mathewhe/aqua_rat huggingface dataset:
Question: The present ratio of students to teachers at a certain school is 35 to 1. If the student enrollment were to increase by 50 students and the number of teachers were to increase by 5, the ratio of students to teachers would then be 25 to 1. What is the present number of teachers?
(A) 5
(B) 8
(C) 10
(D) 12
(E) 15
Rationale: We are given that the ratio of students to teacher is 35 to 1. We can rewrite this using variable multipliers.
students : teachers = 35x : x
We are next given that student enrollment increases by 50 and the number of teachers increases by 5. With this change the new ratio becomes 25 to 1. We can put all this into an equation:
Students/Teachers  25/1 = (35x + 50)/(x + 5)
If we cross multiply we have:
25(x + 5) = 35x + 50
25x + 125 = 35x + 50
7.5 = x
x~8
Since x is the present number of teachers, currently there are 8 teachers.
Answer B.
Answer: (B) 8
Question: Anil can do a work in 15 days while Sunil can do it in 25 days. How long will they take if both work together?
(A) 12 days
(B) 5 days
(C) 9 3/8 days
(D) 8 days
(E) 6 days
Rationale: Explanation:
1/15 + 1/25 = 8/75
75/8 = 9 3/8 days
Answer: C
Answer: (C) 9 3/8 days
Question: Tom, working alone, can paint a room in 6 hours. Peter and John, working independently, can paint the same room in 3 hours and 6 hours, respectively. Tom starts painting the room and works on his own for one hour. He is then joined by Peter and they work together for an hour. Finally, John joins them and the three of them work together to finish the room, each one working at his respective rate. What fraction of the whole job was done by Peter?
(A) 1/2
(B) 1/3
(C) 1/4
(D) 2/3
(E) 2/5
Rationale: Tom paints 1/6 of the room in the first hour.
Tom and Peter paint 1/6+1/3 = 1/2 of the room in the next hour for a total of 4/6.
The three people then paint the remaining 2/6 in a time of (2/6) / (4/6) = 1/2 hours
Peter worked for 3/2 hours so he painted 3/2 * 1/3 = 1/2 of the room.
The answer is A.
Answer: (A) 1/2
Question: A material is purchased for Rs. 600. If one fourth of the material is sold at a loss of 20% and the remaining at a gain of 10%, Find out the overall gain or loss percentage
(A) 4 1/2
(B) 3 1/2
(C) 2 1/2
(D) 1 1/2
(E) None of these
Rationale: Explanation:
We need to get the Total selling price to solve this question. Because after getting selling price we can get profit or loss, then we can calculate profit% or loss%
So lets solve this:
Price Received by selling one fourth of the material at a loss of 20% =
(1/4) * 600 * (80/100) = Rs. 120
Price Received by remaining material at a gain of 10% =
(3/4) * 600 * (110/100) = Rs. 495 [Note: 1-(1/4) = 3/4]
Total Selling Price = 120 + 465 = Rs. 615
Profit = 615 - 600 = 15
Profit%=(Gain/Cost∗100)%=(15/600∗100)%=5/2%=2 1/2%
Option C
Answer: (C) 2 1/2
Question: Two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?
(A) 76 sec
(B) 12 sec
(C) 15 sec
(D) 14 sec
(E) 13 sec
Rationale: Speed of the first train = 120/10 = 12 m/sec.
Speed of the second train = 120/5 = 8 m/sec.
Relative speed = 12 + 8 = 20 m/sec.
Required time = (120 + 120)/20 = 12 sec.
Answer: B
Answer: (B) 12 sec
Question: A train passes a platform in 18 seconds. The same train passes a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, The length of the platform is
(A) 120
(B) 250
(C) 260
(D) 230
(E) 220
Rationale: Speed of the train = 54 km/hr = (54×10)/36 m/s = 15 m/s
Length of the train = speed × time taken to cross the man = 15×20 = 300 m
Let the length of the platform = L
Time taken to cross the platform = (300+L)/15
=> (300+L)/15 = 18
=> 300+L = 15×18 = 270
=> L = 390-270 = 120 meter
Answer is A.
Answer: (A) 120
Question: When m divided by 288, the remainder is 47. Find the remainder when the same m is divided by 24?
(A) 20
(B) 21
(C) 22
(D) 23
(E) 26
Rationale: 23
Option D
Answer: (D) 23
Question: Two good train each 650 m long, are running in opposite directions on parallel tracks. Their speeds are 45 km / hr and 30 km /hr respectively. Find the time taken by the slower train to pass the driver of the faster one.
