mathewhe/aqua_rat huggingface dataset:
Question: If 10^(c-1)< 0.000125 <10^c, what is the value of an integer c?
(A) -4
(B) -3
(C) -2
(D) 3
(E) 4
Rationale: -> Multiply 10^6- > (10^6){10^(c-1)}<125<(10^6)(10^c) -> 125 is bigger than 100
-> (10^6)(10^(c-1))=100 -> 10^(6+c-1)=10^2, c+5=2 -> c=-3
Thus, the answer is B
Answer: (B) -3
Question: The average of the two-digit numbers, which remain the same when the dibits inter-change their positions, is
(A) 88
(B) 28
(C) 55
(D) 25
(E) 71
Rationale: Average = (11 + 22 + 33 + 44 + 55 + 66 + 77 + 88 + 99) / 9
=( (11 + 99) + (22 + 88) + (33 + 77) + (44 + 66) + 55) / 9
= (4 * 110 + 55)/9 = 495 / 9 = 55
Answer: C
Answer: (C) 55
Question: If there is exactly one root of the equation 2x^2 + ax + b, where a and b are positive constants, what is b in terms of a?
(A) a/2
(B) a
(C) 3a/2
(D) a^2/8
(E) a^2/4
Rationale: one root for a quadratic equation ax^2+bx+c is possible only when b^2 = 4ac ---1
Here b = a
c= b
a = 2
substituting these values in 1, we have
a^2 = 8b => b =a^2/8
Answer is D.
Answer: (D) a^2/8
Question: Rodrick mixes a martini that has a volume of 'n' ounces having 40% Vermouth and 60% Gin by volume. He wants to change it so that the martini is 40% Vermouth by volume. How many ounces of Gin must he add?
(A) 0
(B) n/3
(C) 3n/5
(D) 5n/6
(E) 8n/5
Rationale: 4 ounces is vermouth
6 ounces of gin...
Total volume 10.
To make vermouth account for 40% of total volume the new volume must be....
x*0.4=4
x=10 ounces....
So now you see that he must add 0 ounces of gin...
Plug in 0 for n in the answer choices and look for answer 0
A
Answer: (A) 0
Question: If n = 30! + 25, then n is divisible by which of the following?
I. 25
II. 27
III. 29
(A) None
(B) I only
(C) II only
(D) I and II
(E) II and III
Rationale: 25 divides 30! so 25 also divides 30! + 25.
27 and 29 divide 30! so they do not divide 30! + 25.
The answer is B.
Answer: (B) I only
Question: A man buys an article and sells it at a profit of 20%. If he had bought it at 20% less and sold it for Rs.75 less, he could have gained 25%. What is the cost price?
(A) 288
(B) 375
(C) 267
(D) 298
(E) 121
Rationale: CP1 = 100 SP1 = 120
CP2 = 80 SP2 = 80 * (125/100) = 100
20 ----- 100
75 ----- ? => 375
Answer: B
Answer: (B) 375
Question: Insert the missing number
2, 4, 8, 16, ..., 64, 128, 256
(A) 36
(B) 35
(C) 32
(D) 33
(E) 38
Rationale: series is 2* Previous Number.
ANSWER:C
Answer: (C) 32
Question: Two different primes may be said torhymearound an integer if they are the same distance from the integer on the number line. For instance, 3 and 7 rhyme around 5. What integer E between 1 and 20, inclusive, has the greatest number of distinct rhyming primes around it?
(A) 12
(B) 15
(C) 17
(D) E=18
(E) 20
Rationale: Since we are concerned with integers between 1 and 20, write down the primes till 40.
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37
(you should be very comfortable with the first few primes... )
2, 3, 5, 7, 11,12, 13, 17, 19, 23, 29, 31, 37 - Three pairs (11,13), (7,17), (5, 19)
2, 3, 5, 7, 11, 13,15,17, 19, 23, 29, 31, 37 - Three pairs (13, 17), (11, 19), (7, 23)
2, 3, 5, 7, 11, 13,17, 19, 23, 29, 31, 37 - Three pairs (11, 23), (5, 29), (3, 31)
2, 3, 5, 7, 11, 13, 17,18,19, 23, 29, 31, 37 - Four pairs (17, 19), (13, 23), (7, 29), (5, 31)
2, 3, 5, 7, 11, 13, 17, 19,20,23, 29, 31, 37 - definitely cannot be more than 4 since there are only 4 primes more than 20. So must be less than 4 pairs. Ignore.
