mathewhe/aqua_rat huggingface dataset:
Question: A computer program assigns consecutive numbers to the days of the week. Sunday is 1, Monday is 2, ..... and Saturday is 7. Every day, the computer program calculates the value of parameter D according to the following definition: D is the number of the day times the value of D on the previous day. If the computer calculated D to be 12 on Wednesday, what would be the value of D calculated on the following Saturday?
(A) 2140
(B) 2520
(C) 2960
(D) 3360
(E) 3710
Rationale: On Saturday, the value would be 7*6*5*12 = 2520
The answer is B.
Answer: (B) 2520
Question: 4 is what percent of 50?
(A) 0.2%
(B) 8%
(C) 10%
(D) 20%
(E) 500%
Rationale: 4= x*50/100
x = 8%
Ans; B
Answer: (B) 8%
Question: John purchased a house for Rs.45000 and a site for Rs.25000 respectively, if he sold the house for Rs.55000 and the site for Rs.16000, then find the resultant percentage of gain?
(A) 1.39%
(B) 1.40%
(C) 1.41%
(D) 1.42%
(E) 1.43%
Rationale: Sol.
Total CP = 70000 & total SP = 71000 ⇒ gain = SP/CP = 71000/70000 = 1.0142 = 1.42%.
Answer D
Answer: (D) 1.42%
Question: The monthly rent of a shop of dimension 20feet × 18feet is Rs.1440. What is the annual rent per square foot of the shop?
(A) 48
(B) 56
(C) 68
(D) 87
(E) 92
Rationale: Sol. Monthly rent per square feet = 1440/(20*18) = 4
& Annual rent per square feet
=12*4=48
Answer : A
Answer: (A) 48
Question: 1 2 1 2 2 1 2 2 2 1 2 2 2 2 1 2 2 2 2 2 1 .........,sum of first 1230 terms of series
(A) 2311
(B) 2411
(C) 2511
(D) 2611
(E) 2487
Rationale: Start with making two series
1+1*2=3 terms 2
1+2*2=5. 3
1+3*2=7. 4
....
....
....
1+47*2=95. 48
1+48*2=97. 49
And last term
1+5*2=11. 6
Total sum= 48(3+97)/2+11=2411
ANSWER:B
Answer: (B) 2411
Question: A rectangular box of volume Y has width, depth and height in the ratio of 3:2:4 (in that order). What is the height as a function of Y?
(A) (4Y/6)^(1/2)
(B) (Y/6)^(1/2)
(C) (Y/4)^(1/2)
(D) (2Y/3)^(1/2)
(E) (Y)^(1/2)
Rationale: We are given width = 3, depth = 2, height = 4.
Then Volume = Width x Depth x Height = 3*2*4 = 24
i.e. Y = 24
The correct option should result in 4 (the height) on substituting the value of Y=24.
Checking options with Y=24:
A) (4Y/6)^(1/2) = (96/6)^(1/2) = 4 CORRECT ANSWER
B) (Y/6)^(1/2) = (24/6)^(1/2) = 2 INCORRECT ANSWER
C) (6Y/4)^(1/2) = (144/4)^(1/2) = 6 INCORRECT ANSWER
D) (Y/3)^(1/2) = (24/3)^(1/2) = 8^(1/2) INCORRECT ANSWER
E) (Y)^(1/2) = (24)^(1/2) INCORRECT ANSWER
Answer: Option A
Answer: (A) (4Y/6)^(1/2)
Question: Find the principal which yields a simple interest of Rs. 20 and compound interest of Rs. 21 in two years, at the same percent rate per annum?
(A) Rs. 200
(B) Rs. 209
(C) Rs. 202
(D) Rs. 238
(E) Rs. 218
Rationale: Explanation:
SI in 2 years = Rs. 20, SI in 1 year = Rs. 10
CI in 2 years = Rs. 21
% rate per annum = [(CI – SI) / (SI in 1 year)] *100
= [(21 – 20) / 20] * 100
= 5 % p.a.
Let the principal be Rs. X
Time = T = 2 years
% rate = 5% p.a.