(A) 12.4 sec
(B) 24.3 sec
(C) 62.4 sec
(D) 60.1 sec
(E) None
Rationale: Sol.
Relative Speed = (45 + 30) km / hr
= (75 x 5 / 18) m/sec
= (125/6) m/sec.
Distance covered = (650+ 650) m = 1300 m.
Required time = (1300 x 6 / 125) sec = 62.4 sec.
Answer C
Answer: (C) 62.4 sec
Question: How many ways are there for 5 males and 3 females to sit (around a circular table) if no male should sit next to a male (and no female next to female) and Mary wants to sit with her back on the wall?
(A) 6
(B) 12
(C) 240
(D) 100
(E) 720
Rationale: So Mary has her own chair, fixed position. Other two females around the table can sit in 2 ways: the first to the left of Mary and the second to the right or vise-versa. Now, if 5 males will sit between them then no two female or two male will sit next to each other (female-male-female-male-female-male). But these males on their spots can also sit in different ways, namely in 5! different ways, so total 2*5!=240.
Answer C.
Answer: (C) 240
Question: There are 6 boxes numbered 1, 2,…,.6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is
(A) 55
(B) 21
(C) 42
(D) 51
(E) 21
Rationale: List down possibilities: From only 1 box all the way to all 6
If only one of the boxes has a green ball, it can be any of the 6 boxes. So, we have 6 possibilities.
If two of the boxes have green balls and then there are 5 consecutive sets of 2 boxes. 12, 23, 34, 45, 56.
If 3 of the boxes have green balls, there are 4 possibilities: 123, 234, 345, 456.
If 4 boxes have green balls, there are 3 possibilities: 1234, 2345, 3456.
If 5 boxes have green balls, there are 2 possibilities: 12345, 23456.
If all 6 boxes have green balls, there is just 1 possibility.
Total number of possibilities = 6 + 5 + 4 + 3 + 2 + 1 = 21.
Ans: E
Answer: (E) 21
Question: In what ratio should two varieties of sugar of Rs.18 per kg and Rs.24 kg be mixed together to get a mixture whose cost is Rs.20 per kg?
(A) 16.55
(B) 16.59
(C) 16.54
(D) 16.5
(E) 16.51
Rationale: Let 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:D
Answer: (D) 16.5
Question: 19 times a number gives 342. The number is
(A) 18
(B) 19
(C) 16
(D) None
(E) Cannot be determined
Rationale: Explanation:
Let the number be 'N'
19×N=342⇒N=18
Correct Option: A
Answer: (A) 18
Question: A can do a piece of work in 10 days and B can do the same work in 12 days. A and B worked together for 5 days. How many more days are required to complete the remaining work if they work together?
(A) 3 (5/18)
(B) 3 (5/16)
(C) 3 (5/11)
(D) 3 (5/13)
(E) 5/11
Rationale: A can do 1/10 of the work in a day.
B can do 1/12 of the work in a 1 day.
Both of them together can do (1/10 + 1/12) part of work in 1 day = (6 + 5)/60 = 11/60
They take 60/11 days to complete the work together.
Given that they already worked for 5 days.
The number of days required to complete remaining work => 60/11 - 5 = 5/11 = 5/11 days.
Answer:E
Answer: (E) 5/11
Question: If -1<x<0, what is the median N of these six numbers listed below
1/x^3,1/x^2, 1/x,x, x^2,x^3
(A) 1/x
(B) x^2
(C) x^2(x+1)/2
(D) N=x(x^2+1)/2
(E) x^2/2x
Rationale: My approach: Put any value between -1 and 0. you will get the answer. lets say 0.5. so the list will be as follows:
-8,-2,-0.5,-0.125 and last two numbers will be positive so need to see that.
median will be between -0.5 and -0.125.
So, (x^3+x)/2 (D).
Answer: (D) N=x(x^2+1)/2
Question: The average of two numbers is P. If one number is Q, then the other number is
(A) 2Q
(B) 2P
(C) P - Q
(D) 2P-Q
(E) None of these
Rationale: Explanation :
Let the other number be x,
According to the question,
=> ( x + Q ) / 2 = P.
=> x + Q = 2P.
=> x = 2P - Q.
Hence, the required number is 2P - Q.
