mathewhe/aqua_rat huggingface dataset:
Question: Given 2 negative numbers, the greater of the two is quadrupled, the difference between it and the lesser number is 14. what is the greater number if the product of both numbers is 30?
(A) -9
(B) -8
(C) -4
(D) -1
(E) -5
Rationale: Test the options. The options give you the greater number. Start from the middle option.
(C) - 4
quadruple of -4 is -16 and 14 less is -2.
-2 * -4 = 8 (Not correct)
...
(E) - 5
quadruple of -5 is -20 and 14 less is -6.
-6 * -5 = 30
Correct
Answer (E)
Answer: (E) -5
Question: A merchant marks goods up by 75% and then offers a discount on the marked price. The profit that the merchant makes after offering the discount is 22.5%. What % discount did the merchant offer?
(A) 20%
(B) 25%
(C) 30%
(D) 35%
(E) 40%
Rationale: Let P be the original price of the goods and let x be the rate after the markup.
(1.75P)*x = 1.225P
x = 1.225/1.75 = 0.7 which is a discount of 30%.
The answer is C.
Answer: (C) 30%
Question: A cube with its sides numbered 1 through 6 is rolled twice, first landing on a and then landing on b. If any roll of the cube yields an equal chance of landing on any of the numbers 1 through 6, what is the probability W that a + b is prime?
(A)  0
(B)  1/12
(C)  5/12
(D)  7/18
(E)  4/9
Rationale: Total # of outcomes is 6*6=36;
Favorable outcomes:
a-b --> prime
1-1 --> 2;
1-2 --> 3;
2-1 --> 3;
1-4 --> 5;
4-1 --> 5;
2-3 --> 5;
3-2 --> 5;
1-6 --> 7;
6-1 --> 7;
2-5 --> 7;
5-2 --> 7;
3-4 --> 7;
4-3 --> 7;
6-5 --> 11;
5-6 --> 11.
Total of 15 favorable outcomes
W=15/36.
Answer: C.
Answer: (C)  5/12
Question: Calculate the value of 2.34 x 10^7 ?
(A) 2340
(B) 2340000
(C) 23400000
(D) 23400
(E) 234000
Rationale: 3.14 x 10^7 = 2.34 x 10000000 = 23400000.
Answer = C
Answer: (C) 23400000
Question: A string of 30 light bulbs is wired in such a way that if any individual light bulb fails, the entire string fails. If for each individual light bulb the probability of failing during time period T is 0.1, what is the probability that the string of light bulbs will fail during the time period T?
(A) 0.1
(B) (0.1)^30
(C) 1 - (0.1)^30
(D) (0.93)^30
(E) 1 - (0.90)^30
Rationale: The string of light bulbs will fail if at least one light bulb fails. So, let's find the probability of the opposite event and subtract that value from 1.
The opposite event is when none of the 30 light bulbs fails, since the probability of each light bulb not to fail is 1-0.1=0.90 the the probability that none of the 30 light bulbs fails is 0.90^30.
Hence, the probability that at least one light bulb fails is 1-0.90^30.
Answer: E.
Now, you should have spotted that your reasoning was not right because of one simple thing, consider the case when we have 100 light bulbs instead of 30, then according to your logic the probability that the string of light bulbs will fail would be 100*0.1=10, which is not possible since the probability of an event cannot be more than 1 (100%).
Answer: (E) 1 - (0.90)^30
Question: In a class of 70 students, 10 did not opt for math. 5 did not opt for science and 3 did not opt for either. How many students of the class opted for both math and science?
(A) 23
(B) 25
(C) 27
(D) 37
(E) 38
Rationale: 70 students total
10 did not opt for math
5 did not opt for science
3 did not opt for either
Total of 40 students in math and 2 did not opt for sci but did for math
40-2=38
38 students of the class opted for both math and science
Answer:E
Answer: (E) 38
Question: A coin is tossed live times. What is the probability that there is at the least one tail?