Answer (D).
Answer: (D) E=18
Question: The price of 2 skirts and 4 shirts is Rs. 1600. With the same money one can buy 1 skirt and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay ?
(A) Rs. 2300
(B) Rs. 2400
(C) Rs. 2420
(D) Rs. 2460
(E) Rs. 2480
Rationale: Let the price of a skirt and a shirt be Rs. x and Rs. y respectively.
Then, 2x + 4y = 1600 .... (i)
and x + 6y = 1600 .... (ii)
Divide equation (i) by 2, we get the below equation.
=> x + 2y = 800. --- (iii)
Now subtract (iii) from (ii)
x + 6y = 1600 (-)
x + 2y = 800
----------------
4y = 800
----------------
Therefore, y = 200.
Now apply value of y in (iii)
=> x + 2 x 200 = 800
=> x + 400 = 800
Therefore x = 400
Solving (i) and (ii) we get x = 400, y = 200.
Cost of 12 shirts = Rs. (12 x 200) = Rs. 2400.
B
Answer: (B) Rs. 2400
Question: A water tank, having the shape of a rectangular prism of base 100 square centimeters, is being filled at the rate of 1 liter per minute. Find the rate at which the height of the water in the water tank increases. Express your answer in centimeters per minute.
(A) 80 cm
(B) 10 cm
(C) 70 cm
(D) 60 cm
(E) 20 cm
Rationale: The volume of a rectangular prism is given by
area of base ? height
The rate at which the tank is being filled is 1 liter per minute which we need to convert
1 liter = 1 dm3
But 1 dm = 10 cm. Hence
1 liter = (10 cm)3 = 1000 cm3
The height h of the water is related to the volume by
volume = area of base ? h
In one minute the volume increases by 1 liter or 1000 cm3 and the height increases by
h = volume / area of base = 1000 cm3 / 100 cm2 = 10 cm
correct answer B
Answer: (B) 10 cm
Question: Wendy begins sanding a kitchen floor by herself and works for 3 hours. She is then joined by Bruce, and together the two of them finish sanding the floor in 2 hours. If Bruce can sand the floor by himself in 20 hours, how long would it take Wendy to sand the floor by herself?
(A) 9/80 hours
(B) 3/20 hours
(C) 20/3 hours
(D) 80/9 hours
(E) 506/91 hours
Rationale: Let Wendy finishes sanding the floor alone in W hours while B be the hours for Bruce.
Thus in 1 hour Wendy finishes 1/w of the work while Bruce finishes 1/B of the work.
If wendy works for 3 hours and is then joined by Bruce to finish the work in 2 more hours,
3/W + 2/W+2/B = 1 (1 denotes the total amount of work)
5/W + 2/B =1 and given B =20 hours.
Thus W = 506/91 hours , E is the correct answer.
Answer: (E) 506/91 hours
Question: A and B together have Rs. 1210. If 4/15 of A's amount is equal to 2/5 of B's amount, how much amount does A have?
(A) 576
(B) 800
(C) 726
(D) 484
(E) 500
Rationale: (4/15) * A = (2/5) * B
A / B = 3 / 2
Therefore A's share is = (1210 * (3/5)) = 726
Ans - C
Answer: (C) 726
Question: How many randomly assembled people do u need to have a better than 50% probability that at least 1 of them was born in a leap year?
(A) 3
(B) 9
(C) 27
(D) 54
(E) 81
Rationale: Prob[at least one of them was born in a leap year] > 50%
Since P(A) = 1 - P(A')
1 - Prob[none of them was born in a leap year] > 1/2
Prob[none] - 1 < -1/2
Prob[none] < 1/2
Assume that there are n people.
