mathewhe/aqua_rat huggingface dataset:
Question: What is the principal sum?
I.The sum amounts to Rs. 690 in 3 years at S.I.
II.The sum amounts to Rs. 750 in 5 years at S.I.
III.The rate of interest is 5% p.a.
(A) I and III only
(B) II and III only
(C) I and II only
(D) I and III only, or II and III only
(E) Any two of the three
Rationale: Explanation:
Clearly, any of the three will give us the answer.
answer is (E).
Answer: (E) Any two of the three
Question: A merchant gets a 5% discount on each meter of fabric he buys after the first 2,000 meters and a 7% discount on every meter after the next 1,500 meters. The price, before discount, of one meter of fabric is $2, what is the total amount of money the merchant spends on 5,000 meters of fabric?
(A) $8280
(B) $8520
(C) $8710
(D) $8930
(E) $9640
Rationale: For first 2000 meters he does not get any discount.
The price is 2*2000 = $4000
For next 1500 meters, he gets a 5% discount.
The price is 1.9*1500 = $2850
For the next 1500 meters, he gets a 7% discount.
The price is 1.86*1500 = $2790
The total price is $4000 + $2850 + $2790 = $9640
The answer is E.
Answer: (E) $9640
Question: A train crosses a platform of 150 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?
(A) 150
(B) 160
(C) 170
(D) 180
(E) 190
Rationale: Length of the train be ‘X’
X + 150/15 = X + 250/20
4X + 600 = 3X + 750
X = 150m
Answer: Option A
Answer: (A) 150
Question: The average marks of a class of 30 students is 40 and that of another class of 50 students is 60. Find the average marks of all the students?
(A) 52.5
(B) 52.9
(C) 52.1
(D) 52.3
(E) 42.5
Rationale: Sum of the marks for the class of 30 students = 30 * 40 = 1200
Sum of the marks for the class of 50 students = 50 * 60 = 3000
Sum of the marks for the class of 80 students =
1200 + 3000 = 4200
Average marks of all the students = 4200/80
= 52.5
Answer:A
Answer: (A) 52.5
Question: A table is bought for Rs.400/- and sold at Rs.450/- find gain or loss percentage
(A) 10%loss
(B) 12.5%gain
(C) 10%gain
(D) 15%loss
(E) 20% loss
Rationale: Formula = (Selling price ~ Cost price)/Cost price * 100
= (450 - 400)/400 = 12.5% gain
B
Answer: (B) 12.5%gain
Question: Employees at a company will vote for an executive team of five people from eight qualified candidates. The executive team consists of a president, a treasurer, and three warrant officers. If an executive team is considered different if any of the same people hold different offices, then how many possible executive teams A could be selected from the eight candidates?
(A) 56
(B) 120
(C) 210
(D) 1120
(E) 6720
Rationale: If an executive team is considered different if any of the same people hold different offices,....
so you will not have answer as 6720..
president could be by any of 8 person..
treasurer could be any out of remaining 7 person..
remaining three order does not matter, so we have to choose 3 out of 6=6c3=20..
total ways A= 8*7*20=1120..
ans D...
Answer: (D) 1120
Question: Ram works in a bakery. He made cookies that cost $1.75 and made $325. How many customer did he have?
(A) 200 customers
(B) 186 customers
(C) 250 customers
(D) 100customers
(E) 170 customers
Rationale: A cookie costs $1.75 adding another one is $3.5. 325 divided by 3.5 is 92.86 x 2 is 186. He had 186 customers. The correct answer is B.
Answer: (B) 186 customers
Question: George went to a fruit market with certain amount of money. With this money he can buy either 40 oranges or 40 mangoes. He retains 10% of the money for taxi fare and buys 20 mangoes. How many oranges can he buy?
(A) 25
(B) 30
(C) 20
(D) 16
(E) 12
Rationale: Let the amount of money be 200
Let cost of 1 Orange be 4
Let cost of 1 mango be 4
He decides to retain 10% of 200 = 20 for taxi fare, so he is left with 180
He buys 20 mangoes ( @ 4) so he spends 80
Money left is 100(180 - 80)
No of oranges he can buy = 100/4 =>25
So, George can buy 25 Oranges.