SI = (PRT/100)
20 = (X*5*2) / 100
X = Rs. 200
ANSWER: A
Answer: (A) Rs. 200
Question: The total of company C's assets in 1994 was 200% greater than the total in 1993, which in turn was 400% greater than the total in 1992. If the total of company C's assets in in 1992 was N dollars, which one of the following represents company C's assets in 1994:
(A) 7N
(B) 8N
(C) 9N
(D) 12N
(E) 15N
Rationale: Let's use actual numbers. Starting in 1992, let's say company C had $100 in assets.
In 1993, the total assets were 400% GREATER, which means 1992 PLUS 400% of 1992:
$100 + 4x$100 = $100 + $400 =$500
In 1994, the total assets were 200% GREATER than they were in 1993, which means 1993 PLUS 300% of 1993:
$500 +2x$500 = $500 + $1000 =$1500
This is 15 times the 1992 number, so the correct answer is 15N.
Answer: (E) 15N
Question: If n = 8^9 – 8, what is the units digit of n?
(A) 4
(B) 0
(C) 1
(D) 2
(E) 3
Rationale: 8 ^ 9 - 8 = 8 (8 ^ 8 - 1)
==> 8 (2 ^ 24 - 1)
Last digit of 2 ^ 24 is 6 based on what explanation LiveStronger is saying. 2 ^ 24 - 1 yields 6 - 1 = 5 as the unit digit. Now on multiply this with 8, we get unit digit as 0
Answer : B
Answer: (B) 0
Question: How often between 11 O'clock and 12 O'clock are the hands of the clock together at an integral number value?
(A) 55
(B) 56
(C) 4
(D) 5
(E) 3
Rationale: Solution:
At 11 O'clock, the hour hand is 5 spaces apart from the minute hand.
During the next 60 minutes, i.e. between 11' O clock and 12' O clock the hour hand will move five spaces [integral values as denoted by the 56 minute, 57 minute, 58 minute, 59 minute and 60 minute positions].
For each of these 5 positions, the minute hand will be at the 12th minute, 24th minute, 36th minute, 48th minute and 60th minute positions.
Hence the difference between the positions of the hour hand and the minute hand will have an integral number of minutes between them.
i.e. 5 positions.
Answer D
Answer: (D) 5
Question: A bag contains 4 red, 3 blue and 2 green balls. If 2 ballsare picked at random, what is the probability that both are red?
(A) 1/13
(B) 2/23
(C) 1/6
(D) 4/27
(E) 3/23
Rationale: P(Both are red),
=4C29C2=4C29C2
=6/36=1/6
C
Answer: (C) 1/6
Question: 20 people are there, they are shaking hands together, how many hand shakes possible,if they are in pair of cyclic sequence.
(A) 19
(B) 20
(C) 21
(D) 22
(E) 23
Rationale: in case of cycle no of handshakes = no of persons
hence ans = 20
ANSWER:B
Answer: (B) 20
Question: In an election between two candidates, the first candidate got 60% of the votes and the second candidate got 240 votes. What was the total number of votes?
(A) 400
(B) 600
(C) 800
(D) 1000
(E) 1200
Rationale: Let V be the total number of votes.
0.4V = 240
V = 600
The answer is B.
Answer: (B) 600
Question: In the manufacture of a certain product, 5 percent of the units produced are defective and 4 percent of the defective units are shipped for sale. What percent of the units produced are defective units that are shipped for sale?
(A) 0.125%
(B) 0.2%
(C) 0.8%
(D) 1.25%
(E) 2.0%
Rationale: Percent of defective produced = 5%
Percent of the defective units that are shipped for sale = 4%
Percent of units produced are defective units that are shipped for sale = (4/100)*(5/100)*100%
= (20/10000)*100%
= (20/100)%
= .2 %
Answer B
Answer: (B) 0.2%
Question: The weight of a glass of jar is 10% of the weight of the jar filled with coffee beans. After some of the beans have been removed, the weight of the jar and the remaining beans is 60% of the original total weight. What fraction part of the beans remain in the jar?
(A) 1/5
(B) 1/3
(C) 2/5
(D) 1/2
(E) 5/9
Rationale: Let weight of jar filled with beans = 100 g
Weight of jar = 10 g
Weight of coffee beans = 90 g
Weight of jar and remaining beans = 60 g
Weight of remaining beans = 50 g
Fraction remaining = 50/90 = 5/9
Answer is E.
