mathewhe/aqua_rat huggingface dataset:
Question: Find the area of region enclosed by | x | + | y | = 3
(A) 18
(B) 11
(C) 28
(D) 26
(E) 91
Rationale: We have to consider separately the form of the function w.r.t to where x, y lies.
x >0, y >0, x + y = 3
x > 0, y < 0, x - y = 3
x < 0, y >0, x - y = - 3
x < 0, y < 0, x + y = - 3
After having drawn the above 4 lines on the graph, the graph looks like aboe
Now the area of the graph = 4 right angle triangles.
Area of the right angle triangle = 12×3×3=9212×3×3=92
Area of the entire region = 92×492×4 = 18 units
Answer:A
Answer: (A) 18
Question: The mean of four integers W will not change if all the integers are multiplied by any constant. What is always true about this set of numbers?
I. The mean of the set is 0
II. The sum of the largest member and the smallest member of the set is 0
III. The set contains both positive and negative integers
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II, and III
Rationale: If we consider a set {1,2,3,4}, when multiplied with a constant we take that constant as 1 and multiply resulting set will contain the same numbers as the original. so how can the answer be I only.....A
Answer: (A) I only
Question: Two pipes A and B can separately fill a cistern in 10 and 15 minutes respectively. A person opens both the pipes together when the cistern should have been was full he finds the waste pipe open. He then closes the waste pipe and in another 4 minutes the cistern was full. In what time can the waste pipe empty the cistern when fill?
(A) 1/3
(B) 1/9
(C) 1/4
(D) 1/2
(E) 1/6
Rationale: 1/10 + 1/15 = 1/6 * 4 = 2/3
1 - 2/3 = 1/3
1/10 + 1/15 - 1/x = 1/3
x = 8.Answer: A
Answer: (A) 1/3
Question: All the faces of cubes are painted with red colour.It is then cut into 64 equal small cubes.Find How many small cubes have no faces coloured ?
(A) 24
(B) 8
(C) 16
(D) 0
(E) 4
Rationale: There are 64 small cubes,Hence one side side of the big cube is 3√64=4 cm
Number of small cubes having only one faces coloured = (x - 2)^3
Here, x = side of big cube / side of small cube
x = 4 /1
x = 4
Required number = (4 -2)^3
= 8
Answer :B
Answer: (B) 8
Question: In a business, A and C invested amounts in the ratio 2 : 1 , whereas the ratio between amounts invested by A and B was 3 : 2 . If Rs.157300 was their profit, how much amount did B receive?
(A) 48400
(B) 48000
(C) 48100
(D) 48500
(E) 48600
Rationale: Assume that investment of C =x
Then, investment of A =2x
Investment of B =4x/3
A:B:C =2x:(4x)/3:x
=2:4/3:1=6:4:3
B's share =157300×4/(6+4+3)
=157300×4/13=12100×4=48400
Answer is A.
Answer: (A) 48400
Question: The profits of QRS company rose 10% from March to April, then dropped 20% from April to May, then rose 50% from May to June. What was the percent increase for the whole quarter, from March to June?
(A) 15%
(B) 32%
(C) 40%
(D) 62%
(E) 80%
Rationale: We need multipliers.
multiplier for a 10% increases = 1 + 0.10 = 1.1
multiplier for a 20% decreases = 1 – 0.20 = 0.8
multiplier for a 50% increases = 1 + 0.50 = 1.5
Now, multiply these. First, multiply (0.8) and (1.5), using the doubling & halving trick. Half of 0.80 is 0.40, and twice 1.5 is 3
(0.8)*(1.5) = (0.4)*(3) = 1.2
Now, multiply this by 1.1
1.2*1.1 = 1.32
Thus, the three percent changes combined produce a 32% increase. Answer = (B).
Answer: (B) 32%
Question: For what values of 'k' will the pair of equations 3x + 4y = 12 and kx + 12y = 30 NOT have a unique solution?