Prob[none] = (3/4)^n
(3/4)^n < 1/2
3^n < (4^n)/2
3^n < (2^2n)/2
3^n < 2^(2n-1)
If n = 3, 3^3 < 2^5 is true
A is the answer
Answer: (A) 3
Question: A company has found that when x units of a product are manufactured and sold, its revenue is given by x 2 + 100 x dollars and its costs are given by 240 x + 500 dollars. How many units must be produced and sold to make a profit of 10,000 dollars? (HINT: profit = revenue - costs)
(A) 192
(B) 193
(C) 194.
(D) 195
(E) 196
Rationale: Let us use profit = revenue - costs to find a formula for the profit P
P = ( x 2 + 100 x ) - ( 240 x + 500 )
Substitute P in the above equation by 10,000 dollars to obtain
10000 = x 2 - 140 x - 500
Write the equation in standard form and solve for x
x 2 - 140 x - 10500 = 0
Solve the above equation for x
x = 194.10 and x = -54.01
The number of units to produce must be positive, so
x = 194.
As an exercise, check that for the above value of x the profit is approximately (because of the rounding) equal to 10,000.
Answer C
Answer: (C) 194.
Question: If |5x-20| = 100, then find the sum of the values of x?
(A) 1
(B) -2
(C) 8
(D) -3
(E) 4
Rationale: |5x-20| = 100
5x-20 = 100 or 5x-20 = -100
5x = 120 or 5x = -80
x = 24 or x = -16
sum = 24-16 = 8
Answer is C
Answer: (C) 8
Question: The average weight of 25 boys sitting in a boat had some value. A new person added to them whose weight was 46 kg only. Due to his arrival, the average weight of all the boys decreased by 5 kg. Find the average weight of first 25 boys?
(A) 150
(B) 154
(C) 176
(D) 182
(E) 192
Rationale: 25x + 46 = 26(x – 5)
x = 176
C
Answer: (C) 176
Question: Three 6 faced dice are thrown together. The probability that no two dice show the same number on them is?
(A) 4/9
(B) 5/9
(C) 2/9
(D) 3/8
(E) 5/3
Rationale: No two dice show same number would mean all the three faces should show different numbers. The first can fall in any one of the six ways. The second die can show a different number in five ways. The third should show a number that is different from the first and second. This can happen in four ways.
Thus 6 * 5 * 4 = 120 favourable cases.
The total cases are 6 * 6 * 6 = 216.
The probability = 120/216 = 5/9.
Answer:B
Answer: (B) 5/9
Question: Find the invalid no.from the following series 15, 16, 34, 105, 424, 2124, 12756
(A) 15
(B) 16
(C) 34
(D) 424
(E) 2124
Rationale: 2nd term = (1st term) * 1 + 1 = 15 *1 + 1 = 16.
3rd term = (2nd term) * 2 + 2 = 16 * 2 + 2 = 34
4th term = (3th term) *3 + 3 = 34 * 3 + 3 = 105
5th term = (4th term) * 4 + 4 = 105 * 4 + 4 = 424
6th term = (5th term) * 5 + 5 = 424 * 5 + 5 = 2125
6th term should 2125 instead of 2124.
E
Answer: (E) 2124
Question: The average of four positive integers is 69. The highest integer is 93 and the least integer is 39. The difference between the remaining two integers is 28. Which of the following integers is the higher of the remaining two integers?
(A) 29
(B) 86
(C) 25
(D) 18
(E) 12
Rationale: Let the four integers be A, B, C and D where A > B > C > D.
(A + B + C + D)/4 = 69 => A + B + C + D = 276 ---> (1)
A = 93, D = 39 and B - C = 28
(1) => B + C = 276 - (A + D) = 276 - 132 = 144.
B + B -28 = 144
B = (144 + 28)/2 = 86
Answer:B
Answer: (B) 86
Question: A, B, C subscribe Rs. 50,000 for a business. If A subscribes Rs. 4000 more than B and B Rs. 5000 more than C, out of a total profit of Rs. 36,000, what will be the amount A receives?
(A) 15120
(B) 14500
(C) 14900
(D) 14300
(E) 14000
Rationale: Total amount invested = 50000
Assume that investment of C =x.
Then investment of B =5000+x,
Investment of A =4000+5000+x=9000+x
x+5000+x+9000+x=50000
⇒3x+14000=50000
⇒3x=50000–14000=36000
⇒x=36000/3=12000
Investment of C =x=12000
Investment of B =5000+x=17000
Investment of A =9000+x=21000
Ratio of the investment of A, B and C
=21000:17000:12000
=21:17:12
Share of A = Total profit ×21/50
=36000×21/50=15,120
Answer is A.