(A) 31/32
(B) 31/38
(C) 31/31
(D) 61/38
(E) 31/35
Rationale: Let P(T) be the probability of getting least one tail when the coin is tossed five times.
= There is not even a single tail.
i.e. all the outcomes are heads.
= 1/32 ; P(T) = 1 - 1/32 = 31/32
Answer: A
Answer: (A) 31/32
Question: John bought a shirt on sale for 25% off the original price and another 25 % off the discounted price. If the final price was $19, what was the price before the first discount?
(A) $45.10
(B) $34.31
(C) $28.44
(D) $67.54
(E) $33.77
Rationale: let x be the price before the first discount. The price after the first discount is
x - 25%x (price after first discount)
A second discount of 25% of the discounted price after which the final price is 19
(x - 25%x) - 25%(x - 25%x) = 19
Solve for x
x = $33.77
correct answer E
Answer: (E) $33.77
Question: What will be the ratio of simple interest earned by certain amount at the same rate of interest for 2 years and that for 12 years?
(A) 3 : 2
(B) 1 : 3
(C) 1 : 6
(D) 3 : 1
(E) 2 : 1
Rationale: Explanation :
Simple Interest = PRT/100
Here Principal(P) and Rate of Interest (R) are constants
Hence, Simple Interest ∝ T
Required Ratio = Simple Interest for 2 years/Simple Interest for 12 years
=T1/T2
=2/12
=1/6
=1:6
Answer : Option C
Answer: (C) 1 : 6
Question: The sale price of an article including the sales tax is Rs. 616. The rate of sales tax is 10%. If the shopkeeper has made a profit of 18%, then the cost price of the article is:
(A) 500
(B) 474.6
(C) 222
(D) 297
(E) 111
Rationale: Explanation:
110% of S.P. = 616
S.P. = (616 * 100)/110 = Rs. 560
C.P = (100 * 560)/118 = Rs. 474.6
Answer:B
Answer: (B) 474.6
Question: A certain car traveled twice as many miles from Town A to Town B as it did from Town B to Town C. From Town A to Town B, the car averaged 40 miles per gallon, and from Town B to Town C, the car averaged 50 miles per gallon. What is the average miles per gallon that the car achieved on its trip from Town A through Town B to Town C?
(A) 42.85
(B) 40
(C) 35
(D) 41
(E) 39
Rationale: step 1) took LCM of 40 and 50.. came as 200.
step 2) 200 distance between B to C... do 200/50 hence 4 gallons used
step 3) twice distance.. hence 200*2= 400... do as above.. 400/40= 10 gallons used
step 4) total gallons.. 4+10= 14 gallons
step ) total miles= 200+400= 600 miles
hence.. average of whole journey = 600/14 which comes to 42.85
Answer : A
Answer: (A) 42.85
Question: The cost price of a Rs. 100 stock at 4 discount, when brokerage is 15% is
(A) Rs. 96.25
(B) Rs. 96.2
(C) Rs. 97.25
(D) Rs. 97.5
(E) Rs. 97.75
Rationale: Explanation :
Cost Price = 100−4+1/5=96.2
Answer : Option B
Answer: (B) Rs. 96.2
Question: If a+b+c=13, a2+b2+c2=69, then find ab+bc+ca
(A) -50
(B) 50
(C) 69
(D) 75
(E) 89
Rationale: (a+b+c)2= a2+b2+c2+2(ab+bc+ca)
2(ab+bc+ca)= (a+b+c)2- a2+b2+c2
=169-69
=100
ab+bc+ca=50
ANSWER B 50
Answer: (B) 50
Question: Set S consists of integers {1,3,5,7}. If two numbers are chosen from set S at random, what is the probability that the product of 2 numbers is more than 15?
(A) 1/2
(B) 1/3
(C) 1/5
(D) 1/6
(E) 2/3
Rationale: Number of ways you can choose 2 from 4 = 4C2 = 6
E = event of getting the 2 numbers product is more than 15 = (3,7),(5,7) = 2
probability = 2/6 = 1/3
Answer is B
Answer: (B) 1/3
Question: Which of the numbers below is the odd one out
1,65,190,406,749,950,1261.