(A) 12
(B) 9
(C) 3
(D) 7.5
(E) 2.5
Rationale: Explanatory Answer
Condition for Unique Solution to Linear Equations
A system of linear equations ax + by + c = 0 and dx + ey + g = 0 will have a unique solution if the two lines represented by the equations ax + by + c = 0 and dx + ey + g = 0 intersect at a point.
i.e., if the two lines are neither parallel nor coincident.
Essentially, the slopes of the two lines should be different.
What does that translate into?
ax + by + c = 0 and dx + ey + g = 0 will intersect at one point if their slopes are different.
Express both the equations in the standardized y = mx + c format, where 'm' is the slope of the line and 'c' is the y-intercept.
ax + by + c = 0 can be written as y = −abx−ca−abx−ca
And dx + ey + g = 0 can be written as y = −dex−ge−dex−ge
Slope of the first line is −ab−ab and that of the second line is −de−de
For a unique solution, the slopes of the lines should be different.
∴ −ab≠−de−ab≠−de
Or ad≠bead≠be
Condition for the equations to NOT have a unique solution
The slopes should be equal
Or ad=bead=be
Apply the condition in the given equations to find k
In the question given above, a = 3, b = 4, d = k and e = 12.
Therefore, 3k=4123k=412
Or 'k' should be equal to 9 for the pair of equations to NOT have a unique solution.
When k = 9, the system of equations will represent a pair of parallel lines (their y-intercepts are different). So, there will be NO solution.
Answer B
Answer: (B) 9
Question: If two positive numbers are in the ratio 1/6 : 1/5, then by what percent is the second number more than the first?
(A) 70%
(B) 90%
(C) 60%
(D) 50%
(E) 20%
Rationale: Given ratio = 1/6 : 1/5 = 5 : 6
Let first number be 5x and the second number be 9x.
The second number is more than first number by 1x.
Required percentage = x/5x * 100 = 20%.
Answer:E
Answer: (E) 20%
Question: Two trains of length 100 m and 200 m are 90 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. After how much time will the trains meet?
(A) 21/9 sec
(B) 32/3 sec
(C) 18/7 sec
(D) 32/3 sec
(E) 53/2 sec
Rationale: They are moving in opposite directions, relative speed is equal to the sum of their speeds.
Relative speed = (54 + 72)*5/18 = 7*5 = 35 mps.
The time required = d/s = 90/35 = 18/7 sec.
Answer:C
Answer: (C) 18/7 sec
Question: If the annual increase in the population of a town is 10% and the present number of people is 14000, what will the population be in 2 years?
(A) 12100
(B) 15240
(C) 12456
(D) 16940
(E) 10002
Rationale: The required population is = 14000 (1 + 10/100)^2
= 14000 * 11/10 * 11/10
= 16940
Answer is D
Answer: (D) 16940
Question: A reduction of 30% in the price of oil enables a house wife to obtain 5kgs more for Rs.800, what is the reduced price for kg?
(A) s.42
(B) s.46
(C) s.48
(D) s.41
(E) s.34
Rationale: 800*(25/100) = 240 ---- 5
? ---- 1 => Rs.48
Answer: C
Answer: (C) s.48
Question: If a /2= b/3 = c/5, then the value of (a + b + c)/c is :
(A) 1/√5
(B) √2
(C) 2
(D) 5
(E) 6
Rationale: a/2= b/3 = c/5 = k (say).
Then, a = 2k, b = 3k, c = 5k.
(a + b + c)/c = (2k + 3k + 5k)/5k
= 10k/5k
= 2.
ANSWER:C
Answer: (C) 2
Question: In how many of ways can 4 balls be placed in 5 tins if any number of balls can be placed in any tin?
(A)  5C4
(B)  5P4
(C)  54
(D)  4^5
(E)  5^4
Rationale: Now, each of the 4 different balls has 5 choices (5 tins to go to), so total # of distribution is 5*5*5*5=5^4.
Answer: E.
Answer: (E)  5^4
Question: In how many ways Chief Minister and Minister be elected from a team of 12 members?
(A) 124
(B) 131
(C) 132
(D) 145
(E) 165
Rationale: To do this, if captain is elected first, then we have 12 ways of doing this.
For election of vice-captain, we have only 11 ways left, coz 1 way is already consumed. (Situations like this is called dependent situation. One selection depends upon other selection.)