Answer: (A) 15120
Question: There are 60 slots around a circle,numbered 1 to 60. A man starts fromthe first slot and jumps to the 5th slot.From there he jumps to the 9th slot andso on. In which slot will he land in his 2200th jump?
(A) 1
(B) 5
(C) 41
(D) 45
(E) 46
Rationale: every 15th jump, he comes back to 1st position
so, 2200/15 = Remainder 10
Hence 10th position is 41st slot
ANSWER:C
Answer: (C) 41
Question: The age of the daughter is same as the digit in the mother's age, but in reverse order. In thirteen years mother will be twice as old as daughter will be then. what is the difference in their current age ?
(A) 15
(B) 23
(C) 27
(D) 46
(E) 32
Rationale: daughter's age= 10x+y
so mother's age= 10y+x..
after 13 years , 10x+y+13=2*(10y+x+13)....
so 13+19y=8x... check for odd values of y, y=1 satisfies the eqn with x=4... so ages are 41 and 14 and ans as found correctly by u is C..27
Answer: (C) 27
Question: What is the solution of the equations x - y = 5 and 5(x + y)-1 = 2 ?
(A) x = 3.75, y = 1.25
(B) x = 1, y = 0.1
(C) x = 2, y = 1.1
(D) x = 1.2, y = 0.3
(E) None
Rationale: Answer
x - y = 5 ...(i)
and 11(x + y)-1=2
⇒ 5/ (x + y) = 2
⇒ 2(x + y) =5
⇒ x + y = 5/2 ...(ii)
On solving Eqs.(i) and (ii),we get
x = 3.75
and y = 1.25
Correct Option: A
Answer: (A) x = 3.75, y = 1.25
Question: One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in?
(A) 144 min
(B) 250 min
(C) 196 min
(D) 100 min
(E) 112 min
Rationale: Let the slower pipe alone fill the tank in x minutes
Then, faster pipe will fill it in x/3 minutes
1/x + 3/x = 1/36
4/x = 1/36
x = 144 min
Answer is A
Answer: (A) 144 min
Question: Sandy purchased 20 dozen toys at the rate of $360 per dozen. Sandy sold each toy at the rate of $33. What was the percentage profit?
(A) 5%
(B) 6%
(C) 8%
(D) 10%
(E) 12%
Rationale: A dozen toys cost $360, so each toy cost $30.
selling price / cost price = 33/30 = 1.1
The percentage profit is 10%.
The answer is D.
Answer: (D) 10%
Question: If 3^z is a factor of 52!, which of the following could be the value of z?
I. 22
II. 21
III. 23
(A) I ONLY
(B) II ONLY
(C) III ONLY
(D) BOTH I AND II
(E) NONE
Rationale: 3^z is a factor of 52!, what values can z take.
Powers of 3 in 52! = [52/3] + [52/9] +[52/27] , where [x] is the integral part of x
Powers of 3 in 52! = 17 + 5 + 1 = 23
Hence the maximum value of 3^z in 52! = 3^23
Only Statement III satisfies
Correct Option: C
Answer: (C) III ONLY
Question: How many pairs of letters are there in the word 'CASTRAPHONE' which have as many letters between
them in the word as in the alphabet?
(A) 8
(B) 7
(C) 6
(D) 4
(E) 3
Rationale: Looking into the alphabets there are four such pairs namely ON,EH,ST,TO.
Answer: D
Answer: (D) 4
Question: If a wooden bar of length 45 feet is cut into two pieces, what is the length of the shorter piece if the longer bar is 15 feet longer than the shorter bar?
(A) 7
(B) 10
(C) 13
(D) 16
(E) 15
Rationale: Since, 45 is the total length. Shorter is any one from answers.
Try Back solving from D answer, i.e. 16. 16+(16+15) = 47 > 45
Hence, Select next smaller no. : 15 +(15+15) =45. So, 15 is the answer
Answer is E
Answer: (E) 15
Question: A train speeds past a pole in 12 seconds and a platform 160 m long in 17 seconds. Its length is?