Answer: (E) 5/9
Question: A number is increased by 50 % and then decreased by 50 %. Find the net increase or decrease per cent.
(A) 25%
(B) 18%
(C) 17%
(D) 13%
(E) 16%
Rationale: Let the number be 100.
Increase in the number = 50 % = 50 % of 100
= (50/100 Ã— 100)
= 50
Therefore, increased number = 100 + 50 = 150
This number is decreased by 50 %
Therefore, decrease in number = 50 % of 150
= (50/100 Ã— 150)
= 7500/100
= 75
Therefore, new number = 150 - 75 = 75
Thus, net decreases = 100 - 75 = 25
Hence, net percentage decrease = (25/100 Ã— 100) %
= (2500/100) %
= 25 %
Answer:A
Answer: (A) 25%
Question: A certain fraction is equivalent to 3/5. If the numerator of the fraction is increased by 4 and the denominator is doubled, the new fraction is equivalent to 1/3. What is the sum of the numerator and denominator of the original fraction?
(A)  49
(B)  35
(C)  28
(D)  56
(E)  21
Rationale: x/y = 3/5 -> 1
(x+4)/2y = 1/3 -> 2
Divide 1 by 2 :
=> 2x/(x+4) = 9/5
=> 10x = 9x + 36
=> x = 36
=> y = 5/3 * 12 = 20
so x + y = 56
The answer is D.
Answer: (D)  56
Question: Sonika deposited Rs.6200 which amounted to Rs.7200 after 5 years at simple interest. Had the interest been 3% more. She would get how much?
(A) 9680
(B) 8130
(C) 8134
(D) 8556
(E) 9808
Rationale: (6200*5*3)/100 = 930
7200
--------
8130
Answer: B
Answer: (B) 8130
Question: From the given choices select the odd man out
(A) 37, 14, 19, 8
(B) 37, 14, 19, 0
(C) 37, 14, 19, 2
(D) 37, 14, 19, 7
(E) 37, 14, 19, 1
Rationale: Explanation:
All the numbers in those options are prime numbers except 14 in option 4.
Answer:D
Answer: (D) 37, 14, 19, 7
Question: If x is a positive integer, which of the following must be odd?
(A) x+1
(B) x^2+x
(C) x^2+x+1
(D) x^2−1
(E) 3x^2−3
Rationale: A. X+1 = can be odd or even. Since O + O =E or E + O = O
B. X^2 + X = X(X+1). Since from the above derivation we already know the term X+1 can be Odd or Even, directly substitute here. X(ODD) = Even (When X is Even) or X(EVEN) = EVEN [When X is ODD]
C. Here's the answer. Since we know the term x^2 + X can always take a EVEN number, EVEN + 1 = ODD
Hence C.
Answer: (C) x^2+x+1
Question: If |x – 9/2| = 5/2, and if y is the median of a set of s consecutive integers, where s is odd, which of the following must be true?
I. xys is odd
II. xy(s^2 + s) is even
III. x^2y^2s^2 is even
(A) II only is true
(B) III only is true
(C) I and III
(D) II and III
(E) I, II, and III
Rationale: given:
s is Odd
y is the median of odd numbers, hence y is Odd
x = solving the modulus you get 7 and 2. Hence x is Even or Odd
Therefore: s = O, y = O and x = O or E
Statement I = x*y*s = y*s*x = O x O x O/E = O x O/E = Odd or even. So False
Statement II = xy(s^2 + s) = O/E x O (O + O) = O/E x O(E) = O/E x E = Always Even. So true
Statement III. x^2y^2s^2 is even. E/O x O x O = Odd or even. Hence False.
Answer = A.
Answer: (A) II only is true
Question: When the positive integer p is divided by 9, the remainder is 5. What is the remainder when 3p is divided by 9?
(A) 0
(B) 1
(C) 3
(D) 4
(E) 6
Rationale: Lets take the number as p
when p is divided by 9 the remainder is 5 hence p can be written as
p=9k +5
Multiplying by 3 will give
3p = 27k + 15
we can also write
3p = 27k + 9 + 6
Now 27k and 9 are divisible by 9 leaving the remainder as 6 hence E is the answer.
