mathewhe/aqua_rat huggingface dataset:
Question: Integer X represents the product of all integers between 1 to 27 (inclusive). The smallest prime factor of (x+1) must be
(A) Between 1 to 10
(B) Between 11 to 15
(C) Between 15 to 20
(D) Between 20 to 27
(E) Greater than 27
Rationale: Answer = E = Greater than 27
This problem is asking smallest prime factor of (25!+1)
25! already have there prime factors 2,3,5,7,11,13.......... so on upto 23 (1 cannot be considered prime factor)
Just adding 1 to 27! will remove all the factors stated above;
so the smallest possible prime factor has to be greater than 27
Answer = E
Answer: (E) Greater than 27
Question: Score Interval Number of Scores
50-59 2
60-69 10
70-79 16
80-89 27
90-99 17
The table shows a distribution of test scores. Which score interval contains the median of the 72 scores?
(A) a) 60-69
(B) b) 70-79
(C) c) 80-89
(D) d) 90-99
(E) e) Cannot determine.
Rationale: 36th person
80-89 C
Answer: (C) c) 80-89
Question: Find the least number when successively divided by 2, 3 and 7 leaves remainders 1, 2 and 3 respectively?
(A) 67
(B) 65
(C) 75
(D) 61
(E) 60
Rationale: 2) 65 (32 3) 32 (10 7) 10 (1
64 30 7
-------- -------- - -----
1 2 3
=> 65
ANSWER:B
Answer: (B) 65
Question: Two identical machines have the ability to produce both nuts and bolts. However, it takes 1 second to produce a bolt but 2 seconds to produce a nut. What is the fastest the two machines, working together, can produce 1,600 nuts and 1,600 bolts?
(A) 1,250 seconds
(B) 1,500 seconds
(C) 1,750 seconds
(D) 2,400 seconds
(E) 3,000 seconds
Rationale: I used the Rate formula (R=\frac{1}{T})
Rate of 1st machine = Rate of making 1 bolt + Rate of making 1 nut = 1 + \frac{1}{2}
Rate of 1st machine = Rate of 2nd machine
After this I got lost.
Please can you help how to approach using algebra?
I wouldn't complicate:
1 machine needs 1,600*1 seconds to produce 1,600 bolts, so 2 need half of that, so 1,600/2 seconds.=800
1 machine needs 1,600*2 seconds to produce 1,600 nuts, so 2 need half of that, so 1,600*2/2 seconds.=1600
total = 2400
D
Answer: (D) 2,400 seconds
Question: At a certain store, the price of a pair of shoes is twenty dollars more than three times the price of a pair of jeans and the price of a sweater is seventy percent more than the price of a pair of shoes. If the price of a pair of jeans is j dollars at this store, then what is the price, in dollars, of a pair of shoes, a sweater and a pair of jeans, in terms of j ?
(A) 9.1j + 54
(B) 3j + 20
(C) 4.5j + 30
(D) 5.5j + 30
(E) 8.5j + 50
Rationale: Ans A
Given
Price of Jeans = J
Price of shoes = 20+3J
Price of Sweater = 1.7(20+3J)
Total Price of all three items = J+20+3J+1.7(20+3J) = 54+9.1J
Answer: (A) 9.1j + 54
Question: A certain rectangular crate measures 8 feet by 14 feet by 16 feet. A cylindrical gas tank is to be made for shipment in the crate and will stand upright when the crate is placed on one of its six faces. What should the radius of the tank be if it is to be of the largest possible volume?
(A) 4
(B) 5
(C) 6
(D) 8
(E) 10
Rationale: Ans is "B".
For max volume of cylinder (pi*r^2*h) we need to max out r^2*h. We don't know what the dimensions of the crate refer to. . Therefore for max vol base should be 14x20 i.e. of radius 12/2 = 6
C
Answer: (C) 6
Question: Murali travelled from city A to city B at a speed of 40 kmph and from city B to city C at 60 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 1 : 3?
A. 48 kmph
(A) 33
(B) 480/9
(C) 28
(D) 27/8
(E) 16
Rationale: Let the distances between city A to B and B to C be x km and 3x km respectively.
Total time taken to cover from A to C
= (x)/40 + (3x)/60 = (3x + 6x)/120 = 9x/120 Average speed = (x + 3x)/(9x/120) = 480/9 kmph.
Answer: B
Answer: (B) 480/9
Question: In a group of 80 students, each student is registered for at least one of three classes – History, Math and English. 35 students are registered for History, 35 are registered for Math, and 46 students are registered for English. If only three students are registered for all three classes, how many students are registered for exactly two classes?