Answer : D
Answer: (D) 2P-Q
Question: The function F is defined for all positive integers n by the following rule: f(n) is the number of position integer each of which is less than n, and has no position factor in common with n other than 3. If p is any prime number then f(p)=
(A) p-1
(B) p-2
(C) (p+1)/2
(D) (p-1)/2
(E) 2
Rationale: The confusing moment in this question is its wording. Basically question is: how many positive integers are less than given prime number p which has no common factor with p except 1.
Well as p is a prime, all positive numbers less than p have no common factors with p (except common factor 1). So there would be p-1 such numbers (as we are looking number of integers less than p).
If we consider p=7 how many numbers are less than 7 having no common factors with 7: 1, 2, 3, 4, 5, 6 --> 7-1=6.
Answer: D.
Answer: (D) (p-1)/2
Question: The probability that A speaks truth is 1/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact?
(A) 16/35
(B) 16/39
(C) 16/36
(D) 18/33
(E) 18/32
Rationale: If both agree stating the same fact, either both of them speak truth of both speak false.
Probability = 1/5 * 4/7 + 4/5 * 3/7
= 4/35 + 12/35 = 16/35
Answer: A
Answer: (A) 16/35
Question: A rectangular room has the rectangular shaped rug shown as above figure such that the rug’s area is 140 square feet and its length is 4 feet longer than its width. If the uniform width between the rug and room is 4 feet, what is the area of the region uncovered by the rug (shaded region), in square feet?
(A) 32
(B) 36
(C) 40
(D) 46
(E) 256
Rationale: Rug's area = 140
which is (x) x (4+x) = 140
so x= 10
rug maintains a uniform distance of 4 feet
so room has dimension 10+8 and 14+8 i.e. 18 and 22
area of room 18x22 = 396
area covered is 140
so uncovered area is 396-140=256 (ANSWER E)
Answer: (E) 256
Question: Robert is travelling on his cycle andhas calculated to reach point A at 2 PM. if he travels at 10 kmph, he will reach there at 12Pm if he travels at 15 kmph. At what speed musthe travel to reach A at 1 PM?
(A) 9 kmph
(B) 11 kmph
(C) 12 kmph
(D) 15 kmph
(E) 18 kmph
Rationale: Let the distance travelled by x km.
Then, x - x = 2
10 15
3x - 2x = 60
x = 60 km.
Time taken to travel 60 km at 10 km/hr = 60 hrs = 6 hrs.
10
So, Robert started 6 hours before 2 P.M. i.e., at 8 A.M.
Required speed = 60 kmph. = 12 kmph.
5
C
Answer: (C) 12 kmph
Question: A car gets 40 kilometers per gallon of gasoline. How many gallons of gasoline would the car need to travel 210 kilometers?
(A) 8.25 gallons
(B) 7.5 gallons
(C) 6.55 gallons
(D) 5.25 gallons
(E) 4.5 gallons
Rationale: Each 40 kilometers, 1 gallon is needed. We need to know how many 40 kilometers are there in 210 kilometers?
210 / 40 = 5.25 * 1 gallon = 5.25 gallons correct answer D
Answer: (D) 5.25 gallons
Question: Carolyn bought 16 gumballs, Lew bought 12 gumballs, and Bob bought X gumballs. The average (arithmetic mean) number of gumballs the three bought is between 19 and 25, inclusive. What is the difference between the greatest number and the smallest number of gumballs Carey could have bought?
(A) 20
(B) 22
(C) 24
(D) 26
(E) 18
Rationale: Smallest gumballs = (19-16) + (19-12) +19= 29
Largest gumballs = (25-16) + (25-12) +25= 47
Difference = 47 - 29 = 18
E
Answer: (E) 18
Question: Exactly 28% of the reporters for a certain wire service cover local politics in Country X. If 30% of the reporters who cover politics for the wire service do not cover local politics in Country X, what percent of the reporters for the wire service do not cover politics?
(A) 20%
(B) 42%
(C) 44%
(D) 60%
(E) 84%
Rationale: Let's assume there are 100 reporters --> 28 reporters cover local politics.
Now, as 30% of the reporters who cover all politics do not cover local politics then the rest 70% of the reporters who cover politics do cover local politics, so if there are x reporters who cover politics then 70% of them equal to 28 (# of reporters who cover local politics): 0.7x=28 --> x=40, hence 40 reporters cover politics and the rest 100-40=60 reporters do not cover politics at all.
Answer: D.
Answer: (D) 60%
Question: A certain country had a total annual expenditure of $1.2 x 10^11 last year. If the population of the country was 240 million last year, what was the per capita expenditure?