(A) 384
(B) 360
(C) 324
(D) 390
(E) 395
Rationale: Let the length of the train be x meters and its speed be y m/sec.
They, x / y = 12 => y = x/12
x + 160 / 17 = x / 12
x = 384 m.
Answer:A
Answer: (A) 384
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 three 8-hour shifts this week and averaged $40 in orders per hour, how much did Jill earn this week?
(A) 280
(B) 300
(C) 240
(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 3 days -> 80*3=240.
This matches answer choice C.
Answer: (C) 240
Question: Three integers are at random chosen between 0 and 9 inclusive. What is the probability E that each number is different ?
(A) A.18/25
(B) B.4/5
(C) C.81/100
(D) D.9/10
(E) E.1
Rationale: Number of ways of choosing the 3 integers without restriction = 10 * 10 * 10
Number of ways of choosing the 3 integers so that the 3 integers are different = 10 * 9 * 8
Probability E= 10 * 9 * 8/10 * 10 * 10 = 72/100 = 18/25
Answer: A
Answer: (A) A.18/25
Question: A larger hose connected to a swimming pool can fill the pool in 6 hours. A smaller hose can fill the pool in 12 hours. How many hours will it take for both of them to fill the pool?
(A) 3
(B) 7 1/2
(C) 5 3/5
(D) 8
(E) 4
Rationale: Work hrs=AB/(A+B)= 72/18 =4
Answer is E
Answer: (E) 4
Question: Income and expenditure of a person are in the ratio 5:4. If the income of the person is Rs.18000, then find his savings?
(A) Rs.3600
(B) Rs.3689
(C) Rs.3615
(D) Rs.3628
(E) Rs.3618
Rationale: Let the income and the expenditure of the person be Rs.5x and Rs.4x respectively.
Income, 5x = 18000 => x = 3600
Savings = Income - expenditure = 5x - 4x = x
So, savings = Rs.3600.
Answer: A
Answer: (A) Rs.3600
Question: Suppose x is a positive even number, all of whose digits are either 3 or 4. If x is also divisible by both 3 and 4, how many digits are in the smallest possible value of x?
(A) Three
(B) Four
(C) Five
(D) Six
(E) Seven
Rationale: Since the number is positive and even and contains only 3 and 4 as digits, then its numbers digit is 4 and is fixed.
As there are not many possibilities for x, I found the most simple method to just start plug in numbers starting from the first and least value of x, which is answer key A. three
If x would have 3 digits, then we have 4 possibilities (since 4 is always the number digit for an even number):
334: is divisible by 4 but not by 3
344: is divisible by 4 but not by 3
434: is not divisible by 4 nor by 3
444: is divisible by 4 AND by 3 - then CORRECT ANSWER A
Answer: (A) Three
Question: If a Ã— b = 2a - 3b + ab, then 2 Ã— 5 + 5 Ã— 2 is equal to :
(A) 18
(B) 23
(C) 24
(D) 25
(E) 26
Rationale: Explanation:
2 Ã— 5 + 5 Ã— 2 = (2 Ã— 2 - 3 Ã— 5 + 2 Ã— 5) + ( 2 Ã— 5 - 3 Ã— 2 + 5 Ã— 3)
= (4 -15 + 10 + 10 - 6 + 15) = 18.
Answer: A
Answer: (A) 18
Question: what is the least number by which 5,400 must be divided to get a number perfect square
(A) 21
(B) 42
(C) 24
(D) 40
(E) 45
Rationale: 5,400/24=225
225=(15)^2
Ans-24
ANSWER:C
Answer: (C) 24
Question: N and M are each 3-digit integers. Each of the numbers 2, 3,4, 6, 7, and 8 is a digit of either N or M. What is the smallest possible positive difference between N and M?
(A) 39
(B) 49
(C) 58
(D) 113
(E) 131
Rationale: You have 6 digits: 2, 3, 4, 6, 7, 8
Each digit needs to be used to make two 3 digit numbers. This means that we will use each of the digits only once and in only one of the numbers. The numbers need to be as close to each other as possible. The numbers cannot be equal so the greater number needs to be as small as possible and the smaller number needs to be as large as possible to be close to each other.
