (B) 0.5904
Question: In a certain code '13' means 'stop smoking' and '59' means 'injurious habit'. What is the meaning of '9' and '5' respectively in that code ?
I. '157' means 'stop bad habit'.
II. '839' means 'smoking is injurious'.
(A) If the data in statement I alone are sufficient to answer the question
(B) If the data in statement II alone are sufficient answer the question
(C) If the data either in I or II alone are sufficient to answer the question;
(D) If the data even in both the statements together are not sufficient to answer the question
(E) If the data even ether are not sufficient to answer the question
Rationale: Explanation:
'59' means Injurious habit' and '157' means 'stop bad habit' (from I). Thus, the common code number '5' stands for common word 'habit'. So. '9' represents 'injurious'.Hence, I is sufficient.
Also, '59' means Injurious habit' and '839' means 'smoking is injurious'. Thus, the common code number '9' stands for common word 'injurious'. So, '5' represents 'habit'. Thus, II is also sufficient.
Answer: C
Answer: (C) If the data either in I or II alone are sufficient to answer the question;
Question: How many numbers between 100 and 672 are divisible by 2, 3, and 7 together?
(A) 112
(B) 77
(C) 267
(D) 14
(E) 99
Rationale: Explanation:
As the division is by 2, 3, 7 together, the numbers are to be divisible by: 2*3*7 = 42
The limits are 100 and 672
The first number divisible is 42*3 = 126
To find out the last number divisible by 42 within 672:
672/42 = 14
Hence, 42*16 = 672 is the last number divisible by 42 within 672
Hence, total numbers divisible by 2, 3, 7 together are (16 â€“ 2) = 14
ANSWER: D
Answer: (D) 14
Question: Two trains of length 120 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet?
(A) 28
(B) 266
(C) 990
(D) 20
(E) 11
Rationale: Relative speed = (42 + 30) * 5/18 = 4 * 5 = 20 mps.
Distance covered in passing each other = 120 + 280 = 400 m.
The time required = d/s = 400/20 = 20 sec.
Answer: D
Answer: (D) 20
Question: From the word 'JAMIE', how many independent words can be made with-out changing the order of the letters and using each letter only once ?
(A) 5
(B) 8
(C) 3
(D) 2
(E) 1
Rationale: Explanation:
The words formed are
JAM
Answer: E) 1
Answer: (E) 1
Question: 15 51 216 1100 ? 46452
(A) 6630
(B) 6650
(C) 6560
(D) 6530
(E) None of these
Rationale: The format of the series
15*3+6=51
51*4+12=216
216*5+20=1100
1100*6+30=6630
6630*7+42=46452
ANSWER:A
Answer: (A) 6630
Question: The total number of even prime number is
(A) 0
(B) 1
(C) 2
(D) 3
(E) None of these
Rationale: Solution
There is only one prime number, namely 2.
Answer C
Answer: (C) 2
Question: Irin, Ingrid and Nell bake chocolate chip cookies in the ratio of 9.18: 5.17: 2.05. If altogether they baked a batch of 148 cookies, what percent of the cookies did Irin bake?
(A) 0.125%
(B) 1.25%
(C) 12.5%
(D) 56%
(E) 0.152%
Rationale: 9.18x+5.17x+2.05x = 16.4x = 148 cookies
x= 148/16.4 = 9 (approx)
So, irin baked 9*9.18 cookies or 83 cookies (approx)
% share = 83/148 = 56.1 approx
Hence, answer is D
Answer: (D) 56%
Question: What will be the compound interest on a sum of Rs. 24,500 after 3 years at the rate of 12% p.a.?
(A) s.9920.736
(B) s.10823.20
(C) s.10123.20
(D) s.10123.29
(E) s.10123.28
Rationale: Explanation:
Amount = [24500 * (1 + 12/100)3]
= 24500 * 28/25 * 28/25 * 28/25 = Rs. 35123.20
C.I. = (34420.74 - 24500) = Rs. 9920.736
Answer:A
Answer: (A) s.9920.736
Question: In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?
(A) 120
(B) 720
(C) 4320
(D) 2160
(E) None
Rationale: The word 'OPTICAL' contains 7 different letters.
When the vowels OIA are always together, they can be supposed to form one letter.
Then, we have to arrange the letters PTCL (OIA).
Now, 5 letters can be arranged in 5! = 120 ways.
The vowels (OIA) can be arranged among themselves in 3! = 6 ways.