(A) 190
(B) 406
(C) 950
(D) 749
(E) 1261
Rationale: 950 is the odd man.. diff between sucessive are Cube Numbers
ANSWER:C
Answer: (C) 950
Question: At a florist shop on a certain day, all corsages sold for either $25 or $40. If 8 of the corsages that sold for $30 had instead sold for $20, then the store's revenue from corsages that day would have been reduced by 40 percent. What was the store's actual revenue from corsages that day?
(A) $200
(B) $400
(C) $600
(D) $800
(E) $300
Rationale: I am doing it elaborately, hope it will help you.
Let, No. of corsages @ $25 = x, no. of corsages @ $40 = y and revenue= r
so, 25x+40y=r.........(1)
Now,
Given the situation, 25(x+8) + 40(y-8)= r-.4r
=> 25x+200+40y-320 = .6r
=> 25x+40y = .8r+120............(2)
so, r = .6r+120
=> r = 300
The answer is E.
Answer: (E) $300
Question: Solve the equation for x : 2x - 21 + 3x = 4 + 9 - x
(A) 4
(B) 5
(C) 5.6
(D) 9.2
(E) 3.1
Rationale: C
5.6
5 x + x = 13 + 21
6 x = 34 => x = 5.6
Answer: (C) 5.6
Question: Pipe A can fill a tank in 45 hrs and pipe B can fill it in 36 hrs. If both the pipes are opened in the empty tank. In how many hours will it be full?
(A) 10 hr
(B) 15 hr
(C) 20 hr
(D) 25 hr
(E) 28 hr
Rationale: Part filled A in 1 hr= (1/45)
Part filled B in 1 hr= (1/36)
Part filled by (A+B) together in 1 hr=(1/45)+(1/36)=1/20
So, The tank will be full in 20 hr.
Answer : C
Answer: (C) 20 hr
Question: Find a sum for first 6 prime numbers?
(A) 22
(B) 28
(C) 29
(D) 32
(E) 41
Rationale: Required sum = (2 + 3 + 5 + 7 + 11+ 13) = 41
Note: 1 is not a prime number
Option E
Answer: (E) 41
Question: f(x) is a function such that f(2x + 1) = 2f(x) + 1 for all real numbers x and f(0) = 2. Find the value of f(3).
(A) 9
(B) 10
(C) 11
(D) 12
(E) 15
Rationale: f(2x + 1) = 2f(x) + 1 : given
f(3) = 2f(1) + 1 : x = 1 in A
f(1) = 2f(0) + 1 : x = 0 in A
f(3) = 11 : substitute
correct answer is C) 11
Answer: (C) 11
Question: The difference between the compound interest compounded annually and simple interest for 2 years at 20% per annum is Rs.144. Find the principal?
(A) 3377
(B) 2997
(C) 3600
(D) 2799
(E) 7719
Rationale: P = 144(100/5)2 => P
= 3600
Answer:C
Answer: (C) 3600
Question: A computer program generates a single digit by a random process, according to which the probability of generating any digit is directly proportional to the reciprocal of one more than that digit. If all digits are possible to generate, then the probability E of generating an odd prime digit is between
(A) 0 and 1/6
(B) 1/6 and 1/3
(C) 1/3 and 1/2
(D) 1/2 and 2/3
(E) 2/3 and 5/6
Rationale: K (1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1/9+ 1/10) =1
Note that 1/10 is least value and is equal to 0.1 so we can write above series as
K (1+0.5+0.3+0.25+0.2+0.16+0.5+residual) = 1
K=1/3+
P (3 or 5 or 7) =K*13/24
Required probability E= 13/24 × 1/3+ = 4+/24 > 1/6
Answer should be B
P.s. 3+ denotes a value little greater than 3 .
Same for 4+.
Answer: (B) 1/6 and 1/3
Question: A rhombus has area 432 sq m, one diagonal is 36 cm. find other diagonal ?