So, the ans is 12*11 = 132 ways.
C
Answer: (C) 132
Question: When positive integer N is divided by positive integer J, the remainder is 26. If N/J = 150.40, what is value of J?
(A) 75
(B) 65
(C) 60
(D) 130
(E) 30
Rationale: When a number is divided by another number, we can represent it as : Dividend = Quotient * Divisor + Remainder
So, Dividend/Divisor = Quotient + Remainder/Divisor
Given that N/J = 150.40
Here 150 the quotient.
Given that Remainder = 26
So, 150.40 = 150 + 26/J
So, J = 65
Answer: B
Answer: (B) 65
Question: The ratio between the radii of two spheres is 1:3. Find the ratio between their volumes?
(A) 1:28
(B) 1:27
(C) 1:22
(D) 1:21
(E) 1:29
Rationale: r1 : r2 = 1:3
r13 : r23 = 1:27
Answer: B
Answer: (B) 1:27
Question: The speed of a boat in still water is 20 km/hr and the rate of current is 5 km/hr. The distance travelled downstream in 21 minutes is:
(A) 9.75
(B) 5.75
(C) 8.75
(D) 6.75
(E) 5.15
Rationale: Explanation:
Speed downstream = (20+5) kmph = 25 kmph
Distance travelled = (25*(21/60)) km = 8.75 km.
ANSWER:C
Answer: (C) 8.75
Question: The simple form of the ratio 4/3:2/5 is?
(A) 10:6
(B) 10:3
(C) 15:3
(D) 25:3
(E) 30:3
Rationale: 4/3 : 2/5 = 20:6 = 10:3
ANSWER:B
Answer: (B) 10:3
Question: During a sale, the price of a pair of shoes is marked down 15% from the regular price. After the sale ends, the price goes back to the original price. What is the percent of increase to the nearest percent from the sale price back to the regular price for the shoes?
(A) 9%
(B) 10%
(C) 11%
(D) 18%
(E) 90%
Rationale: Assume the price = 100
Price during sale = 85
Price after sale = 100
Percent increase = 15/85*100 = 18% approx.
Correct Option: D
Answer: (D) 18%
Question: The train 160 m long is running with a speed of 80 km/hr. In what time will it pass a man running in same direction with the speed of 8 km/hr.
(A) 16 seconds
(B) 8 seconds
(C) 15 seconds
(D) 6 seconds
(E) 28 seconds
Rationale: Man and train are running in same direction,
Relative Speed = 80 - 8 = 72 kmph. = (72 * 5)/18 = 20 m/sec
Length of the train = 160 m.
Time taken to pass the man = 160/20 = 8 seconds.
Answer: Option B
Answer: (B) 8 seconds
Question: In a college, 70 percent of students study math, 75 percent of students study English, 85 percent study French and 80 percent study German.
Can you find out the percentage of students who study all 4 subjects ?
(A) 12%
(B) 10%
(C) 16%
(D) 18%
(E) 19%
Rationale: B
10% of student study all four subjects.
Answer: (B) 10%
Question: If the perimeter of a rectangular garden is 950 m, its length when its breadth is 100 m is?
(A) 338 m
(B) 778 m
(C) 375 m
(D) 276 m
(E) 971 m
Rationale: 2(l + 100)
= 950 => l
= 375 m
Answer:C
Answer: (C) 375 m
Question: A man is walking at a speed of 10 km per hour. After every kilometre, he takes rest for 5 minutes. How much time will be take to cover a distance of 5 kilometres?
(A) 48 min.
(B) 50 min.
(C) 45 min.
(D) 55 min
(E) None of these
Rationale: explanation
Rest time = Number of rest × Time for each rest
= 4 × 5 = 20 minutes
Total time to cover 5km
= (5⁄10 × 60)minutes + 20 minutes = 50 minutes
Answer B
Answer: (B) 50 min.
Question: A caterer ordered 200 ice-cream bars and 200 sundaes. If the total price was $200.00 and the price of each ice-cream bar was $0.40, what was the price of each sundae?