(A) 13
(B) 10
(C) 9
(D) 8
(E) 30
Rationale: Each student is registered forat least one of three classesmeans thatthere are no students who are registered for none of the classes.
Total = {people in group A} + {people in group B} + {people in group C} - {people in exactly 2 groups} - 2*{people in exactly 3 groups} + {people in none of the groups}:
80 = 35 + 35 + 46 - {people in exactly 2 groups} - 2*3 + 0-->{people in exactly 2 groups}=30
Answer: E
Answer: (E) 30
Question: A sum of money is to be distributed among A, B, C, D in the proportion of 5:2:4:3. If C gets Rs. 1000 more than D, what is B's share?
(A) Rs.2008
(B) Rs.2039
(C) Rs.2000
(D) Rs.2039
(E) Rs.2030
Rationale: Let the shares of A, B, C and D be 5x, 2x, 4x and 3x Rs. respectively.
Then, 4x - 3x = 1000 => x = 1000.
B's share = Rs. 2x = 2 * 1000 = Rs.2000.
Answer: C
Answer: (C) Rs.2000
Question: A qualified worker digs a well in 5 hours. He invites 2 apprentices, both capable of working 3/5 as fast and 2 trainees both working 1/5 as fast as he. If the five-person team digs the same well, how much time does the team need to finish the job?
(A) 1:42
(B) 1:34
(C) 1:44
(D) 1:54
(E) 2:14
Rationale: and answer is correct as you have calculated : 100/59 hrs that is 1.71 hrs - 1 hr and 42minutes, so 1:42, hence,A.
Answer: (A) 1:42
Question: Calculate the value of n from the below equation: n^3âˆ’10n+20=44
(A) 1
(B) 5
(C) 3
(D) 2
(E) 4
Rationale: Use elimination method to find the correct option. you find that of all the options when 4 is the correct value for n
Answer: E
Answer: (E) 4
Question: Which of the following options is the possible total number of people in a hall given that the number of people is a multiple of both 8 and 14.?
(A) 64
(B) 72
(C) 56
(D) 80
(E) 88
Rationale: the number of people are a multiple of both 8 and 14, so it must be divisible by 8 and 14.
using the elimination method look for a number that is both divisible by 8 and 14,
of all the options only 56 is divisible by 8 and 14.
[ 56/8=1 and 56/14=4]
answer :C
Answer: (C) 56
Question: Jill works as a waitress at the local diner where she earns an hourly wage of $4.00 per hour and a standard tip rate of 15% of the cost of the orders she serves. If she worked two 8-hour shifts this week and averaged $40 in orders per hour, how much did Jill earn this week?
(A) 280
(B) 300
(C) 160
(D) 350
(E) 400
Rationale: Jill earns 4 dollars/hour and the hourly tip is (3/20)*40.
Jill thus earns 4*8+8*2*3 per day(or 4(8)+6(8)=10(8)=80).
Jill has worked for 2 days -> 80*2=160.
This matches answer choice C.
Answer: (C) 160
Question: After running a series of television advertisements, a leading beverage producer saw its sales increase by 40% to $1 million dollars per month. Prior to the advertising campaign, about how many dollars in sales did the company average per day?
(A) $1.25 million
(B) $800,000
(C) $750,000
(D) $27,000
(E) $23,000
Rationale: Let sales in previous month = X
1.4 X=1,000,000
7/5 X= 1,000,000 ..........> X=714,285
sales per day= 714,285/30= less than 25,000 so closest number is 23,000
Answer: E
Answer: (E) $23,000
Question: James took a 3-hour bike ride. In the second hour he travlled 18 miles, which was 20 percent farther than he traveled the first hour. If he traveled 25 percent farther in the third hour than he did in the second hour, how many miles did jose travel during the entire ride?
(A) 54.0
(B) 54.9
(C) 55.5
(D) 57.0
(E) 63.0
Rationale: Let the distance travelled in the first hour be x. Thus, 1.2x = 18 , x = 15. Now, the distance travelled in the 3rd hour = 18+1/4∗18= The only option ending with a 0.5 in the decimal place is C.
ANSWER:C
Answer: (C) 55.5
Question: If (1/5)^m * (1/2)^5 = 1/((10)^5), then m =
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: (1/5)^m (1/2)^5 = 1/{(10)^5}
(10)^5/2^5 = 5^m
[(2^5)(5^5)]/[2^5] = 5^m
5^5 = 5^m
m=5
E
Answer: (E) 5
Question: Donovan and Michael are racing around a circular 600-meter track. If Donovan runs each lap in 45 seconds and Michael runs each lap in 40 seconds, how many laps will Michael have to complete in order to pass Donovan, assuming they start at the same time?