Required number of ways = (120 x 6) = 720.
Option B
Answer: (B) 720
Question: The G.C.D. of 1.08, 0.36 and 0.15 is?
(A) 0.03
(B) 0.9
(C) 0.03
(D) 0.108
(E) none of these
Rationale: Given numbers are 1.08,0.36 and 0.15.
H.C.F of 108, 36 and 15 is 3
H.C.F of given numbers=0.03.
Correct Options:C
Answer: (C) 0.03
Question: If a population of women in a town is 30% of men . What is the population of men as a % of population of women ?
(A) A)333%
(B) B)100%
(C) C)50%
(D) D)65%
(E) E)110%
Rationale: We're told that the number of Women in a town is equal to 50% of the number of Men in that town.
IF....
Men = 10
Women = 3
We're asked for the number of Men, as a percentage of the number of Women.
M/W = 10/3 = 333%
Answer is A
Answer: (A) A)333%
Question: Which of the following is equal to 10^-(-3)^1?
(A) 1/(10^5)
(B) 1/(10^6)
(C) 1/(10^3)
(D) 1/(10^8)
(E) 1/(10^9)
Rationale: 10^-(-3)^1 => 10^-(-3^1) => 10^-(3) = 1/(10^3)
Answer : C
Answer: (C) 1/(10^3)
Question: There are 12 red balls, 10 blue balls, 14 green balls and 9 black balls in a bag. What is the minimum number of balls to be taken out of the bag to assure that you have all the balls of one color?
(A) 10
(B) 23
(C) 42
(D) 40
(E) 16
Rationale: The worst case scenario would be if we pick 11 red balls, 9 blue balls, 13 (?) balls and 8 black balls. In this case we'll have 11+9+13+8=41 balls and still won't have all the balls of one color. The next 42rd ball we pick, no matter which color it'll be, will guarantee that we have all the balls of one color.
Answer: C.
Answer: (C) 42
Question: A work can be completed by 12 boys in 24 days and 12 girls in 12 days. In how many days would the 6 boys and 6 girls working together complete the work?
(A) 12
(B) 18
(C) 16
(D) 20
(E) 24
Rationale: In 1 day, 12 boys does 1/24 of the total work.
=> In 1 day, 1 boy does 1/(24*12) of the total work
=> In 1 days, 6 boys do 6/(24*12) = 1/48 of the total work
In 1 day, 12 girls do 1/12 of the total work.
=> In 1 day, 1 girl does 1/(12*12) of the total work
=> In 1 day, 6 girls do 6/(12*12) = 1/24 of the total work
In 1 day, 6 boys and 6 girls do 1/48 + 1/24 of the total work
=> In 1 days, 6 boys and 6 girls do 3/48= 1/16 of the total work
So, 6 boys and 6 girls complete all work in 16 days.
Hence, the answer is C
Answer: (C) 16
Question: Find the greatest number of five digits to which if 7143 is added, the final number becomes exactly divisible by 18, 24, 30, 32 and 36.
(A) 22391
(B) 81111
(C) 27999
(D) 27711
(E) 99417
Rationale: LCM of 18, 24, 30, 32 and 36 is 1440. 99999 + 7143 = 107142. Dividing 107142 by 1440, the remainder is 582. ∴ Required number = 99999 – 582 = 99417 Alternate Method: Cross check with options.
Answer:E
Answer: (E) 99417
Question: In the xy-coordinate system, what is the slope of the line that goes through the point (4, 4) and is equidistant from the two points P = (0, 2) and Q = (12, 8)?
(A) 0.1
(B) 0.3
(C) 0.5
(D) 0.7
(E) 0.9
Rationale: First, get the middle coordinate between (0,2) and (12,8)...
x = 0 + (12-0)/2 = 6
y = 2 + (8-2)/2 = 5
Second, get the slope of (6,5) and (4,4). m = 5-4 / 6-4 = 1/2 = 0.5
Answer: C
Answer: (C) 0.5
Question: 10 positive integers are arranged in ascending order. The range of first seven is 25 and last 7 is 30. What will be the difference in minimum range of the set in following 2 cases
1) when 10 integers are distinct.
2) when the integers can be repeated in the set?
(A) 3
(B) 5
(C) 7
(D) 25
(E) 30
Rationale: Let's assume the set starts from 1.
Case 1) when 10 integers are distinct.