The first digit (hundreds digit) of both numbers should be consecutive integers
Now let's think about the next digit (the tens digit). To minimize the difference between the numbers, the tens digit of the greater number should be as small as possible and the tens digit of the smaller number should be as large as possible . So let's not use 2 and 8 in the hundreds places and reserve them for the tens places . Now what are the options?
Try and make a pair with (3** and 4**). Make the 3** number as large as possible and make the 4** number as small as possible.
387 and 426 (difference is 39) or
Try and make a pair with (6** and 7**). Make the 6** number as large as possible and make the 7** number as small as possible. We get 684 and 723 (difference is 39)
A
Answer: (A) 39
Question: Simple interest on a certain sum is 16/25 of the sum. Find the rate percent and time, If both are numerically equal.
(A) Rate = 7% and Time = 7 years.
(B) Rate = 8% and Time = 8 years.
(C) Rate = 6% and Time = 6 years.
(D) Rate = 5% and Time = 5 years.
(E) None of these
Rationale: Explanation:
Sol: Let sum = X. Then S.I = 16x/25
Let rate = R% and Time = R years.
Therefore, (x * R * R)/100 = 16x/25 or R^2 = 1600/25, R = 40/5 = 8
Therefore, Rate = 8% and Time = 8 years.
Answer: B
Answer: (B) Rate = 8% and Time = 8 years.
Question: A man travels 100km by train at 50km/hr, 200km by ship at 20km/hr, 300km by aeroplane at 100km/hr and 100km by car at 50km/hr. What is the average speed for the entire distance?
(A) 35.3km/hr
(B) 45km/hr
(C) 48.9km/hr
(D) 52.6km/hr
(E) 27.6km/hr
Rationale: Total distance traveled = 100+200+300+100 = 600km
Total time taken = 100/50 + 200/20 + 300/100 + 100/50 = 17 hrs
Average speed = 600/17 = 35.3km/hr approximately ;
Answer is A
Answer: (A) 35.3km/hr
Question: An incredible punch is composed of buttermilk, orange juice, and brandy. How many pints of orange juice are required to make 7 1⁄2 gallons of punch containing twice as much buttermilk as orange juice and three times as much orange juice as brandy? (1 Gallon = 8 Pints )
(A) 16
(B) 18
(C) 20
(D) 22
(E) 24
Rationale: 1 gallon = 8 pints
7.5 gallons = 60 pints
Buttermilk = 2 orange
orange = 3 brandy
buttermilk+orange+brandy = 60
2orange+orange+1/3 orange = 60
10 orange = 180
orange = 18 pints
ANSWER:B
Answer: (B) 18
Question: The total age of A and B is 12 years more than the total age of B and C. C is how many years younger than A ?
(A) 12
(B) 27
(C) 21
(D) 18
(E) 11
Rationale: (A+B) - (B+C) = 12
A - C = 12.
C is younger than A by 12 years.
Answer: A
Answer: (A) 12
Question: For which of the following functions f is f(y) = f(1-y) for all of y?
(A) f(y) = 3y + 2
(B) f(y) = 1-y^2
(C) f(y) = 4y^2 * (2-2y)^2
(D) f(y) = y/(y-1)
(E) f(y) = y/(y+1)
Rationale: y = 2
a) f(2) = 6*2 + 2 = 14; f(-1) = -3 + 2 = -1 NO
b) f(2) =1 - 2^2 = 1 - 4 = -3 ; f(-1) = 1 - (-1)^2 = 1 - 1 = 0 NO
c) f(2) = 4*2^2 * (2-2*2)^2 = 4*4 * (2-4)^2 = 16 * 4; f(-1) = 4*1 * (2-2(-1))^2 = 4 * (2+2)*2 = 4 * 16 YES
Here we could stop and safely pick the number without doing d & e, but just in case:
d) f(2) = 2/1 = 2 ; f(-1) = -1 / -2 = 1/2 NO
e) f(2) = 2/3; f(-1) = -1/0 = 0 (div by 0) NO
So I proved that in all but C case if y=2 the values of f(y) ≠ f(1-y)
Answer: C
Answer: (C) f(y) = 4y^2 * (2-2y)^2
Question: X and Y invest Rs.21000 and Rs.17500 respectively in a business. At the end of the year, they make a profit of Rs.26400. What is the share of X in the profit?