(A) 8
(B) 7
(C) 9
(D) 6
(E) 5
Rationale: One way of approaching this question is by Relative speed method
1. Speed/ Rate of Donovan = Distance/ time => 600/45 =>40/3
2. Speed/ Rate of Michael = Distance/ time => 600/40 => 15
Relative Speed between them = 15 - 40/3 => 5/3 (We subtract the Rates if moving in the same direction and add the rates if moving in the opposite direction)
In order to pass Donovan-
Distance to be covered = 600, Relative Rate = 5/3
Total Time taken by Micheal to surpass Donovan = Distance / rate => 600*3/5 => 360
No. of laps taken by Michael = Total time / Michael's rate => 360/40 => 9
Hence correct answer is 9 Laps.
C
Answer: (C) 9
Question: The profits of QRS company rose 30% 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) 56%
(D) 62%
(E) 80%
Rationale: Assume 100 in march , then 130 in April as 30% increase , Then 104 in may as 20% decrease from April , and then 156 in june which is 150% of 104 .
So overall increase is from 100 to 156 is 56%
Answer C
Answer: (C) 56%
Question: The area of a triangle will be when a = 1m, b = 2m, c = 3m, a, b, c being lengths of respective sides?
(A) 3
(B) 5
(C) 6
(D) 87
(E) 9
Rationale: S = (1 + 2 + 3)/2 = 3
=> No triangle exists
Answer: A
Answer: (A) 3
Question: Every month a man consumes 25 kg rice and 9 kg wheat. The price of rice is 20% of the price of wheat and thus he spends total Rs. 350 on the rice and wheat per month. If the price of wheat is increased by 20% then what is the percentage reduction of rice consumption for the same expenditure of Rs. 350? Given that the price of rice and consumption of wheat is constant :
(A) 40%
(B) 25%
(C) 36%
(D) 24%
(E) Cannot determined
Rationale: Solution: Let the price of wheat is x per kg. Then price of wheat will be 5x per kg.
Expenditure on rice = 25*x = 25x.
Expenditure of wheat = 9*5x = 45x.
Total cost,
25x + 45x = 350.
70x = 350.
x = 5.
Hence, price of Rice = Rs. 5 per kg.
Price of wheat = 25 per kg.
Now, price of wheat = 25 ---- 20% ↑----> Rs. 30 per kg.
Let the new amount of rice is N kg, then
N*5 + 9*30 = 350.
N = 16 kg.
%decrease in the amount of rice = [(25-16)*100]/25 = 36%
Answer: Option C
Answer: (C) 36%
Question: How much water must be added to 52 litres of milk at 1 1⁄2 litres for 20 so as to have a mixture worth 10 2⁄3 a litre?
(A) 10 litres
(B) 13 litres
(C) 15 litres
(D) 18 litres
(E) None of these
Rationale: C.P. of 1 litre of milk = (20 × 2⁄3) = 40⁄3
∴ Ratio of water and milk = 8⁄3 : 32⁄3 = 8 : 32 = 1 : 4
∴ Quantity of water to be added to 52 litres of milk
= (1⁄4 × 52) litres = 13 litres.
Answer B
Answer: (B) 13 litres
Question: Look at this series: 53, 53, 43, 43, 33, 33, ... What number should come next?
(A) 50
(B) 40
(C) 23
(D) 13
(E) 10
Rationale: In this series, each number is repeated, then 10 is subtracted to arrive at the next number.
Answer is C
Answer: (C) 23
Question: In how much time will a train of length 100 m, moving at 34 kmph cross an electric pole?
(A) 15.59 sec
(B) 12.59 sec
(C) 10.59 sec
(D) 11.59 sec
(E) 15 sec
Rationale: Convert kmph to mps. 34 kmph = 34 * 5/18 = 9.44 mps.
The distance to be covered is equal to the length of the train.
Required time t = d/s = 100/9.44 = 10.59 sec.
ANSWER:C
Answer: (C) 10.59 sec
Question: The savings of employee equals income minus expenditure.If the income of A,B,C are in the ratio 1:2:3 and their expense ratio 3:2:1 then what is the order of the employees in increasing order of their size of their savings?