1st position = 1
4th position = 4
7th position = 26
10th position = 34
Minimum Range of the set = 33
Case 2) when the integers can be repeated in the set.
1st position = 1
4th position = 1
7th position = 26
10th position = 31
Minimum Range of set = 30
Difference in Minimum Range = 33 - 30 = 3
Answer: A
Answer: (A) 3
Question: A man can swim in still water at 4.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
(A) 1.6
(B) 1.3
(C) 1.4
(D) 1.5
(E) 1.1
Rationale: M = 4.5
S = x
DS = 4.5 + x
US = 4.5 + x
4.5 + x = (4.5 - x)2
4.5 + x = 9 -2x
3x = 4.5
x = 1.5
Answer:D
Answer: (D) 1.5
Question: John began driving from home on a trip averaging 30 miles per hour. How many miles per hour must Carla drive on average to catch up to him in exactly 3 hours if she leaves 30 minutes after John?
(A) 35
(B) 55
(C) 39
(D) 40
(E) 60
Rationale: Carla starts 30 minutes later and it takes 3 hr for carla to meet John
So John total time travelled = 3hr + 30 minutes
John distance = 30 * (3 1/2) = 105
so carla need to travle 105 to meet John in 3 hrs
speed of carla = 105/3 = 35 miles per hour
Answer is A
Answer: (A) 35
Question: A box contains 6 white, 5 red and 8 white marbles. 5 marbles are drawn from the box at random. What is the probability that both the marbles are of the same color?
(A) 19/11628
(B) 36/11628
(C) 613/11628
(D) 6113/11628
(E) 63/11628
Rationale: Explanation:
Total marbles in a box = 6 black + 5 red + 8 green marbles = 19 marbles
5 marbles are drawn from 19 marbles at random. Therefore,
n(S) = 19C5 = 11628 ways
Let A be the event that 2 marbles drawn at random are of the same color. Number of cases favorable to the event A is
n(A) = 6C5+ 5C5 + 8C5 = 6 +1+ 56= 63
Therefore, by definition of probability of event A,
P(A) = n(A)/n(S) = 63/11628
ANSWER:E
Answer: (E) 63/11628
Question: The cost price of 11 articles is equal to the selling price of 10 articles. What is the profit percent?
(A) 5%
(B) 10%
(C) 15%
(D) 20%
(E) 25%
Rationale: 10*SP = 11*CP
SP = 1.1*CP
The profit percent is 10%.
The answer is B.
Answer: (B) 10%
Question: A restaurant sells salmon pizzas for $13 each and pepperoni pizzas for $9 each. On every salmon pizza the restaurant makes a profit of $3 while on every pepperoni pizza it makes a profit of $1. If on a given day the restaurant's sales amounted to $468, which of the following cannot be the profit made on that day?
(A) 108
(B) 94
(C) 88
(D) 80
(E) 66
Rationale: $88 is the only option that does not fit into a combination of salmon and pepperoni pizza sales profits, given the total sales of the day. Answer: C
Answer: (C) 88
Question: Percentage of profit earned by selling a book for $3360 is equal to the percentage loss incurred by selling the same book for $2640. What price should the book be sold to make 20% profit?
(A) $3600
(B) $4000
(C) $3500
(D) $3700
(E) $4000
Rationale: Let C.P. be Rs. x.
Then,(3360 - x)	x 100 =(x - 2640) x 100
3360 - x = x - 2640
2x = 6000
x = 3000
Required S.P. = 120% of 3000 = 1.20	x 3000 = $3600
Answer : A
Answer: (A) $3600
Question: Sarah's seafood restaurant gets a delivery of fresh seafood every day, 5 days per week, and her delivery company charges herddollars per delivery plusccents per item delivered. If lst week Sarah's seafood restaurant had an average ofxitems per day delivered, then which of the following is the total cost, in dollars, of last week's deliveries ?
(A) 5cdx/100
(B) d + 5cx/100
(C) 5d + xc/100
(D) 5d + 5xc/100
(E) 5cdx
Rationale: Answer is D. Straight forward question.