(A)  $ 500
(B)  $1,000
(C)  $2,000
(D)  $3,000
(E)  $5,000
Rationale: Total expenditure / Population = per capita expenditure
Hence, (1,2 x 10^11) / 240 000 000 = (12 x 10^10) / (2,4 x 10^8) = 5 x 10^(10-8) =
5 x 10^2 = 500.
Answer is A.
Answer: (A)  $ 500
Question: 8796 x 223 + 8796 x 77 = ?
(A) 2736900
(B) 2738800
(C) 2658560
(D) 2716740
(E) None of them
Rationale: =8796 x (223+77) (by distributive law)
=8796 x 300
=2638800
Answer is B
Answer: (B) 2738800
Question: The no. of gift pack bought by Dexter is 1 more than the price, in rupees, of each gift pack. The amount of Rs.380 which Dexter had, fell short of the required amount. What is theamount by which he might have fallen short.
(A) 20
(B) 40
(C) 50
(D) 60
(E) 90
Rationale: Let the price of gift pack be 'aa'
Then number of packs bought =a+1=a+1
Hence total cost is a(a+1)a(a+1)
It is given that 380<a(a+1)380<a(a+1)
If a=19a=19, the total cost =19×20=380=19×20=380
Dexter would not have fallen short, If:
a=20a=20, a(a+1)=420a(a+1)=420
So he would have fallen short by Rs 40.
This is the minimum amount by which he may have fallen short.
B
Answer: (B) 40
Question: Last month, John rejected 0.5% of the products that he inspected and Jane rejected 0.8 percent of the products that she inspected. If total of 0.75 percent of the products produced last month were rejected, what fraction of the products did Jane inspect?
(A) 1/6
(B) 1/2
(C) 5/8
(D) 5/6
(E) 15/16
Rationale: X - fraction of products Jane inspected
(1 - X) - fraction of products John inspected
0.8(X) + 0.5(1-X) = 0.75
0.3X = 0.75 - 0.5
X = 0.25/0.3
X = 5/6
Therefore the answer is D: 5/6.
Answer: (D) 5/6
Question: If x and y are integers such that (x+1)^2 is less than or equal to 9 and (y-1)^2 is less than 64, what is the sum of the maximum possible value of xy and the minimum possible value of xy?
(A)  -16
(B)  -8
(C)  0
(D)  14
(E)  16
Rationale: (x+1)^2 <= 9
x <= 2
x >= -4
(y-1)^2 < 64
y < 9
y > -7
Max possible value of xy is -4 × -6 = 24
minimum possible value of xy is -4 × 8 = -32
-32 + 24 = -8
Answer : B
Answer: (B)  -8
Question: Suppose you have access to a large vat of distilled water, several gallons large. You have two precise measuring pipettes, one to measure exactly 1/5 of an ounce and one to measure exactly 1/6 of an ounce. You can pour precisely measured amounts into a beaker, which initially is empty. You can use either pipette to remove distilled water from the vat or from the beaker and use either pipette to dispense water into either of those receptacles, but you cannot use either pipette to take any quantity of distilled water other than the amount for which it is designed. Which of the following represents, in ounces, a precise amount of distilled water you can transfer from the vat to the beaker?
I. 1/6
II. 1/7
III. 1/12
(A) I only
(B) III only
(C) 1/30 and 11/30
(D) II and III only
(E) I, II, and III
Rationale: 1/5-1/6=1/30
1/5+1/6=11/30
Answer: C
Answer: (C) 1/30 and 11/30
Question: A year ago the proportion between Sham and Amir’s age was 4:3. 1 year hence the proportion of their ages will be 5:4. The total of their current ages is :
(A) 16 years
(B) 17 years
(C) 18 years
(D) 19 years
(E) 20 years
Rationale: A
16 years
A year ago, Sham’s age = 4A years
And, Amir’s age = 3A years
Current age of Sham = (4A + 1) years
Current age of Amir = (3A + 1) years
1 year hence, Sham’s age = (4A + 2) years
and Amir’s age = (3A + 1) years
So,
{ (4A + 2)/(3A +2) } = 5 /4
=> 16 + 8 = 15A + 10
or, A = 2
Total of their current ages = 4A + 1 + 3A + 1
= 7(A) + 2
= 7(2) + 2 = 16 years.