A
Answer: (A) 25
Question: If e is a positive integer and 10^e – 74 in decimal notation has digits whose sum is 440, what is the value of e?
(A) 40
(B) 44
(C) 45
(D) 46
(E) 50
Rationale: Answer E = 50
We have (10^e)-74, where the sum of the digits is 440.
100-74 = 26, so we already have 2+6 = 8 from the 440.
Because we have a power of 10, we will have numbers like 100, 1000, 10000 and so on. This minus 74 rests 26 and a lot of 9s. E.g: 1000-74 = 9926.
So dividing the 432/9 = 48, that`s the number of 9s. and we have 2 other numbers (2 and 6) wich were 00 before the subtraction.
So we have 48 + 2 as an e = 50
Answer: (E) 50
Question: There is a 1 km long wire placed on some number of poles which are in equal distance. If the number of poles is reduced by 1 then the distance of wire between each poles
increases 1(2/3).How many poles are there initially.
(A) 24
(B) 25
(C) 26
(D) 27
(E) 28
Rationale: 26
ANSWER:C
Answer: (C) 26
Question: Working alone, printers X, Y, and Z can do a certain printing job, consisting of a large number of pages, in 12, 10, and 20 hours, respectively. What is the ratio of the time it takes printer X to do the job, working alone at its rate, to the time it takes printers Y and Z to do the job, working together at their individual rates?
(A) 5/3
(B) 7/4
(C) 9/5
(D) 11/6
(E) 13/7
Rationale: The time it takes printer X is 12 hours.
The combined rate of Y and Z is 1/10 + 1/20 = 3/20
The time it takes Y and Z is 20/3
The ratio of times is 12 / (20/3) = 3*12/20 = 9/5
The answer is C.
Answer: (C) 9/5
Question: Julian owes his classmate Jenny 20 dollars. If he borrows 8 dollars how much will he owe her?
(A) 28
(B) 12
(C) -28
(D) 12
(E) 0
Rationale: Add how he has already borrowed and how much he is going to borrow
-20+-8
correct answer C)-28
Answer: (C) -28
Question: Last year a certain bond price with a face value of 5000 yielded 10% of its face value in interest. If that interest was approx 6.5 of the bond's selling price approx what was the bond's selling price?
(A) 7692
(B) 5325
(C) 5351
(D) 6000
(E) 6154
Rationale: Interest = 0.08*5000 = 0.065*selling price --> selling price = 0.1*5000/0.065 --> selling price = ~7692
Answer: A.
Answer: (A) 7692
Question: A girl was asked to multiply a certain number by 43. She multiplied it by 34 and got his answer less than the correct one by 1224. Find the number to be multiplied.
(A) 130
(B) 132
(C) 134
(D) 136
(E) 138
Rationale: Let the required number be x. Then,
43x – 34x = 1224 or 9x = 1224 or x = 136.
Required number = 136.
ANSWER:D
Answer: (D) 136
Question: A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 650 m long?
(A) 29
(B) 89
(C) 77
(D) 55
(E) 12
Rationale: Speed = 240/24 = 10 m/sec.
Required time = (240 + 650)/10 = 89 sec.Answer:B
Answer: (B) 89
Question: The probability that A speaks truth is 3/5 and that of B speaking truth is 5/7. What is the probability that they agree in stating the same fact?
(A) 19/35
(B) 19/39
(C) 19/36
(D) 19/33
(E) 19/32
Rationale: If both agree stating the same fact, either both of them speak truth of both speak false.
Probability = 3/5 * 5/7 + 2/5 * 2/7
= 15/35 + 4/35 = 19/35
Answer: A
Answer: (A) 19/35
Question: A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec. What is the length of the platform?
(A) 266
(B) 350
(C) 327
(D) 267
(E) 256
Rationale: Speed = 300/18 = 50/3 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/39 = 50/3
3x + 900 = 1950 => x = 350 m.
Answer:B
Answer: (B) 350
Question: In how many ways letters of the word HAPPY be arranged?