(A) 2400m
(B) 2500m
(C) 2600m
(D) 2700m
(E) 2900m
Rationale: area of rhombus =1/2*d1*d2
432=1/2*d1*.36
d1=2400m
ANSWER:A
Answer: (A) 2400m
Question: In the Forestside summer camp there are 50 children. 90% of the children are boys and the rest are girls. The camp administrator decided to make the number of girls only 5% of the total number of children in the camp. How many more boys must she bring to make that happen?
(A) 50.
(B) 45.
(C) 40.
(D) 30.
(E) 25.
Rationale: Given there are 50 students In the Forestside summer camp , 90% of 50 = 45 boys and remaining 5 girls.
Now here 90% are Boys and 10% are Girls.
Now question is asking about how many boys do we need to add, to make the girls percentage to 5 or 5%..
If we add 50 to existing 45 then the count will be 95 and the girls number will be 5 as it.
Now boys are 95% and girls are 5%. ( out of 100 students = 95 boys + 5 girls ).
IMO option A is correct.
Answer: (A) 50.
Question: Sandy gets 3 marks for each correct sum and loses 2 marks for each incorrect sum. Sandy attempts 30 sums and obtains 65 marks. How many sums did Sandy get correct?
(A) 19
(B) 21
(C) 23
(D) 25
(E) 27
Rationale: Let x be the correct sums and (30-x) be the incorrect sums.
3x - 2(30-x) = 65
5x = 125
x = 25
The answer is D.
Answer: (D) 25
Question: Length of a rectangular plot is 26 mtr more than its breadth. If the cost of fencin gthe plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr?
(A) 53 m
(B) 63 m
(C) 73 m
(D) 83 m
(E) 93 m
Rationale: Let breadth = x metres.
Then, length = (x + 26) metres.
Perimeter = 5300 m = 200 m.
26.50
2[(x + 26) + x] = 200
2x + 26 = 100
2x = 74
x = 37
Hence, length = x + 26 = 63 m
B
Answer: (B) 63 m
Question: A dress on sale in a shop is marked at $D. During the discount sale its price is reduced by 15%. Staff are allowed a further 10% reduction on the discounted price. If a staff member buys the dress what will she have to pay in terms of D ?
(A) 0.75D
(B) 0.76D
(C) 0.765D
(D) 0.775D
(E) 0.805D
Rationale: Successive doscounts = - a - b +ab/100
Putting the values,
Total discount = -15 - 10 + 150/100 = -25 + 1.5 = 23.5% discount
Hence the final price of the dress = D - 0.235D = 0.765D
Correct Option: C
Answer: (C) 0.765D
Question: George is 8 years more than Christopher and Ford is 2 years younger than Christopher. The sum of their ages is 60. Find the ages of Christopher.
(A) 18
(B) 19
(C) 20
(D) 21
(E) 22
Rationale: Christopher age = x
George age, y = x + 8---------->(1)
Ford age, z = x - 2------------>(2)
Sum of their ages, x+y+z=60---->(3)
Substitute z and y values in equation (3)
Therefore, x+(x+8)+(x-2)=60
=> 3x+8-2=60
=> 3x=60-6
=> 3x=54 =>x=54/3
x=18
ANSWER:A
Answer: (A) 18
Question: The ratio of investments of two partners P and Q is 7:5 and the ratio of their profits is 7:10. If P invested the money for 7 months, find for how much time did Q invest the money?
(A) 11
(B) 10
(C) 18
(D) 16
(E) 14
Rationale: 7*5: 7*x = 7:10
x = 14
Answer:E
Answer: (E) 14
Question: How many 3-digit numerals end with a digit that represents a prime number?
(A) 16
(B) 80
(C) 160
(D) 180
(E) 400
Rationale: prime digits 2,3,5 and 7.
three digit numbers _ _ _
1st place can be filled in 4 ways
2nd place can be filled in 10 ways
3rd place can be filled in 10 ways
Total=4*10*10=400
Ans : E
Answer: (E) 400
Question: A person was asked to state his age in years. His reply was , "Take my age 3 years hence, multiply it by 4 and subtract 4 times my age 3 years ago and you will know how old I am." What was the age of the person ?