Answer: (A) 16 years
Question: The total marks obtained by a student in Mathematics and Physics is 60 and his score in Chemistry is 20 marks more than that in Physics. Find the average marks scored in Mathamatics and Chemistry together.
(A) 40
(B) 99
(C) 77
(D) 66
(E) 12
Rationale: Let the marks obtained by the student in Mathematics, Physics and Chemistry be M, P and C respectively.
Given , M + C = 60 and C - P = 20 M + C / 2 = [(M + P) + (C - P)] / 2 = (60 + 20) / 2 = 40.
Answer: A
Answer: (A) 40
Question: What approximate value should come in place of question mark (?) in the following equation
287.532 + 1894.029 – 657.48 = 843.095 + ?
(A) 870
(B) 790
(C) 680
(D) 770
(E) 890
Rationale: ? = 285 + 1895 – 655 – 845 or, ? = 680
Answer C
Answer: (C) 680
Question: A van takes 5 hours to cover a distance of 435 km. What speed in kph should the van maintain to cover the same distance in 3/2 of the previous time?
(A) 50
(B) 52
(C) 54
(D) 56
(E) 58
Rationale: (3/2)*5 = 7.5 hours
435 / 7.5 = 58 kph
The answer is E.
Answer: (E) 58
Question: What is the CP of Rs 100 stock at 8 discount, with 1/5% brokerage?
(A) 99.6
(B) 96.2
(C) 97.5
(D) 92.2
(E) None of these
Rationale: Explanation:
Use the formula,
CP= 100 â€“ discount + brokerage%
CP= 100-8+1/5
92.2
Thus the CP is Rs 92.2.
ANSWER D
Answer: (D) 92.2
Question: A TV is purchased at Rs. 5000 and sold at Rs. 4000, find the lost percent.
(A) 10%
(B) 20%
(C) 25%
(D) 28%
(E) 30%
Rationale: Explanation:
We know, C.P. = 5000
S.P. = 4000
Loss = 5000 - 4000 = 1000
Loss%=(LossCost∗100)%=(10005000∗100)%=20%
ANSWER IS B
Answer: (B) 20%
Question: A glass was filled with 10 ounces of water, and 0.03 ounce of the water evaporated each day during a 20-day period. What percent of the original amount of water evaporated during this period?
(A) 0.006%
(B) 0.06%
(C) 0.6%
(D) 6%
(E) 60%
Rationale: We are given that 0.03 ounces of water evaporated EACH DAY. Furthermore, we know that this process happened over a 20-DAY PERIOD. To calculate the total amount of water that evaporated during this time frame we need to multiply 0.01 by 20. This gives us:
0.03 x 20 = 0.6 ounces
Finally, we are asked for “What percent” of the original amount of water evaporated during this period. To determine this percentage, we have to make sure we translate the expression correctly. We can translate it to:
(Amount Evaporated/Original Amount) x 100%
(0.6/10) x 100%
(6/100) x 100% = 6%
Answer D
Answer: (D) 6%
Question: An investor purchased 100 shares of stock X at 6 1/8 dollars per share and sold them all a year later at 12 dollars per share. If the investor paid a 2 percent brokerage fee on both the total purchase price and the total selling price, which of the following is closest to the investor's percent gain on this investment?
(A) 192%
(B) 94%
(C) 280%
(D) 300%
(E) 380%
Rationale: If the purchase price was 6$ per share then the investor would have made a profit of 100%.
Since the purchase price is slightly more than 6$ the profit would be slightly less than 100%.
Also a 2% brokerage is negligible and it brings down the profit percentage only by a small value. Approximation is very useful to solve these kind of problems as the answer choices are far apart.
Answer:B
Answer: (B) 94%
Question: The price of a cycle is reduced by 25 per cent. The new price is reduced by a further 70 per cent. The two reductions together are equal to a single reduction of
(A) 45%
(B) 40%
(C) 35%
(D) 77.5%
(E) 30%
Rationale: Price = p
initially price reduced by 25% which means new price is 3/4P
Now on this new price further 70percent is reduced which means the new price is merely 30percent of 3/4P
==> (3/4)x(3/10)P = 9/40P is the new price after both deduction which is 22.5percent of the original value P. This implies this entire series of deduction is worth having discounted 77.5% of P. So answer is D = 77.5%
Answer: (D) 77.5%
Question: In a mixture of 13 litres, the ratio of milk and water is 3 : 2. If 3 liters of this mixture is replaced by 3 liters of milk, then what will be the ratio of milk and water in the newly formed mixture?