(A) 10
(B) 60
(C) 120
(D) 25
(E) 40
Rationale: HAPPY has 5 letters, out of which P repeated 2 times Hence total ways = 5! / 2!= 60 ways
B
Answer: (B) 60
Question: For 2consecutive yrs, my incomes are in the ratio of 4:7 and expenses in the ratio of 3:5. If my income in the 2nd yr is Rs. 42000 & my expenses in the first yr in Rs.23000, my total savings for the two-year is
(A) s. 8000
(B) s. 9000
(C) s. 9900
(D) s. 9990
(E) s. 10000
Rationale: Sol. Income in first year = * x 42000 = Rs. 24000
Expenses in second year = \ x 21000 = Rs. 35000 Total savings = Total income - Total expenses = (42000 + 24000)- (23000 + 35000)
= 66000 - 58000 = Rs. 8000
A
Answer: (A) s. 8000
Question: In 1950, Richard was 4 times as old as Robert. In 1955, Richard was 3 times as old as Robert. In which year was Richard 1.25 as old as Robert?
(A) 1960
(B) 1965
(C) 1970
(D) 2050
(E) 2060
Rationale: In 1950: Ri = 4 Ro -------------- eq1
In 1955: Ri +5 = 3(Ro+5)---------eq2
Thus in 1950, solving eq1 and eq2
Ro= 10 , Ri =40
Now for each year we can calculate:
1960: Ri = 50 , Ro =20
1965: Ri= 55, Ro=25
2060: Ri= 120, Ro = 150
Thus Ans:E
Answer: (E) 2060
Question: A is twice as good a work man as B and together they finish the work in 10 days. In how many days A alone can finish the work?
(A) 23
(B) 15
(C) 77
(D) 92
(E) 61
Rationale: WC = 2:1
2x + x = 1/10 => x = 1/30
2x = 1/15
A can do the work in 15 days.
Answer: B
Answer: (B) 15
Question: A company that ships boxes to a total of 12 distribution centers uses color coding to identify each center. If either a single color or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors, what is the minimum number of colors needed for the coding? (Assume that the order of the colors in a pair does not matter.)
(A) 4
(B) 5
(C) 6
(D) 12
(E) 24
Rationale: Let's start with 4 minimum number of colors
So single color code we can make 4 nos.
Now if we need to make 2 color combination out of 4 we can do so in 4!/2!*2! or 4*3/2 or 6
So total we can make 4+6=10 color combinations but we have 12 boxes
So let's look at 5 we get 5 single color codes
and out 5 color choices, we can choose 2 in 5!/2!*3! ways or 10 ways.
So total we can have 5+10=15 color combinations.
So, minimum number we need will be 5
Ans is B.......
Answer: (B) 5
Question: Three candidates contested an election and received 600, 7025 and 11620 votes respectively. What percentage of the total votes did the winning candidate get?
(A) 57%
(B) 60.3%
(C) 65%
(D) 90%
(E) 80%
Rationale: total votes are 19245 ( sum of votes obtained by 3 candidates)
percentage of the total votes recd by the winning candidate = 100*11620/19245 = 60.3%
ANSWER:B
Answer: (B) 60.3%
Question: You collect baseball cards. Suppose you start out with 16. Since you're nice, you give John 6 baseball cards. How many baseball cards do you have at the end?
(A) 11
(B) 12
(C) 13
(D) 14
(E) 10
Rationale: Solution
Start with 16 baseball cards.
John takes 6 baseball cards from you: 16 - 6 = 10 baseball cards.
So you have 10 at the end.
Correct answer : E
Answer: (E) 10
Question: In how many different number of ways 6 men and 4 women can sit on a shopa which can accommodate persons?
(A) 17
(B) 90
(C) 20
(D) 21
(E) 23
Rationale: 10p2 = 10 Ã— 9 = 90
Answer : B
Answer: (B) 90
Question: the present average age of a couple and their daughter is 35 years. Fifteen years from now, the age of the mother will be equal to the sum of present ages of the father and the daughter. Find the present age of mother?