(A) 22
(B) 281
(C) A<B<C
(D) 28
(E) 272
Rationale: As the the ratio of their incomes are in ascending order, and their expenses are in descending order, their savings also in their incomes order.
So savings order = A < B < C
Answer:B
Answer: (B) 281
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 36 kilometers, Maxwell's walking speed is 3 km/h, and Brad's running speed is 6 km/h. What is the distance traveled by Maxwell when they meet in the middle?
(A) 12
(B) 14
(C) 15
(D) 13
(E) 11
Rationale: Consider Max starts from Point A and Brad Starts from Point B and move towards each other.
Assume they shall meet at point O after Time 'T'. The question asks us to find OA.
From the question stem we can make out :- Distance OA = 50km - Distance OB
=> 3xT = 36 - 6xT (i.e distance =Speed x Time)
=> 9T = 36
Hence T = 4
OA = 3 x 4 = 12 Km
Answer : A
Answer: (A) 12
Question: Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. What are the marks obtained by them?
(A) 42, 33
(B) 42, 31
(C) 40, 33
(D) 39, 33
(E) 41, 35
Rationale: Let the marks secured by them be x and (x + 9)
Then sum of their marks = x + (x + 9) = 2x + 9
Given that (x + 9) was 56% of the sum of their marks
=>(x+9) = 56/100(2x+9)
=>(x+9) = 14/25(2x+9)
=> 25x + 225 = 28x + 126
=> 3x = 99
=> x = 33
Then (x + 9) = 33 + 9 = 42
Hence their marks are 33 and 42
A)
Answer: (A) 42, 33
Question: There are three prizes to be distributed among ten students. If no students gets more than one prize, then this can be done in?
(A) 10
(B) 45
(C) 95
(D) 120
(E) None of these
Rationale: Explanation :
3 prize among 10 students can be distributed in 10C3 ways = 120 ways.
Answer : D
Answer: (D) 120
Question: Difference between two numbers is 5, six times of the smaller lacks by 10 from the four times of the greater. Find the numbers?
(A) 10,5
(B) 9,7
(C) 11,9
(D) 13,11
(E) 13,9
Rationale: Explanation:
x – y = 5
4x – 6y = 10
x = 10 y = 5
A)
Answer: (A) 10,5
Question: Two numbers are in the ratio 3:5. If 9 be subtracted from each, they are in the ratio of 9:17. The first number is?
(A) 36
(B) 76
(C) 98
(D) 27
(E) 24
Rationale: (3x-9):(5x-9)
= 9:17
x = 12 => 3x
= 36
Answer:A
Answer: (A) 36
Question: An urn contains 10 balls, numbered from 1 to 10. If 2 balls are selected at random with replacement from the urn, what is the probability F that the sum of the 2 numbers on the balls will be even?
(A) 25%
(B) 37.5%
(C) 50%
(D) 62.5%
(E) 75%
Rationale: Correct Answer: C
Since there are 5 even numbered balls and 5 odd numbered balls, the probability F of selecting either an even or an odd is 5/10= 1/2. In order for the sum of the numbers on the two balls to be even, either both numbers must be even or both numbers must be odd; one even and one odd number would add to an odd number. The probability of selecting two even numbers is:
1/2 * 1/2= 1/4
The probability of selecting two odd numbers is also:
1/2 * 1/2= 1/4
Adding both probabilities gives 1/4+1/4= 1/2 , or 50%, as the probability that the sum of the numbers will be even. Thus, the correct answer is (C).
Answer: (C) 50%
Question: If (z + 3)/5 is an integer, what is remainder when z is divided by 5?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: Assume the answer choices as the value of z
A) 2; (2+3)/5 = 1 satisfies the equation
B) 3; (3+3)/5 = 1.2 Not an integer
C) 4; (4+3)/5 = 1.4 Not an integer
D) 5; (5+3)/5 = 1.6 Not an integer
E) 6; (6+3)/5 = 1.8 Not an integer
Answer: A
Answer: (A) 2
Question: A round table conference to be held between 20 delegates of 20 countries. In how many ways can they seated if two particular delegates are always to sit together?
(A) 14!*5!
(B) 22!*7!
(C) 18!*2!
(D) 28!*1!
(E) 16!*3!
Rationale: Regarding two particular delegates who are to sit together as on one person, we have only 18+1=19 persons.these 19 persons can be seated at the round table in 18! ways.
But two particular persons can be arranged among themselves in 2! ways.
Required number =18!*2!
Answer is C
Answer: (C) 18!*2!