(A) 18
(B) 92
(C) 27
(D) 24
(E) 19
Rationale: Explanation:
Let the present age of person be x years.
Then, 4(x + 3) - 4(x - 3 ) = x <=> (4x + 12) - (4x - 12) = x <=> x = 24..
Answer: D
Answer: (D) 24
Question: A comittee of three people is to be chosen from four married couples. What is the number of different comittees that can be chosen if two people who are married to each other cannot both serve on the comittee.
(A) 16
(B) 24
(C) 26
(D) 30
(E) 32
Rationale: Steps to the answer:
- Set up the Slots -> _ _ _ (3 choices)
- put in the numbers and multiply: 8*6*4= 192
The right answer choice is E.
Answer: (E) 32
Question: A dishonest dealer professes to sell goods at the cost price but uses a weight of 800 grams per kg, what is his percent?
(A) 22
(B) 25
(C) 66
(D) 77
(E) 91
Rationale: 800 --- 200
100 --- ? => 25%
Answer: B
Answer: (B) 25
Question: A 250 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?
(A) 230 m
(B) 240 m
(C) 250 m
(D) 320 m
(E) 330 m
Rationale: Relative speed = (120 + 80) km/hr
=	(200 x(5/18))m/sec
=	(500/9)m/sec.
Let the length of the other train be x metres.
Then,	(x + 250)/9 = 500/9
x + 250 = 500
x = 250.
C
Answer: (C) 250 m
Question: In the x- y plane, there are 4 points (0,0), (0,4), (4,4), and (4,0). If these 4 points makes a rectangle, what is the probability that x+y<4?
(A) 1/2
(B) 1/3
(C) 1/4
(D) 1/5
(E) 1/6
Rationale: If x+y<4, then y<-x+4.
The line y=-x+4 intersects the rectangle and these three points of intersection (0,0), (0,4) and (4,0) form a triangle.
The points below the line y=-x+4 satisfy x+y<4.
The area of this triangle is (1/2)(4)(4)=8
The area of the rectangle is 16.
P(x+y<4) = 8/16 = 1/2
The answer is A.
Answer: (A) 1/2
Question: If the area of circle is 684 sq cm then its circumference?
(A) 11
(B) 88
(C) 93
(D) 266
(E) 12
Rationale: 22/7 r2 = 684 => r = 14.8
2 * 22/7 * 14.8 = 93 Answer: C
Answer: (C) 93
Question: At a certain college there are three as many English majors as history majors and two times as many English majors as mathematics majors. What is the ratio of the number of history majors to the number of mathematics majors?
(A) 6 to 1
(B) 3 to 2
(C) 1 to 3
(D) 1 to 5
(E) 2 to 3
Rationale: This is how I translated the question:
At a certain college there are twice as many english majors as history majors
E = 3H
and three times as many english majors as mathematics majors.
E = 2M
What is the ratio of the number of history majors to the number of mathematics majors?
What is H:M?
Just set E equal to each other to get the ratio in terms of H and M.
2H = 3M
H/M = 2/3
The answer is 2:3
Answer : E
Answer: (E) 2 to 3
Question: If the length of the diagonal of a square is 20cm,then its perimeter must be
(A) 40
(B) 38
(C) 27
(D) 29
(E) 11
Rationale: Explanation:
d=√2l
Answer: A) 40
Answer: (A) 40
Question: The simple form of the ratio 5/8:3/2 is?
(A) 5:8
(B) 5:5
(C) 5:9
(D) 5:3
(E) 5:1
Rationale: 5/8 : 3/2 = 5:8
Answer: A
Answer: (A) 5:8
Question: What is the tens' digit T of the sum of the first 40 terms of 1, 11, 111, 1111, 11111, 111111, ...?
(A) T=2
(B) T=3
(C) 4
(D) 8
(E) 9
Rationale: All of the first 40 terms have 1 at the units place.