(A) 22 years
(B) 77 years
(C) 76 years
(D) 45 years
(E) 56 years
Rationale: (f + m + d)/3 = 35
=> f + m + d = 105 --- (1)
m + 15 = f + d
Substituting f + d as m + 15 in (1), we get
2m + 15 = 105
2m = 90 => m = 45 years.
Answer: D
Answer: (D) 45 years
Question: Find four consecutive even integers so that the sum of the first two added to twice the sum of the last two is equal to 766.
(A) 124 ,126, 128, 130
(B) 120 ,122 , 124 ,128
(C) 120 ,121 , 122 ,123
(D) 123 ,125 , 127 ,129
(E) None of these
Rationale: Let x, x + 2, x + 4 and x + 6 be the four integers. The sum of the first two
x + (x + 2)
twice the sum of the last two is written as
2 ((x + 4) + (x + 6)) = 4 x + 20
sum of the first two added to twice the sum of the last two is equal to 766 is written as
x + (x + 2) + 4 x + 20 = 766
Solve for x and find all four numbers
x = 124 , x + 2 = 126 , x + 4 = 128 , x + 6 = 130
Answer A
Answer: (A) 124 ,126, 128, 130
Question: Select a card from pack of 52 playing cards, 2cards are drawn together at random. Find the probability of both the cards being king ?
(A) 1/111
(B) 2/121
(C) 1 by 221
(D) 2/213
(E) 3/412
Rationale: Two cards can be drawn from a pack of 52 playing cards in 52C2 ways. i,e., 52 x 51 / 2 = 1326 ways. The event that two kings appear in a single drawn of cards is 4C2 ways, i.e 6 ways.
∴ The probability that the two cards drawn from a pack of 52 cards are kings = 6/1326 = 1/221
C
Answer: (C) 1 by 221
Question: If Dev works alone he will take 20 more hours to complete a task than if he worked with Tina to complete the task. If Tina works alone, she will take 5 more hours to complete the complete the task, then if she worked with Dev to complete the task? What is the ratio of the time taken by Dev to that taken by Tina if each of them worked alone to complete the task?
(A) 4 : 1
(B) 2 : 1
(C) 10 : 1
(D) 3 : 1
(E) 1 : 2
Rationale: Let time taken by Dev to complete the work alone be x days and that by Tina be y days
Work done by Dev in 1 day = 1/x
Work done by Tina in 1 day = 1/y
Work done by DevTina in 1 day = 1/x + 1/y = (x+y)/xy
Thus working together they will complete the work in xy/(x+y) days
Acc. to the ques :
1)If Dev works alone he will take 20 more hours to complete a task than if he worked with Tina'
x - xy/(x+y) = 20
=> (x^2)/(x+y) = 20.............(i)
2)If Tina works alone, she will take 5 more hours to complete the complete the task, then if she worked with Dev
y - xy/(x+y) = 5
=> (y^2)/(x+y) = 5..............(ii)
Dividing (i) by (ii)
x^2/y^2 = 4
=> x/y = 2
Ans : B
Hope it helps
Answer: (B) 2 : 1
Question: 6x – 5y + 3z = 27
4x + 8y – 11z = 7
5x – 6y + 2z = 12
Given the equations above, x + y + z = ?
(A)  11
(B)  12
(C)  13
(D)  14
(E)  15
Rationale: (6x – 5y + 3z) - (5x – 6y + 2z ) = 27-12
or, x+y+z = 15
Option E is the ans
Answer: (E)  15
Question: In how many different number of ways a combination of 3 persons can be selected from 4 boys and 2 girls.
(A) 152
(B) 160
(C) 176
(D) 180
(E) 200
Rationale: 6C3 × 5C2
6C3
= 6!/(3! . 3!)
= (6 × 5 × 4)/(3 × 2)
= 5 × 4 = 20.
5C2
= 5!/(3! . 2!)
= 5 × 2 = 10
= 20 × 10 = 200.
E)
Answer: (E) 200
Question: What is the tens digit of 36^4?