(A) 10 : 3
(B) 8 : 5
(C) 9 : 4
(D) 1 : 1
(E) 2:3
Rationale: EXPLANATION:
Given: Total quantity of mixture = 13 liters
3 litres of mixture is removed from the container – So, let's forget this altogether!
Now, you are left with only 10 litres of mixture in 3:2 ratio.
Milk in 10 litres mix = 10 x	3/(2+3)= 6 litres
Water in 10 litres mix = 10 x	2/(2+3)= 4 litres
We add 3 litres milk to this.
So, milk in new mix is = 6 liters + 3 litres = 9 litres
Water= 4 litres
Ratio of milk : water = 9 : 4
ANSWER IS C
Answer: (C) 9 : 4
Question: In a certain random experiment, exactly one of the outcomes A, B, and D will occur. In each random experiment, the probability that outcome A will occur is 1/3 , and the probability that outcome B will occur is 1/3. What is the probability that when the random experiment is conducted 6 independent times, each of outcomes A, B, and D will occur twice?
(A) 5/243
(B) 1/12
(C) 10/81
(D) 1/6
(E) 16/81
Rationale: Number of ways in which a group of 2A,2B,2D can be formed in any order = 6!/(2!*2!*2!) [ formula for total of 6 items with 2 each of similar kind)
Total number of ways in which the die can be thrown independently = _ _ _ _ _ _ ; there are 6 places .First can be filled in 3 different ways A/B/D; Second in 3 diff ways again and so on.
So total number of ways = 3X3X3X3X3X3 = 3^6
There fore probability = 6!/(2!x2!x2!) by 3^6 = 90/3^6 = 10/81 Answer C
Answer: (C) 10/81
Question: Bunny's brother Sunny is 562 days older to him while his sister Jenny is 75 weeks older to Sunny. If Jenny was born on Tuesday, on which day was Bunny born?
(A) Monday
(B) Tuesday
(C) Friday
(D) Saturday
(E) Thursday
Rationale: 562-(75*7)=37
37--------7*5=35
remaing 2+tuesday
ans:thursday
ANSWER:E
Answer: (E) Thursday
Question: 39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 3 hours a day, complete the work?
(A) 10
(B) 26
(C) 14
(D) 15
(E) 16
Rationale: Let the required number of days be x.
Less persons, More days (Indirect Proportion)
More working hours per day, Less days (Indirect Proportion)
Persons	30	:	39	:: 12 : x
Working hours/day	3	:	5
30 x 3 x x = 39 x 5 x 12
x =	(39 x 5 x 12)/(30 x 3)
x = 26.
ANSWER:B
Answer: (B) 26
Question: Carol and Jordan draw rectangles of equal area. If Carol's rectangle measures 5 inches by 24 inches and Jordan's rectangle is 2 inches long, how wide is Jordan's rectangle, in inches?
(A) 65
(B) 63
(C) 52
(D) 60
(E) 68
Rationale: Area of Carol's rectangle = 24*5 = 120
Let width of Jordan's rectangle= w
Since , the areas are equal
2w = 120
=>w = 60
Answer D
Answer: (D) 60
Question: Find the equation of a line which passes through A(4, -1) and is parallel to x axis.
(A) y=-2
(B) y=3
(C) y=2
(D) y=-1
(E) y=0
Rationale: The slope of a line which is parallel to x-axis is zero. So
y+1=0(x−4)→y+1=0→y=−1
ANSWER : D y=-1
Answer: (D) y=-1
Question: A function g(n), where n is an integer, is defined as the product of all integers from 1 to n. How many of the followings must be a prime number?
g(12) + 5; g(12) + 6; g(12) + 7; and g(12) + 8?
(A) 1
(B) 2
(C) 3
(D) 4
(E) none
Rationale: g(12) is the product of all integers from 1 to 12, so g(12) = 12!
Thus g(12) is a multiple of all the integers from 1 to 12.
Then g(12) is a multiple of 7, 8, 9, and 10.
7 divides g(12)+7
8 divides g(12)+8
9 divides g(12)+9
10 divides g(12)+10
The answer is E.
Answer: (E) none
Question: The value of P, when 4864 x 9P2 is divisible by 12, is:
(A) 2
(B) 5
(C) 8
(D) 9
(E) 1
Rationale: Since 4864 is divisible by 4, so 9P2 must be divisible by 3.
Therefore (11+P) must be divisible by 3.
Therefore least value of P is 1
ANSWER:E
Answer: (E) 1