Question: Dany bought a total of 24 game cards some of which cost $0.25 each and some of which cost $0.15 each. If Dany spent $4.2 to buy these cards, how many cards of each type did he buy?
(A) 4
(B) 10
(C) 7
(D) 18
(E) 12
Rationale: Let X be the number of cards that cost $0.25 each and Y the number of cards that cost $0.15 each. The total number of cards is 24. Hence
X + Y = 24
If X is the number of cards at $0.25, then the X cards cost
0.25 X
If Y is the number of cards at $0.15, then the Y cards cost
0.15 Y
The total cost of the X cards and the the Y cards is known to be $4.2 and also given by
0.25 X + 0.15 Y = 4.2
We now need to solve the system of equations
X + Y = 24
0.25 X + 0.15 Y = 4.2
The first equation gives Y = 24 - X. Substitute y by 24 - x in the second equation and solve
0.25 X + 0.15 (24 - X) = 4.2
X(0.25 - 0.15) + 3.6 = 4.2
0.1 X = 0.6
X = 6 and Y = 24 - 6 = 18
correct answer D
Answer: (D) 18
Question: For a certain set of numbers, if x is in the set, then x - 1 is also in the set. If the number 1 is in the set , which of the following must also be in the set ?
a) 4
b) 0
c) -3
(A) a only,
(B) b only,
(C) a and b only
(D) c only,
(E) b and c only
Rationale: Notice that the question asks which of the following MUST be in the set, not COULD be in the set.
Since 1 is in the set, then so must be 1-1=0. Similarly, since 0 is in the set, then so must be 0-3=-3. Could 4 and -1 be in the set? Certainly, but we don't know that for sure.
Answer: E.
Regarding your question: we don't know which is the source integer in the set, if it's 1, then 4 won't be in the set but if the source integer is say 7, then 4 will be in the set. So, 4 may or may not be in the set.
Answer: (E) b and c only
Question: Find the amount on Rs.5000 in 2 years, the rate of interest being 20% per first year and 25% for the second year?
(A) 3377
(B) 2678
(C) 5460
(D) 7500
(E) 1671
Rationale: 5000 * 120/100 * 125/100 => 7500
Answer: D
Answer: (D) 7500
Question: five children — A, B, C, D, E, F, and G — are going to sit in seven chairs in a row. Children AB must sit next to each other, and child C must be somewhere to the right of AB. How many possible configurations are there for the children?
(A) 600
(B) 560
(C) 1440
(D) 4320
(E) 4800
Rationale: A, B, C, D, E, F, G- seven children, of which AB must sit next to each other. Considering them as one X (A, B), we have X, C, D, E, F, G. These can be arranged in 6! ways. But A,B can arrange themselves in 2! ways. So a total of 6!*2! ways = 1440. Since in exactly half of them, C will be to the right of AB, and exactly half, C will be to the left of AB, therefore 1440/2 = 560.
B is the right answer.
Answer: (B) 560
Question: The present age of a father is 3 years more than three times the age of his son.Three years hence,father as age will be 13 years more than twice the age of the son.Find the present age of the father.
(A) 88
(B) 77
(C) 33
(D) 42
(E) 55
Rationale: Explanation:
Let the present age be 'x' years. Then father's present age is 3x+3 years. Three years hence (3x+3)+3=2(x+3)+13 x=13 Hence father's present age = 3x+3 =[ (3 x 13) + 3] = 42 years.
Answer: D
Answer: (D) 42
Question: 20 throws of a die produces following results
SCORE -- NUMBER OF OCCURRENCES
---1-------------------4
---2-------------------3
---3-------------------5
---4-------------------2
---5-------------------2
---6-------------------4
What is the probability P that one more throw to this series will increase the mean score?
(A) 1/6
(B) 1/3
(C) 1/2
(D) 2/3
(E) 5/6
Rationale: I get the mean as 67/20 --> 3.35. Thus in order to raise this mean we would need a 4,5,or 6.
Thus probability P is 1/2.C
Answer: (C) 1/2
Question: In how many ways can an answer key for a quiz be written if the quiz contains 5 true-false questions followed by 2 multiples-choice questions with 4 answer choices each, if the correct answers to all true-false questions cannot be the same?
(A) 160
(B) 320
(C) 480
(D) 600
(E) 720
Rationale: There are 2^5 = 32 possibilities for the true-false answers.
However we need to remove two cases for TTTTT and FFFFF.
There are 4*4 = 16 possibilities for the multiple choice questions.
The total number of possibilities is 30*16 = 480.
The answer is C.