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
Rationale: 36^10 = 6^20
(6^2)=6*6 = 36
(6^3)= 36*6 = .16
(6^4)= .16*6 = ..96
(6^5) = ..96*6 = ..76
(6^6) = ..76*6 = ...56
(6^7) = ....56*6 = ....36
If you see there is a pattern here in tens digits 3,1,9,7,5,3,1 and so on...
Continue the pattern up to 6^6 ( dont actually calculate full values) and answer is C: 5
Answer: (C) 5
Question: A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
(A) 350m
(B) 380m
(C) 350m
(D) 320m
(E) 150m
Rationale: Speed = [300 / 18] m/sec = 50/3 m/sec.
Let the length of the platform be x meters.
Then, x + 300 / 39 = 50/3
3(x + 300) = 1950 è x = 350m.
Answer: C
Answer: (C) 350m
Question: The average of 10 numbers was calculated as 17. It is discovered later on that while calculating the average, one number, namely 56, was incorrectly read as 26. What is the correct average?
(A) 19
(B) 20
(C) 21
(D) 22
(E) 23
Rationale: 10*17 - 26 + 56 = 200
200 / 10 = 20
The answer is B.
Answer: (B) 20
Question: In how many different number of ways 5 men and 2 women can sit on a shopa which can accommodate persons?
(A) 190
(B) 200
(C) 205
(D) 210
(E) 220
Rationale: Answer: Option 'D'
7p3 = 7 × 6 × 5 = 210
Answer: (D) 210
Question: How many kilograms of sugar costing Rs.9 per kg must be mixed with 27 kg of sugar costing Rs.7 per Kg so that there may be a gain of 10% by selling the mixture at Rs.9.24 per Kg?
(A) 36 Kg
(B) 42 Kg
(C) 54 Kg
(D) 63 Kg
(E) None of these
Rationale: Solution
Ratio of quantities of 1st and 2nd kind = 14 : 6 = 7 : 3.
Let x kg of sugar of 1st kind be mixed with 27 kg of 2nd kind.
Then, 7 : 3 = x : 27 or x = (7 x 27 / 3) = 63 kg
Answer D
Answer: (D) 63 Kg
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is ?
(A) 1:3
(B) 3:2
(C) 3:5
(D) 3:7
(E) None of these
Rationale: Explanation:
Let the speeds of the two trains be x m/sec and y m/sec respectively.
Then, length of the first train = 27x metres,
Length of the second train = 17y metres.
[because distance = speed*time]
27x+17y /x+y=23
=>27x+17y=23x+23y
=>4x=6y
=>x/y=6/4
So ratio of the speeds of train is 3:2
Option B
Answer: (B) 3:2
Question: If two numbers are in the ratio 5:2. If 10 is added to both of the numbers then the ratio becomes 5:4 then find the largest number?
(A) 3
(B) 7
(C) 4
(D) 5
(E) 6
Rationale: 5:2
5x + 10 : 2x + 10 = 5 : 4
5[2x + 10] = 4[5x + 10]
10x + 50 = 20x + 40
20x - 10x = 50 - 40
x = 1
Then the first number is = 5X
5x = 5
Option 'D'
Answer: (D) 5
Question: The sale price Laptops listed for Rs.30000 after successive discount is 30% and 20% is?
(A) 18600
(B) 17600
(C) 18600
(D) 16800
(E) 16700
Rationale: 30000*(70/100)*(80/100)
= 16800
Answer: D
Answer: (D) 16800
Question: Find the length of the wire required to go 15 times round a square field containing 69696 m^2.
(A) 15840
(B) 26480
(C) 15642
(D) 15640
(E) 15849
Rationale: a^2 = 69696 => a = 264
4a = 1056
1056 * 15 = 15840
Answer: A
Answer: (A) 15840
Question: Excluding stoppages, the speed of a train is 48 kmph and including stoppages it is 40 kmph. Of how many minutes does the train stop per hour?
(A) 16
(B) 17
(C) 15
(D) 10
(E) 12
Rationale: T = 8/48 * 60
= 10
Answer: D
Answer: (D) 10
Question: A cyclist traveled for two days. On the second day the cyclist traveled 4 hours longer and at an average speed 10 mile per hour slower than she traveled on the first day. If during the two days she traveled a total of 240 miles and spent a total of 12 hours traveling, what was her average speed on the second day?