Answer: (D) 5d + 5xc/100
Question: At a certain resort, each of the 39 food service employees is trained to work in a minimum of 1 restaurant and a maximum of 3 restaurants. The 3 restaurants are the family buffet, the dining room, and the snack bar. Exactly 21 employees are trained to work in the family buffet, 18 are trained to work in the dining room, and 12 are trained to work in the snack bar. If 4 employees are trained to work in exactly 2 restaurants, how many employees are trained to work in all 3 restaurants?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: 39 = 21 + 18 + 12 - 4 - 2x
2x = 21 + 18 + 12 - 4 - 39
= 47 - 39
= 8
x = 4
C
Answer: (C) 4
Question: A sum of Rs. 2665 is lent into two parts so that the interest on the first part for 8 years at 3% per annum may be equal to the interest on the second part for 3 years at 5% per annum. Find the second sum?
(A) Rs.450
(B) Rs. 1640
(C) Rs.523
(D) Rs.458
(E) Rs.796
Rationale: Explanation:
(x*8*3)/100 = ((2665 - x)*3*5)/100
24x/100 = 39975/100 - 15x/100
39x = 39975 => x = 1025
Second sum = 2665 – 1025 =Rs. 1640
Answer: B
Answer: (B) Rs. 1640
Question: Firm A's revenues are described by the equation Ra = 17.12x and its costs by Ca = 12.87x + 2200.
Firm B's revenues are described by the equation Rb = 13.27x and its costs by Cb = 8.77x + 1500.
(x denotes the quantity of sales).
If A's volume of sales increases from 1000 to 2000 over the same period that B's volume increases from 2000 to 3000, the percent increase in profits for the firm with the biggest dollar increase in profits is
(A) 20%
(B) 30%
(C) 60%
(D) 50%
(E) 33%
Rationale: Ok, I do not know whether it is exactly what you want to hear but I did it that way: first look at difference between revenue and variable cost => take the bigger one (b) which gives you: 4.5x-1500 just plug in 2000 and 3000. you get 7500 and 12000 (difference 4500). 4500> 0.5*7500 so 33%
E
Answer: (E) 33%
Question: If the selling price is doubled,the profit is tripled,what is the percentage of profit??
(A) 50%
(B) 100%
(C) 150%
(D) 200%
(E) 250%
Rationale: Let the profit be 10, then
SP-CP=10 and 2SP-CP=30
Solving the above equations we get SP=20 and CP=10, so CP=Profit
Hence the answer is B (100%)
Answer: (B) 100%
Question: What is the greatest prime factor of 4^17 - 2^26?
(A) 2
(B) 3
(C) 5
(D) 127
(E) 11
Rationale: I'm happy to help with this.
We know 4 = 2^2, so 4^17 = (2^2)^17 = 2^(2*17) = 2^34
That takes advantage of a law of exponents that says (a^n)^m = a^(n*m)
So, 4^17 - 2^26 = 2^34 - 2^26 = 2^(26 + 8) - 2^26 = (2^26)*(2*8) - 2^26 = (2^8 - 1) *(2^26)
= (128 - 1)*(2^26) = 127*(2^26)
The prime factors of 63 are 127, so the largest prime factor is 127, answer choice D.
Here's a blog you may find helpful.
http://magoosh.com/gmat/2012/gmat-math-factors/
Does all that make sense? Please let me know if you have any further questions.
Mike
Wow. I am floored by how great of an explanation you provided. Posts like that make me really think that doing thousands of practice problems with good explanations beats out reading books on math every day of the week.
D
Answer: (D) 127
Question: Calculate the average of first 9 even numbers is?
(A) 10
(B) 13
(C) 12
(D) 15
(E) 17
Rationale: Explanation:
Sum of 10 even numbers = 9 * 10 = 90
Average = 90/9 = 10
Answer: Option A
Answer: (A) 10
Question: There are 7 fictions and 6 non-fictions. How many cases are there such that 2 fictions and 2 non-fictions are selected from them?
(A) 90
(B) 120
(C) 315
(D) 180
(E) 200
Rationale: Number of ways of selecting 2 fiction books = 7C2
Number of ways of selecting 2 non fiction books = 6C2
7C2 * 6C2 = 21 * 15 = 315
Answer: C
Answer: (C) 315
Question: Find the average of all the numbers between 6 and 34 which are divisible by 7.
(A) 18
(B) 20
(C) 17.5
(D) 30
(E) 32
Rationale: Solution
Average	= (7+14+21+28)/4)
= 70 / 4
= 17.5.
Answer C
Answer: (C) 17.5
Question: The radius of a wheel is 20.4 cm. What is the distance covered by the wheel in making 400 resolutions?
(A) 512.448 m
(B) 704 m
(C) 510.448 m
(D) 706 m
(E) 204 m
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 400 resolutions.