(A) Rs.14400
(B) Rs.26400
(C) Rs.12000
(D) Rs.12500
(E) Rs.13500
Rationale: Ratio of the investment=21000:17500=210:175
=42:35=6:5
Share of X in the profit=(26400×6)/11=2400×6
=14400
ANSWER:A
Answer: (A) Rs.14400
Question: An amount of money is to be divided among P, Q and R and in the ratio of 5:11:23 respectively. If the difference between the total share of P and Q together and R’s share is Rs. 2,800 what is the difference between Q and R’s share? [Bank 2000]
(A) Rs. 6,400
(B) Rs. 3,600
(C) Rs. 4,800
(D) Rs. 3,200
(E) Rs. 3,700
Rationale: Explanation:
Let he shares of P, Q and R be 5x,11x and 23x respectively, by given condition.
R-(P+Q) = 2800
23x -16x = 2800
7x =2800
x=400
Difference between Q’s an R’s share = 23x-11x = 12x= Rs. 4800
Answer: C
Answer: (C) Rs. 4,800
Question: The cross-section of a well is a trapezium in shape. If the well is 15 m wide at the top and 5 m wide at the bottom and the area of cross-section is 700 sq m, the depth of well is?
(A) 20 m
(B) 60 m
(C) 40 m
(D) 80 m
(E) 70 m
Rationale: 1/2 * d (15 + 5) = 700
d = 70
ANSWER:E
Answer: (E) 70 m
Question: 20 men can complete a work in 10days. Six days after they started working, 10 more men joined them. How many days will they now take to complete the remaining work?
(A) 1/2
(B) 8/3
(C) 4/5
(D) 6
(E) 4
Rationale: 20*10 men can complete the work in 1 day
1 man's 1 day work = 1/200
20 men 6days work = 6*1/10 = 3/5
remaining work = 1-3/5 = 2/5
30 men's 1 day's work = 30/200 = 3/20
2/5 work is done by them in 20/3 * 2/5 = 8/3days
Answer is B
Answer: (B) 8/3
Question: A number consists of two digits whose sum is 11. If 27 is added to the number, then the digits change their places. What is the number ?
(A) 47
(B) 65
(C) 83
(D) 92
(E) 95
Rationale: If number is xy , then x +y =11
and
10x+y +27 = 10y+x
solving these eqns, we get
x=4 and y =7
so number is 47.
ANSWER:A
Answer: (A) 47
Question: Six points are marked on a straight line and five points are marked on another line which is parallel to the first line. How many straight lines, including the first two, can be formed with these points?
(A) 36
(B) 28
(C) 23
(D) 27
(E) 32
Rationale: Explanation:
We know that, the number of straight lines that can be formed by the 11 points in which 6 points are collinear and no other set of three points, except those that can be selected out of these 6 points are collinear.
Hence, the required number of straight lines
= + 1 + 1
= 55 - 15 - 10 + 2 = 32
Answer: E
Answer: (E) 32
Question: A sum of money becomes 7/6 of itself in 6 years at a certain rate of simple interest. The rate per annum is?
(A) 50/9
(B) 50/13
(C) 50/17
(D) 25/9
(E) 5 5/1
Rationale: Let sum = x. Then, amount = 7x/6
S.I. = 7x/6 - x = x/6; Time = 6 years.
Rate = (100 * x) / (x * 6 * 6) = 25/9 %.
Answer:D
Answer: (D) 25/9
Question: Tarun bought a T.V. with 20% discount on the labelled price. Had he bought it with 25% discount, he would have saved Rs. 500. At what price did he buy the T.V.?
(A) Rs. 5000
(B) Rs. 10000
(C) Rs. 12000
(D) Rs. 16000
(E) None of these
Rationale: Let the labeled price be Rs. 100.
S.P. in 1st case=Rs. 80, S.P. in 2nd case=Rs. 75.
5 : 100 : : 500 : x.
So, x=[(100X500)/5]=10000.
i.e Required CP = 80 % of 10000 = 8000
ANSWER:E
Answer: (E) None of these