(A) 5 mph
(B) 10 mph
(C) 20 mph
(D) 30 mph
(E) 40 mph
Rationale: SOLUTION:
D = 280 Mi
T = 12 hrs
Đây 1 time = T1
Dây 2 time = T2
T2 - T1 = 4 hrs ----- (I)
T1 + T2 = 12 hrs ----- (II)
Adding I and II, T2 = 8 hrs and T1 = 4 hrs
Dày 1 Rate = R1
Dây 2 Rate = R2
R1 - R2 = 10 mph
í.ẹ. R1 = 10 + R2
280 = 8R2 + 4R1
í.ẹ. 280 = 8R2 + 4 (10 + R2)
í.ẹ. R2 = 20 mph
ANSWER: B
Answer: (B) 10 mph
Question: A, B and C, each working alone can complete a job in 6, 8 and 12 days respectively. If all three of them work together to complete a job and earn $ 1170, what will be B's share of the earnings?
(A) $390
(B) $520
(C) $1080
(D) $1170
(E) $630
Rationale: Explanatory Answer
A, B and C will share the amount of $1170 in the ratio of the amounts of work done by them.
As A takes 6 days to complete the job, if A works alone, A will be able to complete 1/6 th of the work in a day.
Similarly, B will complete 1/8th and C will complete 1/12th of the work.
So, the ratio of the work done by A : B : C when they work together will be equal to 1/6 : 1/8 : 1/12
Multiplying the numerator of all 3 fractions by 24, the LCM of 6, 8 and 12 will not change the relative values of the three values.
We get 24/6 : 24/8 : 24/12 = 4 : 3 : 2.
i.e., the ratio in which A : B : C will share $1170 will be 4 : 3 : 2.
Hence, B's share will be 3*1170/9 = 390.
correct choice is (A)
Answer: (A) $390
Question: What is the number of different committees of 4 women that can be selected from a group of 7 women?
(A) a) 20
(B) b) 35
(C) c) 80
(D) d) 120
(E) e) 210
Rationale: 7c4 = 35
Answer is B.
Answer: (B) b) 35
Question: If there are only 2 wheelers and 4 wheelers parked in a school located at the heart of the city, find the number of 4 wheelers parked there if the total number of wheels is 54?
(A) 11
(B) 12
(C) 13
(D) 14
(E) 15
Rationale: four wheeler=13*4=52(max)
2 wheel=1
so no of 4 wheeler=13
ANSWER:C
Answer: (C) 13
Question: If A, B and C together can finish a piece of work in 4 days. A alone in 12 days and B in 18 days, then C alone can do it in?
(A) 20
(B) 21
(C) 30
(D) 9
(E) 7
Rationale: C = 1/4 - 1/12 â€“ 1/18 = 1/9 => 9 days
ANSWER D
Answer: (D) 9
Question: Kim bought a total of $2.65 worth of postage stamps in four denominations. If she bought an equal number of 5-cent and 25-cent stamps and twice as many 10-cent stamps as 5-cent stamps, what is the least number of 2-cent stamps she could have bought ?
(A)  5
(B)  10
(C)  7.5
(D)  20
(E)  25
Rationale: 2.65 = 0.05x + 0.25x + 2 * 0.10x + 0.02y
=> 2.65 = 0.30x + 0.20x + 0.02y
=> 265 = 50x + 2y
So Max value of 50x < 265 = 250
Hence y = 7.5
Answer - C
Answer: (C)  7.5
Question: A 340-liter solution of Kola is made from 88% water, 5% concentrated Kola and the rest is made from sugar. If 3.2 liters of sugar, 10 liter of water and 6.8 liters of concentrated Kola were added to the solution, what percent of the solution is made from sugar?
(A) 6%
(B) 7.5%.
(C) 9.2%
(D) 10.5%.
(E) 11%.
Rationale: Denominator:
340+10+3.2+6.8=360
Numerator:
340(1-.88-.05)+3.2
340(0.07)+3.2
23.8+3.2
27
Ratio:
27/360=3/40
Answer: B
Answer: (B) 7.5%.