(A) $0.60
(B) $0.80
(C) $1.00
(D) $1.20
(E) $1.60
Rationale: Let price of a sundae = S
Price of ice cream bar = .4 $
200 * .4 + 200*S = 200
=> 200*S = 200
=> S =0.6
Answer A
Answer: (A) $0.60
Question: A card is drawn from a pack of 52 cards.The probability of getting a queen club or a king of heart?
(A) 3/26
(B) 1/26
(C) 4/26
(D) 6/26
(E) 10/26
Rationale: n(s)=52
Let e=event of getting a queen of club or a king of heart.
n(e)=2
P(e)=n(e)/n(s)
=2/52
=1/26
Option:B
Answer: (B) 1/26
Question: Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety of tea in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, what is the price of the third variety per kg ?
(A) Rs.182.50
(B) Rs.170.5
(C) Rs.175.50
(D) Rs.180
(E) Rs.190
Rationale: Explanation:
Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed in the ratio 1 : 1
So their average price
=(126 + 135)/2=130.5
Hence let's consider that the mixture is formed by mixing two varieties of tea, one at Rs. 130.50 per kg and the other at Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. Now let's find out x
By rule of alligation,
(xâˆ’153):22.5=1:1
â‡’xâˆ’153=22.50
â‡’x=153+22.5=175.5
Answer IS C
Answer: (C) Rs.175.50
Question: M is a certain set of numbers with an average (arithmetic mean) of 10 and a standard deviation of 3. Q is a subset of M consisting of 5 terms. Exactly 80% of the numbers in Q are located within 2 standard deviations from the average of M. Which of the following could Q be?
(A) {3, 4, 5, 10, 14}
(B) {4, 6, 7, 10, 12}
(C) {3, 5, 5, 10, 17}
(D) {1, 5, 7, 10, 18}
(E) {5, 6, 7, 10, 12}
Rationale: Exactly 80% of the numbers in Q, so 4 out of 5 numbers are from 10 - 2*{SD} = 4 to 10 + 2*{SD} = 16.
A. {3, 4,5, 10, 14} --> 4 numbers are in this range. Ok
B. {4,6, 7, 10, 12} --> all 5 numbers are in this range. Discard.
C. {3,5, 5, 10, 17} --> only 3 numbers are in this range. Discard.
D. {1,5, 7, 10, 18} --> only 3 numbers are in this range. Discard.
E. {5, 6, 7, 10, 12} --> all 5 numbers are in this range. Discard.
Answer: A.
Answer: (A) {3, 4, 5, 10, 14}
Question: At a certain paint store forest green is made by mixing 4 parts blue paint with 3 parts yellow paint.Verdant green is made by mixing 4 parts yellow paint with 3 parts blue paint.How many liters of yellow paint must be added to 35 liters of forest green to change it to Verdant green?
(A) 1/3
(B) 2/3
(C) 4/3
(D) 35/3
(E) 10/3
Rationale: 35 liter of Forset green have 20 liter of blue and 15 liter of yellow
Suppose we add x liter of yellow to make it a verdant green so the ratio of blue to yellow in verdant green is ¾ so the equation is
Blue/yellow =20/(15+x) = ¾
45+3x=80 => x =35/3
Answer : D
Answer: (D) 35/3
Question: Which of these numbers is not divisible by 3?
(A) 339
(B) 342
(C) 552
(D) 1111
(E) 672
Rationale: One may answer this question using a calculator and test for divisibility by 3. However we can also test for divisibilty by adding the digits and if the result is divisible by3 then the number is divisible by 3.
3 + 3 + 9 = 15 , divisible by 3.
3 + 4 + 2 = 9 , divisible by 3.
5 + 5 + 2 = 12 , divisible by 3.
1 + 1 + 1 + 1 = 4 , not divisible by 3.
The number 1111 is not divisible by 3 the answer is D.