Answer: (E) 6
Question: The sum of the squares of the first 15 positive integers (1^2 + 2^2 + 3^2 + . . . + 15^2) is equal to 1270. What is the sum of the squares of the second 15 positive integers (16^2 + 17^2 + 18^2 + . . . + 30^2) ?
(A)  2480
(B)  3490
(C)  6785
(D)  8245
(E)  9255
Rationale: You'll never need a formula for the sums of squares on the actual GMAT. You don't need to use that formula here, though it's not all that straightforward to solve without one. Two different approaches:
16^2 + 17^2 + 18^2 + ... + 30^2 = (15 + 1)^2 + (15 + 2)^2 + (15 + 3)^2 + ... + (15 + 15)^2
Now we can expand each square; they are all in the (x + y)^2 = x^2 + 2xy + y^2 pattern.
= (15^2 + 2*15 + 1^2) + (15^2 + 4*15 + 2^2) + (15^2 + 6*15 + 3^2) + ... + (15^2 + 30*15 + 15^2)
Now we have fifteen 15^2 terms, so adding these gives 15*15^2 = 15^3 = 3375. We also have the entire sum 1^2 + 2^2 + ... + 15^2, which we know is equal to 1240. Finally adding the middle terms, we have:
2*15 + 4*15 + 6*15 + ... + 30*15 = 15(2 + 4 + 6 + .... + 30) = 15*2*(1 + 2 + 3 + ... + 15) = 15*2*8*15 = 3600
So the sum must be 3375 + 1240 + 3600 = 8215
Alternatively, we can use a different factoring pattern. We want to find the value of 30^2 + 29^2 + ... + 17^2 + 16^2. Well if we subtract 15^2 + 14^2 + .... + 2^2 + 1^2 from this, the answer will be 1240 less than what we want to find. So if we can find the value of
30^2 + 29^2 + ... + 17^2 + 16^2 - (15^2 + 14^2 + .... + 2^2 + 1^2)
then we can add 1240 to get the answer. Now grouping the terms above to get differences of squares, we have
= (30^2 - 15^2) + (29^2 - 14^2) + ... + (16^2 - 1^2)
and factoring each of these using x^2 - y^2 = (x + y)(x - y), we have
= 45*15 + 43*15 + 41*15 + ... + 17*15 = 15(45 + 43 + 41 + ... + 17)
In brackets we have an equally spaced sum with fifteen terms, which we can evaluate using the familiar formula. So the above equals
15*15*62/2 = 6975
and adding back the 1270, we get the answer of 8245. (ANS D)
Answer: (D)  8245
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 present salary.
(A) 32000
(B) 34000
(C) 38000
(D) 40000
(E) None of these
Rationale: Explanation:
Let the original Salaries of Ravi and Sumit is 2x and 3x.
So as per question
2x+4000/3x+4000=40/57
=>57(2x+4000)=40(3x+4000)
=>6x=68000
=>3x=34000
Sumit Salary =3x+4000
34000+4000=38000
Option C
Answer: (C) 38000
Question: A retailer sold an appliance for $100. If the retailer's gross profit on the appliance was 25 percent of the retailer's cost for the appliance, how many dollars was the retailer's gross profit?
(A) $10
(B) $16
(C) $20
(D) $24
(E) $25
Rationale: Let P be the original price paid by the retailer.
1.25*P = 100
P = 80
The profit is $20.
The answer is C.
Answer: (C) $20
Question: Suresh started a business, investing Rs.18000. After 3 months and 4 months respectively, Rohan and Sudhir joined him with capitals of 12000 and 9000. At the end of the year the total profit was Rs.3982. What is the difference between Rohan’s and Sudhir’s share in the profit?
(A) Rs.345
(B) Rs.350
(C) Rs.352
(D) Rs.362
(E) Rs.368
Rationale: Suresh : Rohan : Sudhir
Ratio of their investments = 18000 × 12 : 12000 × 9 : 9000 × 8
= 6 : 3: 2
The difference between Rohan’s and Sudhir’s share = 1 share
:.i.e. = Rs. 3982 × 1/11 = Rs.362.
D
Answer: (D) Rs.362
Question: six friends go to pizza corner where there are different types of pizza available. six different flavours are there and they have to select 2 flavours from 6 flavours.In how many ways they can select?