Except the first term, the tens digit of all the remaining 39 terms is 1.
So now if you do the addition
1 1
1 1
. . .
. . .
. . .
1 1
0 1
3 0
Answer is B
Answer: (B) T=3
Question: The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?
(A) 4 years
(B) 5 years
(C) 11 years
(D) 15 years
(E) 22 years
Rationale: Explanation:
Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.
Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50
5x = 20
x = 4.
Age of the youngest child = x = 4 years.
Answer: A
Answer: (A) 4 years
Question: Jane makes toy bears. When she works with an assistant, she makes 80 percent more bears per week and works 20 percent fewer hours each week. Having an assistant increases Jane’s output of toy bears per hour by what percent?
(A) 20%
(B) 80%
(C) 100%
(D) 180%
(E) 200%
Rationale: We can use fractional equivalents here to solve the problem
80% = 4/5; this means that in 1st case if she prepares 5 bears, in 2nd case she prepares 9 bears
10% = 1/10; this means that in 1st case if she needs 10 hours, in 2nd case she needs 9 hours
Now we come to productivity
Based on above fractional values the productivity in 1st case is 0.5 bears / hour and in the 2nd case it is 1 bear / hour
Hence the productivity is double with the assistant i.e. the increase in productivity is 180%
D
Answer: (D) 180%
Question: What should come in place of the question-mark (?) in the following number series?
5690 5121 4552 3983 3414 2845?
(A) 2276
(B) 2516
(C) 2746
(D) 2356
(E) None of these
Rationale: the diff of the numbers in the series is same i.e 569.
5690-5121=569
5121-4552=569
4552-3983=569
3983-3414=569
3414-2845=569
so,2845-2276=569
so ans is 2276.
ANSWER:A
Answer: (A) 2276
Question: An old truck uses 16 gallons of diesel fuel in traveling 224 miles. In order for the truck to travel the same distance using 8 gallons of diesel fuel, by how many miles per gallon must the truck’s fuel mileage be increased?
(A) 16
(B) 8
(C) 14
(D) 12
(E) 24
Rationale: There are two sets 16G1 gallons and 8G2 gallons details given.
16 gallons covering 224 miles
Then 1 G1 is used to cover 14 miles.
Now for 8 G2 covering 224 miles.
then 1 G2 is used to cover 28 miles.
There must 28 - 14 = 14 miles per gallon increment is needed for 8 gallons to improve the mileage to cover 224 miles.
IMO C is correct answer.
Answer: (C) 14
Question: Jamshid can paint a fence in 50 percent less time than Taimour can when each works alone. When they work together, they can paint the fence in 3 hours. How long would it take Taimour to paint the fence alone?
(A) 6 hours
(B) 9 hours
(C) 14 hours
(D) 24 hours
(E) 32 hours
Rationale: I believe the answer is B. Please see below for explanation.
if Jamshid can paint a dence in 50 percent less time then Taimour we can infer the following rate J = 2T
if working together they can do the job in 8 hours we can infer 1 = 2T+T * 3 => 1/9
Working alone Taimour can do the job in 1 = 1/9 * hours => 9
Answer B
Answer: (B) 9 hours
Question: How many prime numbers K exist such that 90 < K < 106 and K is a factor of 99999919?
(A) 1. Zero
(B) 2. One
(C) 3. Two
(D) 4. Three
(E) 5. More than three
Rationale: I found that considering the constraint..K is a prime num in between 90 to 106 not inclusive , only 3 numbers (91,97 and 101) are present but those numbers are not the factors of the number mentioned....Therefore, i doubt the answer.C
Answer: (C) 3. Two
Question: Twelve percent of the programmers in a startup company weigh 200 pounds or more. Twenty-five percent of the programmers that are under 200 pounds in that same company weigh 100 pounds or less. What percent of the programmers in the startup company weigh between 100 and 200 pounds?