Answer: (D) 1111
Question: If (t-8) is a factor of t^2-kt-40, then k=
(A) 16
(B) 1
(C) 2
(D) 6
(E) 14
Rationale: t^2-kt-48 = (t-8)(t+m) where m is any positive integer.
if 48/8 = 6, then we know as a matter of fact that:
m = +6
and thus k = 8-6 = 1
t^2-kt-m = (t-a)(t+m) where a>m
t^2+kt-m = (t-a)(t+m) where a<m
t^2-kt+m = (t-a)(t-m)
t^2+kt+m = (t+a)(t+m)
B
Answer: (B) 1
Question: A man buys a cycle for Rs. 1750 and sells it at a loss of 8%. What is the selling price of the cycle?
(A) s. 1090
(B) s. 1610
(C) s. 1190
(D) s. 1202
(E) s. 1092
Rationale: S.P. = 92% of Rs. 1750 = Rs.	92	x 1750/100 = Rs. 1610
Answer: Option B
Answer: (B) s. 1610
Question: A train passes a station platform in 42 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) 123
(B) 166
(C) 240
(D) 157
(E) 330
Rationale: Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, (x + 300) / 42 = 15
x + 300 = 630
x = 330 m.
Answer: E
Answer: (E) 330
Question: The value of Underrot 72pi/9 + Underrot 4 is most nearly equal to which of the following integers? (Please refer to the picture below for the exact version of the question)
(A) 27
(B) 14
(C) 18
(D) 19
(E) 21
Rationale: Under root (72pi/9) ~ 25
Under root (4) = 2
Hence, 9+1 = 10 is the approx answer. A is the correct answer.
Answer: (A) 27
Question: A boy swims downstream 91 km and upstream 21 km taking 7 hours each time, what is the speed of the boy in still water?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: 91 --- 7 DS = 13
? ---- 1
21 ---- 7 US = 3
? ---- 1 M = ?
M = (13 + 3)/2 = 8
Answer:C
Answer: (C) 8
Question: Pipes A and B can fill a tank in 5 hours and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in.
(A) 3 9/5
(B) 3 9/17
(C) 3 7/5
(D) 3 7/17
(E) None of these
Rationale: Explanation:
Net part filled in 1 hour =(1/5 + 1/6 - 1/12)
=17/60hrs
=3 9/17
Answer is B
Answer: (B) 3 9/17
Question: If 1/(6 + 3/x) = 1, then x =
(A) -3/5
(B) 1
(C) 1/3
(D) -1/3
(E) -3
Rationale: The expression 1/(6 + 3/x) = 1/x) should have been equal to something .
If 1/(6 + 3/x) = 1
=> x/(6x + 3) = 1
=> x = 6x + 3
=>-5x = 3
=>x = -3/5
Correct Option: A
Answer: (A) -3/5
Question: How many 7-letter words can be formed using the letters of the English alphabet that contain 2 different vowels and 5 different consonants?
(A) 4!*5c2 *21c2
(B) 4!*5c3 *21c2
(C) 5!*5c2 *21c2
(D) 7!*5c2 *21c5
(E) 6!*5c2 *21c2
Rationale: combination for 2 vowels out of 5 = 5c2 ways
combination for 5 consonants of 21 = 21c5 ways
Additionally the arrangement can be = 7!
total arrangements =7!*5c2 *21c5
D
Answer: (D) 7!*5c2 *21c5
Question: A box contains 90 nuts each of 100 gms and 100 bolts each of 150 gms. If the entire box weighs 35.5 kg., then the weight of the empty box is
(A) 8
(B) 9.5
(C) 10
(D) 11.5
(E) 12
Rationale: Let w(e) be weight of empty box.
Total weight = 35.5 Kg
Weight of nuts, w(n) = 90 * 100 = 9000gms = 9 kg
Weight of bolts, w(b) = 100 * 150 = 15000gms = 15 kg
Total weight = w(n)+w(b)+w(e)
w(e) = Total weight-w(n)-w(b)
=> w(e) = 35.5-15-9=11.5 Answer : D
Answer: (D) 11.5
Question: January 1, 2007 was Monday. What day of the week lies on Jan. 1, 2008 ?
(A) Monday
(B) Tuesday
(C) wednesday
(D) Sunday
(E) None of these
Rationale: Solution
The year 2007 is an ordinary year. So, it has 1 odd day.
1st day of the year 2007 was Monday.