(A) 11
(B) 12
(C) 13
(D) 14
(E) 15
Rationale: 6c2 then ans is 6*5/1*2=15
ANSWER:E
Answer: (E) 15
Question: A card player holds 13 cards of four suits, of which seven are black and six are red. There are twice as many hearts as clubs and twice as many diamonds as hearts. How many spades does he hold?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: Sol.
The player holds 1 club, 2 hearts and 4 diamonds.
As he holds 13 cards (or seven black cards), it follows that there must be 6 spades.
Answer : A
Answer: (A) 6
Question: A certain bag contains 100 balls — 50 white, 30 green, 10 yellow, 7 red, and 3 purple. If a ball is to be chosen at random, what is the probability that the ball will be neither red nor purple?
(A) 0.9
(B) 0.75
(C) 0.6
(D) 0.8
(E) 0.5
Rationale: According to the stem the ball can be white, green or yellow, so the probability is (white + green + yellow)/(total) = (50 + 30 + 10)/100 = 90/100 = 0.9.
Answer is A
Answer: (A) 0.9
Question: y and z represents 2 gas stations which are 270 km apart. if two cars leave each gas station and drive towards each other, at what time will they meet each other given that the first car left the gas station at 10 a.m. and travels at a speed of 75 kmph while the second car left the station at 11 a.m. and travels at a speed of 55 kmph.
(A) 12.00 p.m
(B) 11.30 p.m
(C) 2.30 p.m
(D) 12.30 p.m
(E) 1.30 p.m
Rationale: Suppose they meet x hours after 10 a.m.
Distance moved by first car in x hours + distance moved by 2nd car in x-1 hrs = 270
75x+55(x-1) = 270
75x+55x-55= 270
130x= 325
x = 2.5
So they meet 2.5 hr after 10 a.m. which is at 12.30 p.m.
Answer is D
Answer: (D) 12.30 p.m
Question: What should come in place of question mark (?) in the following equation?
5 3⁄5 ÷ 3 11⁄15 + 5 1⁄2 = ?
(A) 7
(B) 8 1⁄2
(C) 7 1⁄2
(D) 6 1⁄2
(E) None of these
Rationale: ? = 5 3⁄5 ÷ 3 11⁄15 + 5 1⁄2 = 28⁄5 ÷ 56⁄15 + 11⁄2
= 28⁄5 × 15⁄56 + 11⁄2 = 3⁄2 + 11⁄2 = 14⁄2 = 7
Answer A
Answer: (A) 7
Question: The cost of 2 chairs and 3 tables is Rs.1500. The cost of 3 chairs and 2 tables is Rs.1200. The cost of each table is more than that of each chair by?
(A) 228
(B) 287
(C) 277
(D) 188
(E) 300
Rationale: Explanation:
2C + 3T = 1500 --- (1)
3C + 2T = 1200 --- (2)
Subtracting 2nd from 1st, we get
-C + T = 300 => T - C = 300
Answer:E
Answer: (E) 300
Question: Maxwell leaves his home and walks toward Brad's house at the same time that Brad leaves his home and runs toward Maxwell's house. If the distance between their homes is 30 kilometers, Maxwell's walking speed is 4 km/h, and Brad's running speed is 6 km/h, what is the distance traveled by Brad?
(A)  16
(B)  18
(C)  20
(D)  24
(E)  30
Rationale: Time taken = Total Distance / Relative Speed
Total Distance = 30 kms
Relative Speed (Opposite side) (As they are moving towards each other speed would be added ) = 6+ 4 = 10 kms/hr
Time taken = 30 / 10 = 3 hrs
Distance traveled by Brad = Brad's speed * time taken = 6 * 3 = 18 kms... Answer - B
Answer: (B)  18
Question: If x^2+(1/x^2)=3, x^4+(1/x^4)=?
(A) 7
(B) 11
(C) 12
(D) 14
(E) 15
Rationale: -> x^4+(1/x^4)=(x^2)^2+(1/x^2)^2=(x^2+1/x^2)^2-2x^2(1/x^2)=3^2-2=7.
Thus, the answer is A.
Answer: (A) 7
Question: A man leaves a point P at 6 a.m. and reaches the point Q at 10 a.m. another man leaves the point give at 8 a.m. and reaches the point P at 12 noon. At what time do they meet?