(A) 15%
(B) 20%
(C) 25%
(D) 66%
(E) 75%
Rationale: Initially 88% and 12% split
80% is further divided as 25% and 75%
Q is asking about that 75%
let total be '100' then that 75% is (3/4)∗88
so, the required % is [(3/4)∗88/100]∗100 = 66%
ANSWER:D
Answer: (D) 66%
Question: Equal weights of two alloys containing tin, copper and lead in the ratio 5:2:7 and 8:11:9 are melted and mixed together. What is the ratio of tin, copper and lead in the resultant alloy?
(A) 35:81:45
(B) 33:91:81
(C) 17:28:27
(D) 18:15: 23
(E) 20:15: 22
Rationale: Let the weight of the two alloys be w each
Required ratio =
(5w/14 +8w/28): ( 2w/14+11w/28 ): (7w/14+9w/28)
= 18w/28 : 15w/28 : 23w/28
=18:15: 23
ANSWER:D
Answer: (D) 18:15: 23
Question: Working simultaneously and independently at an identical constant rate, 10 machines of a certain type can produce a total of x units of product P in 4 days. How many of these machines, working simultaneously and independently at this constant rate, can produce a total of 3x units of product P in 6 days?
(A) 14
(B) 15
(C) 18
(D) 20
(E) 22
Rationale: The rate of 10 machines is rate=job/time=x/4 units per day --> the rate of 1 machine 1/10*(x/4)=x/40 units per day;
Now, again as {time}*{combined rate}={job done}
then 6*(m*x/40)=3x --> m=20.
Answer: D.
Answer: (D) 20
Question: A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Explanation:
Area of the park = (60 x 40) = 2400m2
Area of the lawn = 2109m2
Area of the crossroads = (2400 - 2109) = 291m2
Let the width of the road be x metres. Then,
60x +40x - x2 = 291
x2 - 100x + 291 =0
(x - 97)(x - 3) = 0
x = 3. Answer: C
Answer: (C) 3
Question: A trader sells 85 meters of cloth for $8925 at the profit of $15 per metre of cloth. What is the cost price of one metre of cloth?
(A) $69
(B) $78
(C) $90
(D) $86
(E) $77
Rationale: C
$90
SP of 1m of cloth = 8925/85 = $105
CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth
= $105 - $15 = $90.
Answer: (C) $90
Question: If a and n are integers, and a^3=360n, then n must be divisible by which of the following?
(A) 2
(B) 6
(C) 25
(D) 27
(E) 60
Rationale: a^3=360n = 2^3*3^2*5*n
and a^3 is a perfect cube due to a being an integer
hence 360n must have powers of each prime number as multiple of 3
hence 360n = 2^3*3^2*5*(3*5^2) for least value of n
i.e. n must have 5^2
Answer: Option C
Answer: (C) 25
Question: Some persons can do a piece of work in 12 days. Two times the number of such persons will do half of that work in
(A) 7 days
(B) 7 days
(C) 9 days
(D) 3 days
(E) 2 days
Rationale: Explanation:
Let x men can do the in 12 days and the required number of days be z
More men, Less days [Indirect Proportion]
Less work, Less days [Direct Proportion ]
Answer: D
Answer: (D) 3 days
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 : 2
(B) 3 : 2
(C) 3 : 1
(D) 4 : 7
(E) 2 : 3
Rationale: Let the speeds of the two trains be x m/sec and y m/sec respectively.
Then, length of the first train = 27 x meters, and
length of the second train = 17 y meters.
(27 x + 17 y) / (x + y) = 23
=> 27 x + 17 y = 23 x + 23 y
=> 4 x = 6 y
=> x/y = 3/2.
Answer : B
Answer: (B) 3 : 2
Question: Adam can do a job in 15days, John can do the same job in 20days. If they work together for 4days on this job. What fractionof job is incomplete ?
(A) 3/11
(B) 4/11
(C) 13/13
(D) 8/15
(E) 9/11
Rationale: Adam can do 1/15 of the job per day
John can do 1/20 of the job per day
If they work together they can do 7/60 of the work together
Remaining job 1 - 4*7/60 = 32/60 = 8/15
(D)
Answer: (D) 8/15