1st day of the year 2008 will be 1 day beyond Monday.
Hence, it will be Tuesday. Answer B
Answer: (B) Tuesday
Question: a is the hundreds digit of the three digit integer x, b is the tens digit of x, and c is the units digit of x. 4a = 2b = c, and a > 0.
What is the difference between the two greatest possible values of x?
Tip: Dont stop till you have exhausted all answer choices to arrive at the correct one.
(A) 124
(B) 297
(C) 394
(D) 421
(E) 842
Rationale: Ratio of a:b:c= 1:2:4
Two possible greatest single digit values for c are 8 and 4
if c is 8, then x= 248
if c is 4, then x= 124
difference= 248-124= 124
A is the answer
Answer: (A) 124
Question: If (c - a)/(c - b) = 1, then (5b - 2a)/(c - a) =
(A) 0.5
(B) 1
(C) 1.5
(D) 2
(E) 6
Rationale: Let's say c=3, b=2, a=2 so that our 1st expression holds true. Now, ibsert those numbers in the second expression and we'll get 6
Answer E (hopefully )))
Answer: (E) 6
Question: Michael cashed a check for $1,300 and received only $10 and $50 bills in return. During the course of a day, he used 15 bills and then lost the rest of the money. If the number of $10 bills used was either one more or one less than the number of $50 bills used, what is the minimum possible amount of money that was lost?
(A)  $830
(B)  $800
(C)  $770
(D)  $730
(E)  $700
Rationale: 1. 15 bills spent
2. Number of $10 bills is one more or one less than number of $50 bills.
So, 2 choices
1. 7*10 + 8*50 = $470
2. 8*10 + 7*50 = $430
Least money lost implies most money spent. i.e $470
Therefore, lost money = 1300 - 470 = 830.
Answer A
Answer: (A)  $830
Question: A baseball team won 55 percent of the first 80 games it played. How many of the remaining 82 games will the team have to win in order to have won exactly 50 percent of all the games it played?
(A) 36
(B) 45
(C) 50
(D) 55
(E) 37
Rationale: Games won out of first 80 questions = (55/100)*80 = 44
Total Games = 80+82 = 162
Games to be won = (50/100)*162 = 81
Remaining games to be won = 81-44 = 37
Answer: Option E
Answer: (E) 37
Question: If there are 9 horizontal lines and 9 vertical lines in a chess board, how many rectangles can be formed in the chess board?
(A) 1452
(B) 1243
(C) 1564
(D) 1296
(E) 1234
Rationale: Number of rectangles that can be formed by using m horizontal lines and n vertical lines
= mC2 × nC2
Here m = 9, n = 9
Hence, number of rectangles that can be formed
= mC2 × nC2
= 9C2 × 9C2 = (9C2)2
=(9×82×1)2=362=1296=(9×82×1)2=362=1296
Ans: D
Answer: (D) 1296
Question: In the coordinate plane, Line A has a slope of -2 and an x-intercept of 2. Line B has a slope of 5 and a y-intercept of -10. If the two lines intersect at the point (a,b), what is the sum a+b?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: The equation of Line A is y = -2x + 4
The equation of Line B is y = 5x - 10
5x - 10 = -2x + 4
x = 2
y = 0
The point of intersection is (2,0) and then a+b = 2.
The answer is C.
Answer: (C) 2
Question: A train 100 m long crosses a platform 125 m long in 15 sec; find the speed of the train?
(A) 29
(B) 28
(C) 54
(D) 27
(E) 21
Rationale: D = 100 + 125 = 225
T = 15
S = 225/15 * 18/5 = 54 kmph.Answer: C
Answer: (C) 54
Question: How many numbers between 190 and 580 are divisible by 4,5 and 6?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: Every such number must be divisible by L.C.M of 4,5,6 i.e, 60.
Such numbers are 240,300,360,420,480,540.
Clearly, there are 6 such numbers
ANSWER:A
Answer: (A) 6
Question: A and B started a partnership business investing some amount in the ratio of 3 : 5. C joined then after six months with an amount equal to that of B. In what proportion should the profit at the end of one year be distributed among A, B and C?