(A) 2
(B) 5
(C) 9
(D) 6
(E) 3
Rationale: 9 a.m.
Answer: C
Answer: (C) 9
Question: Anil grows tomatoes in his backyard which is in the shape of a square. Each tomato takes 1 cm2 in his backyard. This year, he has been able to grow 131 more tomatoes than last year. The shape of the backyard remained a square. How many tomatoes did Anil produce this year?
(A) 4225
(B) 4096
(C) 4356
(D) Insufficient Data
(E) None of these
Rationale: DETAILED SOLUTION
Let the area of backyard be x2 this year and y2 last year
∴ X2- Y2 = 131
=) (X+Y) (X-Y) = 131
Now, 131 is a prime number (a unique one too. Check out its properties on Google). Also, always identify the prime number given in a question. Might be helpful in cracking the solution.
=) (X+Y) (X-Y) = 131 x 1
=) X+Y = 131
X-Y = 1
=) 2X = 132 =) X = 66
and Y = 65
∴ Number of tomatoes produced this year = 662 = 4356
Correct Choice (C)
Answer: (C) 4356
Question: A football team lost 5 yards and then gained 9. What is the team's progress?
(A) 2
(B) 4
(C) 5
(D) 6
(E) 8
Rationale: For lost, use negative. For gain, use positive.
Progress = -5 + 9 = 4 yards
Answer: (B) 4
Question: Pipe A can fill a tank in 8 hours. Due to a leak at the bottom, it takes 12 hours for the pipe A to fill the tank. In what time can the leak alone empty the full tank?
(A) 5
(B) 24
(C) 78
(D) 90
(E) 54
Rationale: Let the leak can empty the full tank in x hours 1/8 - 1/x = 1/12
=> 1/x = 1/8 - 1/12 = (3 - 2)/24 = 1/24
=> x = 24.
Answer: B
Answer: (B) 24
Question: How many odd three-digit integers smaller than 500 are there such that all their digits are different?
(A) 72
(B) 88
(C) 112
(D) 122
(E) 144
Rationale: Case 1: Numbers starting with 1
1 _ _
The unit digit can take 4 numbers (3,5,7,9) to be ODD so 4 ways.
The tens digit can take remaining 8 numbers left after using 2 numbers so 8 ways.
Total = 8*4=32
Case 2: Numbers starting with 2
2 _ _
The unit digit can take 5 numbers (1,3,5,7,9) to be ODD so 5 ways.
The tens digit can take remaining 8 numbers left after using 2 numbers so 8 ways.
Total = 8 *5 = 40
Case 3: Numbers starting with 3
3 _ _
The unit digit can take 4 numbers (1,5,7,9) to be ODD so 4 ways.
The tens digit can take remaining 8 numbers left after using 2 numbers so 8 ways.
Total = 8 *4 = 32
Case 4: Numbers starting with 4
4 _ _
The unit digit can take 5 numbers (1,3,5,7,9) to be ODD so 5 ways.
The tens digit can take remaining 8 numbers left after using 2 numbers so 8 ways.
Total = 8 *5 = 40
Hence 32+40+32+40=144, correct answer is E
Answer: (E) 144
Question: Kiran travels from A to B by car and returns from B to A by cycle in 7 hours. If he travels both ways by car he saves 3 hours. What is the time taken to cover both ways by cycle?
(A) 10 hours
(B) 23 hours
(C) 18 hours
(D) 20 hours
(E) 12 hours
Rationale: Let the time taken to cover from A to B in car and cycle be x hours and y hours respectively.
x + y = 7 --- (1) ; 2x = 4 --- (2)
solving both the equations, we get y = 5
So, time taken to cover both ways by cycle = 2y hours =10 hours.
Answer: A
Answer: (A) 10 hours
Question: A class is 6 meters 24 centimeters in length and 4 meters 32 centimeters in width. Find the least number of square tiles of equal size required to cover the entire floor of the class room ?
(A) 115
(B) 117
(C) 116
(D) 114
(E) NONE OF THESE
Rationale: Explanation:
Length = 6 m 24 cm = 624 cm
Width = 4 m 32 cm = 432 cm
HCF of 624 and 432 = 48
Number of square tiles required = (624 x 432)/(48 x 48) = 13 x 9 = 117.