= 400 * 2 * 22/7 * 20.4 = 51244.8 cm
= 512.448 m
Answer:A
Answer: (A) 512.448 m
Question: If 5a = 6b and ab ≠0, what is the ratio of a/6 to b/5?
(A) 36/25
(B) 10/12
(C) 1
(D) 1/5
(E) 25/36
Rationale: A nice fast approach is the first find a pair of numbers that satisfy the given equation: 5a = 6b
Here's one pair: a =6and b =5
What is the ratio of a/6 to b/5?
In other words, what is the value of (a/6)/(b/5)?
Plug in values to get: (a/6)/(b/5) = (6/6)/(5/5)
= 1/1
= 1
C
Answer: (C) 1
Question: In what time will a train 140 m long cross an electric pole, it its speed be 190 km/hr?
(A) 2.6 sec
(B) 2.9 sec
(C) 2.7 sec
(D) 8.7 sec
(E) 8.5 sec
Rationale: Speed = 190 * 5/18 = 53 m/sec
Time taken = 140/53 = 2.6 sec.
Answer: A
Answer: (A) 2.6 sec
Question: Jim is twice as old as Stephanie, who, four years ago, was three times as old as Kate. If, five years from now, the sum G of their ages will be 51, how old is Stephanie ?
(A) 6
(B) 10
(C) 14
(D) 20
(E) 24
Rationale: 1) take C (14y.o.), so mean that S=14, J=28, their sum itself is 42+10 years from now is 52, it is over the 51,
so eliminate C,D,E
2) take B (10y.o.),G= meaning S=10,J=20, so 20+10+10=40 and for K=10-4/3=2+9=11, finally 40+11=51. It is correct
B
Answer: (B) 10
Question: In order to fulfill a local school’s request for x cakes, y parents agreed to each bake an equal number of cakes. If z of the parents did not bake any cakes, which of the following represents the additional number of cakes that each of the other parents had to bake in order for the school’s request for x cakes to be fulfilled?
(A) xy
(B) xyz
(C) xy/z
(D) zx/(y(y - z))
(E) zy/x
Rationale: No of cakes each parent has to bake : x/y
No of parents did not bake cake = z
No of cakes that were not baked by p parents = z*x/y
No of parents has to bake additional cakes = y-z
additional number of cakes that each of the other parents had to bake in order for the school’s request for x cakes = zx/(y(y - z))
Answer D
Answer: (D) zx/(y(y - z))
Question: Simplify: 200 x 200 - 150 x 150
(A) 761200
(B) 761400
(C) 761800
(D) 17500
(E) None of them
Rationale: (200)^2 - (150)^2 = (200 + 150) (200 - 150) = 350 x 50 = 17500.
Answer is D
Answer: (D) 17500
Question: Walking 7/6 of his usual rate, a boy reaches his school 4 min early. Find his usual time to reach the school?
(A) 21
(B) 16
(C) 16
(D) 28
(E) 12
Rationale: Speed Ratio = 1:7/6 = 6:7
Time Ratio = 7:6
1 -------- 7
4 --------- ? è 28 m
Answer: D
Answer: (D) 28
Question: You need to unlock a secret code using following clues,
Can you?
Here you have the clues:
Clue-1 : 0 7 9 (One of the numbers is correct and is placed in its correct position)
Clue-2 : 0 3 2 (Nothing is correct)
Clue-3 : 1 0 8 (Two numbers are correct but not placed at its correct position.)
Clue-4 : 9 2 6 (One number is correct but not placed at its correct position.)
Clue-5 : 6 7 8 (One number is correct but not placed at its correct position.)
(A) 819
(B) 918
(C) 198
(D) 189
(E) 891
Rationale: 0 7 9 : 9 is placed correctly
* 0 3 2 : None of the numbers is in the code
* 1 0 8 : 1 and 8 are correct number of code but placed at wrong position
* 9 2 6 : Number 9 is there but placed at wrong position
* 6 7 8 : Number 8 is there but placed at wrong position
correct answer is A)819
Answer: (A) 819
Question: On a map, 1 inch represents 28 miles. How many V inches would be necessary to represent a distance of 383.6 miles?
(A) 5.2
(B) 7.4
(C) 13.7
(D) 21.2
(E) 28.7
Rationale: V inches necessary to represent a distance of 383.6 miles = 383.6/28
= 13.7
Answer C
Answer: (C) 13.7
Question: In a particular state, 60% of the counties received some rain on Monday, and 55% of the counties received some rain on Tuesday. No rain fell either day in 25% of the counties in the state. What percent of the counties received some rain on Monday and Tuesday?