Answer: (C) 480
Question: 20.036 divided by 0.04 gives :
(A) 50.09
(B) 5.06
(C) 50.06
(D) 100.9
(E) 500.9
Rationale: = 20.036/0.04
= 2003.6/4
= 500.9
Answer is E.
Answer: (E) 500.9
Question: A square is drawn inside a right-angled triangle with the two perpendicular sides as 12 cm and 8 cm. what is the side of the largest possible square that can be drawn?
(A) 4 cm
(B) 4.8 cm
(C) 4.5 cm
(D) 4.4 cm
(E) 5 cm
Rationale: consider the origin as the point of right angle thus (8,0)and (0,12) are the 2 vertices. equation of hypotenuse : 8y+12x=96.
now solve this with y=x(the diagonal of the largest square)
x=4.8, y=4.8 .
ANSWER:B
Answer: (B) 4.8 cm
Question: A sum of Rs.4800 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years.
(A) 2777
(B) 3120
(C) 6877
(D) 1699
(E) 1667
Rationale: Let A be the amount received at the end of the three years.
A = 4800[1 + 10/100][1 + 20/100][1 + 25/100]
A = (4800 * 11 * 6 * 5)/(10 * 5 * 4)
A = Rs.7920
So the interest = 7920 - 4800 = Rs.3120
Answer: B
Answer: (B) 3120
Question: By selling an article for $90, a person gains $15. What is the gain %?
(A) 25%
(B) 30%
(C) 50%
(D) 20%
(E) 10%
Rationale: S.P. = $90
Gain = $15
C.P. = 90-15 = 75
Gain% = 15/75 * 100 = 20%
Answer is D
Answer: (D) 20%
Question: Three friends (Tony, Ben and George) are employees of a company. Their respective salaries are in the ratio of 3 : 4 :5. Ben and George's salaries together is Rs. 8550. By what percent is George's salary than that of Sarah?
(A) 61.7%
(B) 46.7%
(C) 66.7%
(D) 63.7%
(E) 62.7%
Rationale: Explanation:
Let the salaries be 3x, 4x and 5x respectively.
Then,4x + 5x = 8550 => x = 950.
Tony's salary = Rs. 2850, , , Ben's salary = Rs. 3800, and and George's salary Rs. 4750.
Excess of George's salary over Tony's=[ (1900 /2850) x 100] = 66.7%.
Answer: C
Answer: (C) 66.7%
Question: 4000 was divided into two parts such a way that when first part was invested at 3% and the second at 5%, the whole annual interest from both the investments is Rs.144, how much was put at 3%?
(A) 2808
(B) 2829
(C) 2800
(D) 2829
(E) 2821
Rationale: (x*3*1)/100 + [(4000 - x)*5*1]/100 = 144
3x/100 + 200 – 5x/100 = 144
2x/100 = 56 è x = 2800
Answer:C
Answer: (C) 2800
Question: The area of the square formed on the diagonal of a rectangle as its side is 108 1/3 % more than the area of the rectangle. If the perimeter of the rectangle is 28 units, find the difference between the sides of the rectangle?
(A) 8
(B) 12
(C) 6
(D) 2
(E) 4
Rationale: Let the sides of the rectangle be l and b respectively.
From the given data,
(√l2 + b2) = (1 + 108 1/3 %)lb
=> l2 + b2 = (1 + 325/3 * 1/100)lb
= (1 + 13/12)lb
= 25/12 lb
=> (l2 + b2)/lb = 25/12
12(l2 + b2) = 25lb
Adding 24lb on both sides
12l2 + 12b2 + 24lb = 49lb
12(l2 + b2 + 2lb) = 49lb
but 2(l + b) = 28 => l + b = 14
12(l + b)2 = 49lb
=> 12(14)2 = 49lb
=> lb = 48
Since l + b = 14, l = 8 and b = 6
l - b = 8 - 6 = 2m.
ANSWER:D
Answer: (D) 2
Question: 70,75, 76,75,90,105,105,130,130,130
The list consists of the times in seconds that it took each of the 10 school children to run a distance of 400 mts . If the standard deviation of the 10 running times is 22.4, rounded to the nearest tenth of a second, how many of the 10 running times are more than 1 standard deviation below the mean of the 10 running times.
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: How many of the 10 running times are more than one SD below the meanmeans how many data points from given 10 are less thanmean-1SD.
We are given that SD=22.4, so we should find mean --> mean=100 --> there are only 4 data points below 100-22.4=77.6, namely 70,75, 76 and 75.
Answer: D.
Answer: (D) 4