(A) 3 : 5 : 2
(B) 3 : 5 : 5
(C) 6 : 10 : 5
(D) Data inadequate
(E) None
Rationale: EXPLANATION
Let the initial investments of A and B be 3x and 5x.
A : B : C = (3x x 12) : (5x x 12) : (5x x 6) = 36 : 60 : 30 = 6 : 10 : 5.
Answer C
Answer: (C) 6 : 10 : 5
Question: During a trip on an expressway, Don drove a total of x miles. His average speed on a certain 5-mile section of the expressway was 20 miles per hour, and his average speed for the remainder of the trip was 60 miles per hour. His travel time for the x-mile trip was what percent greater than it would have been if he had traveled at a constant rate of 60 miles per hour for the entire trip?
(A) 8.5%
(B) 50%
(C) x/12%
(D) 300/x%
(E) 500/x%
Rationale: Say x = 5 miles (so no remainder of the trip).
Time to cover x = 5 miles at 20 miles per hour = (time) = (distance)/(rate) = 5/30 = 1/6 hours = 10 minutes.
Time to cover x = 5 miles at 60 miles per hour = (time) = (distance)/(rate) = 5/60 = 1/12 hours = 5 minutes.
(Or simply, half rate will result in doubling the time.)
So, we can see that the time to cover x = 3 miles at 30 miles per hour (10 minutes) is 100% greater than the time to cover x = 3 miles at 60 miles per hour (5 minutes).
Now, plug x = 3 miles into the answer choices to see which one yields 100%. Only answer E works.
Answer: D.
Answer: (D) 300/x%
Question: The equation x = 2y^2 + 5y - 16, describes a parabola in the xy coordinate plane. If line l, with slope of 3, intersects the parabola in the upper-left quadrant at x = -5, the equation for l is
(A) 3x + y + 15 = 0
(B) y + 3x - 1 = 0
(C) -3x + y - 16.5 = 0
(D) -2x - y - 7 = 0
(E) -3x + y + 13.5 = 0
Rationale: The line has a point (-5, y) on it where y is positive (since the point lies in upper left quadrant).
In options B , if you put x = -5, you get -ve value for y co-ordinate.
Answer must be (B)
Answer: (B) y + 3x - 1 = 0
Question: If four coins are tossed, the probability of getting heads only?
(A) 4/16
(B) 2
(C) 1/16
(D) 2/16
(E) 3/16
Rationale: Since four coins are tossed, sample space = 16
Getting heads=1
p(E) = 1/16
ANSWER:C
Answer: (C) 1/16
Question: Rs.1040 is divided amongst A, B, C so that 2 times A's share, 3 times B's share and 4 times C's share are all equal. Find A's share?
(A) 177
(B) 150
(C) 817
(D) 480
(E) 616
Rationale: A+B+C = 10402A = 3B = 4C = xA:B:C = 1/2:1/3:1/4= 6:4:36/13 * 1040= Rs.480Answer: D
Answer: (D) 480
Question: A train starts full of passengers at the first station it drops 1/3 of the passengers and takes 280 more at the second station it drops one half the new total and takes twelve more. On arriving at the third station it is found to have 250 passengers. Find the no of passengers in the beginning?
(A) 292
(B) 180
(C) 192
(D) 144
(E) 294
Rationale: Let no of passengers in the beginning be X
After first station no passengers=(X-X/3)+280=2X/3 +280
After second station no passengers =1/2(2X/3+280)+12
1/2(2X/3+280)+12=250
2X/3+280=2*238 = 476 - 280 = 196
2X/3=196
X=294. So the answer is option E) 294.
Answer: (E) 294
Question: A bag contains 5 green balls and 9 white balls. If two balls are drawn simultaneously, what is the probability that both balls are the same colour?
(A) 11/21
(B) 17/42
(C) 23/42
(D) 46/91
(E) 51/91
Rationale: The total number of ways to draw two balls is 14C2 = 91
The number of ways to draw two green balls is 5C2 = 10
The number of ways to draw two white balls is 9C2 = 36
P(two balls of the same colour) = 46/91
The answer is D.
Answer: (D) 46/91