ANSWER IS B
Answer: (B) 117
Question: If a - b = 3 and a2 + b2 = 29, find the value of ab.
(A) 10
(B) 12
(C) 15
(D) 18
(E) 19
Rationale: 2ab = (a2 + b2) - (a - b)2
= 29 - 9 = 20
ab = 10.
Answer: A
Answer: (A) 10
Question: A rectangular field is 20 yards long and 18 yards wide. A fence is needed for the perimeter of the
field. Fencing is also needed to divide the field into three square sections. How many feet of fencing
are needed? (It is a good idea to make a drawing for this one.)
(A) 330 ft
(B) 336 ft
(C) 430 ft
(D) 330 ft
(E) 230 ft
Rationale: 20 + 18 + 20 + 18 = 76 yds. for
outside of field.
18 + 18 = 36 yds. for dividing sections
76 + 36 = 112 yds. of fencing
112 x 3 = 336 ft. of fencing
correct answer B
Answer: (B) 336 ft
Question: On a business trip, 30 percent of 60 sales representatives will be given accommodations at Hotel XYZ and the remaining 70 percent will be given accommodations at Hotel ABC. However, 45 percent of the sales representatives prefer to stay at Hotel XYZ and 55 percent prefer to stay at Hotel ABC. What is the highest possible number of sales representatives NOT given accommodations at the hotel they prefer?
(A) 36
(B) 39
(C) 42
(D) 45
(E) 48
Rationale: 18 people stay in XYZ and 42 people stay in ABC.
27 people prefer XYZ and 33 people prefer ABC.
Let's put all 27 people who prefer XYZ in hotel ABC.
Then 18 people who prefer ABC will stay in XYZ.
The highest possible number who are not given their preference is 27+18=45.
The answer is D.
Answer: (D) 45
Question: A does a work in 20days and B does the same work in 5days. In how many days they together will do the same work?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: A+B can finish =AB/A+B = 20*5/(20+5) = 4days
Answer is D
Answer: (D) 4
Question: A park shaped like a rectangle has a length of 24 meters and a width of 18 meters. If trees are planted on its sides with gaps of 2 meters between them, how many trees are needed?
(A) 32 trees.
(B) 42 trees.
(C) 52 trees.
(D) 62 trees.
(E) None of these
Rationale: Solution:
The perimeter of the rectangle is 2 × (24 + 18) = 2 × 42 = 84 meters, so there will be 84 ÷ 2 = 42 trees.
Answer B
Answer: (B) 42 trees.
Question: Of the 8 temporary employees in a certain company, 4 will be hired as permanent employees. If 5 of the 8 temporary employees are women, how many of the possible groups of 4 employees consist of 3 women and one man?
(A) 30
(B) 35
(C) 56
(D) 70
(E) 105
Rationale: another approach :
one scenario : [WWWM]
now we have 5 ways for the first women , 4 ways for the 2nd women and , 3 ways for the third women.
and 8 ways to select one man
so 5*4*3*3 = 180
now the three women are same so combinations with win them are irrelevant the 3 women can we arranged in 3! ways
hence 180/3!= 180/6= 30
A
Answer: (A) 30
Question: If equation |x/5| + |y/5| = 2 encloses a certain region on the coordinate plane, what is the area of this region?
(A) 20
(B) 50
(C) 200
(D) 100
(E) 400
Rationale: The equation can be reduced to intercept form as |x/10| + |y/10| = 1, so these are lines in four quadrants with x and y intercept as 10, so it is a rhombus with diagonals of 20 each and hence area = 1/2*d1*d2 = 1/2*20*20 = 200. Answer C.
Answer: (C) 200
Question: In traveling from a dormitory to a certain city, a student went 1/5 of the way by foot, 2/3 of the way by bus, and the remaining 15 kilometers by car. What is the distance, in kilometers, from the dormitory to the city?
(A) 67
(B) 45
(C) 60
(D) 90
(E) 120
Rationale: I believe there is a better way to do it.
Basically one of the options should satisfy the given criteria.
60 did
1/5 *60 =12
2/3*60=40
so total distance
52 + remaining 15 =67
Answer: (C) 60