Question: A train of length 150 metres takes 40.5 seconds to cross a tunnel of length 300 metres. What is the speed of the train in km/hr ?
(A) 13 33
(B) 26.67
(C) 40
(D) 66.67
(E) None
Rationale: Solution
speed	=(150 + 300 / 40.5)m/sec
=(450/40.5x18/ 5) km/hr
= 40 km/hr
Answer C
Answer: (C) 40
Question: 48% of respondents to a survey consisted of those who used both M and N and those who used neither M nor N. 38% of respondents did not use M. 32% used N. What percent of respondents used only N?
(A) 19.5%
(B) 11%
(C) 20%
(D) 18.5%
(E) 17.5%
Rationale: From the question, we can summarize the information as follows:
N Not N
M X
Not M Ans y 38
32 100
Then we can set a system of 3 equations 3 unknowns described below:
X + Y = 48
X + Ans = 32
Y + Ans = 38
Sum up all three equations to get 2X + 2Y + 2Ans = 118
Divide both sides by 2 to get X + Y + Ans = 59
Replace X + Y with 48 to get 48 + Ans = 59
Substract 48 from both sides to get Ans = 59 - 48 = 11
The answer must be B.
Answer: (B) 11%
Question: A farmer needs to plant seeds on a plot of land. She will plant 300 seeds in a rectangle in the field. The rectangle will have E seeds in a row and F seeds in a column. If the number of seeds in a row is no less than 10 and no more than 30, how many different combinations of rectangular shapes are possible?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: firstly factors of 300 = 1,2,3,4,5,6,10,12,15,20,25,30,50,60,75,100,150,300
the question says each row will have seeds no less than 10 and no more than 30,
therefore, we should be interested in the factors between 10 and 30 (inclusive)
10(in each row) * 30(number of columns) =300, similarly
12 * 25
15 * 20
20 * 15
25 * 12
30 * 10
total possibilities = 6
option B
Answer: (B) 6
Question: How many multiples of 7 are there between 14 and 252 ?
(A) 33
(B) 46
(C) 59
(D) 66
(E) 80
Rationale: It should be mentioned whether 14 and 252 are inclusive.
If 14 and 252 are inclusive, then the answer is (252-14)/7+1=35.
If 14 and 252 are NOT inclusive, then the answer is (245-21)/7+1=33.
Since OA is A, then we have NOT inclusive case.
Answer: (A) 33
Question: If a train, travelling at a speed of 90 kmph, crosses a pole in 5 sec, then the length of train is?
(A) 167 m
(B) 125 m
(C) 761 m
(D) 143 m
(E) 132 m
Rationale: D = 90 * 5/18 * 5
= 125 m
Answer:B
Answer: (B) 125 m
Question: If n=4p where p is a prime number greater than 2, how many different positive even divisors does n have, WITHOUT N VALUE?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: We're told that N = 4P and that P is a prime number greater than 2. Let's TEST P = 3; so N = 12
The question now asks how many DIFFERENT positive EVEN divisors does 12 have, including 12?
12:
1,12
2,6
3,4
How many of these divisors are EVEN? 2, 4, 6, …..3 even divisors.
ANSWER:C
Answer: (C) 3
Question: Ritesh and Co. generated revenue of Rs. 1,600 in 2006. This was 12.5% of its gross revenue. In 2007, the gross revenue grew by Rs. 2,500. What is the percentage increase in the revenue in 2007?
(A) 12.5%
(B) 19.53%
(C) 25%
(D) 50%
(E) None of these
Rationale: Explanation :
Given, Ritesh and Co. generated revenue of Rs. 1,600 in 2006 and that this was 12.5% of the gross revenue.
Hence, if 1600 is 12.5% of the revenue, then 100% (gross revenue) is:
=>(100/12.5)×1600.
=>12,800.
Hence, the total revenue by end of 2007 is Rs. 12,800. In 2006, revenue grew by Rs. 2500. This is a growth of:
=>(2500/12800)×100.
=>19.53%.
Answer : B
Answer: (B) 19.53%