(A) 12.5%
(B) 40%
(C) 50%
(D) 60%
(E) 67.5%
Rationale: 60 + 55 + 25 = 140%
The number is 40% above 100% because 40% of the counties were counted twice.
The answer is B.
Answer: (B) 40%
Question: A Washing machine is available for $39000 cash or $17000 as down payment followed by five equal monthly instalments of $4800 each. The simple rate of interest per annum under the instalment plan would be
(A) 18%
(B) 19%
(C) 21.2%
(D) 21.81%
(E) 22.07%
Rationale: Simple interest SI = (P*R*T)/100
where P is the principal amount
R is the rate of interest
and T is time in years
the way I see it:Washing machine on down payment of 17,000, customer is not paying any interest. it is the remaining sum which will be paid for 5 months that will bear an interest. Therefore, the principal amount for which interest is being charged is 39,000 - 17,000 = 22,000
For this 22,000 a total sum of 5*4800 = 24,000 was pain. (Time is five months, so T = 5/12, as T is in years.)
thus, SI = 2000 or
2000 = (P*R*T)/100
2000 = (22,000*R*5)/(100*12)
R = (2,000*12*100)/22,000*5
R = 21.81%
Therefore answer is D
Answer: (D) 21.81%
Question: Certain stocks in January were 30% greater than they were in February and 20% lesser than they were in March. What was the percentage decrease in the stocks from February to March?
(A) 44%
(B) 30%
(C) 40%
(D) 47.5%
(E) 50%
Rationale: Let stocks value in Feb = 100 => In Jan = 70 and March = 70 * 80/100 = 56
Thus, percent decrease in stocks from Feb to March = 100 - 56 = 44%
Hence Answer is A
Answer: (A) 44%
Question: A solid yellow stripe is to be painted in the middle of a certain highway. If 1 gallon of paint covers an area of e square feet of highway, how many gallons of paint will be needed to paint a stripe of t inches wide on a stretch of highway m miles long? (1 mile = 5,280 feet and 1 foot = 12 inches)
(A) (5,280 mt) / 12 e
(B) (5,280 pt) / 12m
(C) (5,280 pmt) /12
(D) (5,280)(12m) / pt
(E) (5,280)(12p) / mt
Rationale: Given that: 1 gallon of paint covers an area ofesquare feet. Question:how many gallonsof paint will be needed ...
In any case you will have:(total area in square feet)/(gallons per feet)=(total area in square feet)/e, so e must be in the denominator: eliminate all but A and D.
Now, lets see where should be t: (area in square feet)=(width in feet)*(length in feet) --> width=tinchesas1 feet=12 inchesthent inches=t/12 feet, so (area in square feet)=(t/12) * (length in feet), so t must be in the nominator: only A is left.
Answer: A.
Answer: (A) (5,280 mt) / 12 e
Question: In a certain book club, the members are voting between two books – a mystery novel and a biography – to decide which book the group will read next. There are 4 times as many votes for the mystery novel as there are votes for the biography. The ratio of biography votes to the total number of votes is
(A) 1 to 2
(B) 1 to 3
(C) 1 to 4
(D) 1 to 5
(E) 3 to 4
Rationale: IMO : Answer D 1 to 5
Answer: (D) 1 to 5
Question: A student committee that must consists of 3 members is to be formed from a pool of 8 candidates. How many different committees are possible
(A) 5
(B) 8
(C) 40
(D) 56
(E) 336
Rationale: I think the answer is 56.
Out of 8 people, any 3 can be selected for a committee. So 8c3 is the answer.
D
Answer: (D) 56
Question: A cement block balances evenly on the scales with 3 quarters of a pound and 3 quarters of a block. What is the weight of the whole block?
(A) 1 pounds
(B) 2 pounds
(C) 3 pounds
(D) 4 pounds
(E) 5 pounds
Rationale: x= 3/4 +x*3/4
x/4 = 3/4
x= 3 pounds
ANSWER:C
Answer: (C) 3 pounds
Question: How many different sets of positive square integers P, each greater than 1, add up to 75?
(A)  1
(B)  4
(C)  7
(D)  11
(E)  13
Rationale: E= 13 is the correct answer.
Answer: (E)  13