mathewhe/aqua_rat huggingface dataset:
Question: for a computer a password uses five digits from 0 to 9, inclusive. What is the probability that the digits of the password solely consist of prime numbers or zero?
(A) A)1/32
(B) B)1/16
(C) C)1/8
(D) D)2/5
(E) E)1/2
Rationale: Favorable outcomes will be obtained by making Password using {0, 2, 3, 5, 7} i.e. 5 digits
Total Such Passwords = 5*5*5*5*5 = 5^5
Total Possible Password = 10*10*10*10*10 = 10^5
Probability = (5^5) / (10^5) = 1/2^5 = 1/32
Answer: option A
Answer: (A) A)1/32
Question: What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 50?
(A) A)Rs.3400
(B) B)Rs.3948
(C) C)Rs.3988
(D) D)Rs.3949
(E) E)Rs.3923
Rationale: Let the side of the square plot be a ft.
a2 = 289 => a = 17
Length of the fence = Perimeter of the plot = 4a = 68 ft.
Cost of building the fence = 68 * 50 = Rs.3400
Answer: A
Answer: (A) A)Rs.3400
Question: Maths, Physics and chemistry books are stored on a library shelf that can accommodate 25 books. Currently, 20% of the shelf spots remain empty. There are twice as many maths books as physics books and the number of physics books is 4 greater than that of chemistry books. Among all the books, 12 books are soft cover and the remaining are hard-cover. If there are a total of 7 hard-cover books among the maths and physics books. What is the probability W, that a book selected at random is either a hard cover book or a chemistry book?
(A) 1/10
(B) 3/20
(C) 1/5
(D) 1/4
(E) 9/20
Rationale: First phase of this problem requires you to determine how many mathematics and chemistry books are even on the shelf. To do so, you have the equations:
m + p + c = 20 (since 4/5 of the 25 spots are full of books)
m = 2p
p = 4 + c
From that, you can use Substitution to get everything down to one variable.
c = p - 4
m = 2p
p = p
Then (p - 4) + 2p + p = 20, so 4p = 24 and p = 6. That means that there are 12 math, 6 physics, and 2 chemistry books on the shelf.
With those numbers, you also know that there are 8 total hardcovers, 1 of which is chemistry. So if your goal is to get either a hardcover or a chemistry, there are 9 ways towin- either one of the 7 hardcovers that aren't chemistry or the two chemistry books. So out of the 20 total, W=9 provide the desired outcome, making the answer E.
Answer: (E) 9/20
Question: If a = 1 and b = -2, then (2a^2 + b)(m + y) + (a + b)(m - y) =
(A) 0
(B) 2x
(C) y - m
(D) x - y
(E) x + y
Rationale: Putting A=1 and B = -2 => 2A^2-B=0 ; so the first part of the term is zero
with second term => (1-2) *(m+y)=y-m => Smash C
Answer: (C) y - m
Question: The number of sequences in which 7 boys can throw a apple, so that the youngest player may not be the last is
(A) 2300
(B) 2400
(C) 4320
(D) 4500
(E) 4550
Rationale: The last ball can be thrown by any of the remaining 6 players.
The first 6 players can throw the ball in ⁶P₆ ways.
The required number of ways = 6(6!) = 4320
C
Answer: (C) 4320
Question: The sum of the factors of a number is 124. What is the number?
(A) Number lies between 40 and 50
(B) Number lies between 50 and 60
(C) Number lies between 60 and 80
(D) More than one such number exists
(E) None of these
Rationale: Solution:
Any number of the form paqbrc will have (a + 1) (b + 1)(c + 1) factors, where p, q, r are prime. (This is a very important idea)
For any number N of the form paqbrc, the sum of the factors will be (1 + p1 + p2 + p3 + …+ pa) (1 + q1 + q2 + q3 + …+ qb) (1 + r1 + r2 + r3 + …+ rc).
Sum of factors of number N is 124. 124 can be factorized as 22 * 31. It can be written as 4 * 31, or 2 * 62 or 1 * 124.
2 cannot be written as (1 + p1 + p2…pa) for any value of p.
4 can be written as (1 + 3)
So, we need to see if 31 can be written in that form.
The interesting bit here is that 31 can be written in two different ways.
31 = (1 + 21 + 22 + 23 + 24)
31 = ( 1 + 5 + 52)
Or, the number N can be 3 * 24 or 3 * 52. Or N can be 48 or 75 . Option D
Answer: (D) More than one such number exists
Question: Which of the following are divisible by both 2 and 3?
I. 234,124,422
II. 88,865,544,264
III. 5,555,554,678
(A) I​ only
(B) I and II​
(C) II and III
(D) II Only
(E) I​ and III
Rationale: III. is not divisible by 2 & 3
I. is divisible by 3 since sum of the digits is 24 , which is divisible by 3
II. is divisible by 3 since sum of the digits is 60 , which is divisible by 3
Thus among the given options only (B) holds true.
Answer: (B) I and II​
Question: In a restaurant, the profit is 120% of the cost. If the cost increases by 12% but the selling price remains constant, approximately what percentage of the selling price is the profit?
(A) 30%
(B) 49%
(C) 90%
(D) 100%
(E) None of these
Rationale: Explanation :
Let C.P.= Rs. 100. Then, Profit = Rs. 120, S.P. = Rs. 220.
New C.P. = 112% of Rs. 100 = Rs. 112
New S.P. = Rs. 220.
Profit = Rs. (220 - 112) = Rs. 108.
Required percentage = (108 /220 *100) % = 49 % appox
Answer : B
Answer: (B) 49%
Question: 275 metres long yard, 26 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between 2consecutive trees
(A) 11
(B) 12
(C) 14
(D) 16
(E) 17
Rationale: 26 trees have 25 gaps between them,
Required distance (275/25) = 11
A
Answer: (A) 11
Question: A train travelling at a speed of 75 mph enters a tunnel miles long. The train is mile long. How long does it take for the train to pass through the tunnel from the moment the front enters to the moment the rear emerges?
(A) 2
(B) 3
(C) 5
(D) 7
(E) 8
Rationale: Explanation:
Total distance covered =miles
=miles
Time taken = hrs
= hrs
= min
= 3 min
Answer: B) 3 min
Answer: (B) 3
Question: Minute hand overlaps hour hand in 65 mins. In how many days it will gain 1440 hours ?
(A) 58.384 days
(B) 59.384 days
(C) 57.384 days
(D) 69.384 days
(E) 55.384 days
Rationale: In this problem , it has considered that 65 mins = 1hr
so mins has increased by 5 mins so multiply 5*24=120 mins extra ,
That is now per day it adds 2hr extra so divide 1440/26=59.384 days
ANSWER:B
Answer: (B) 59.384 days
Question: A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that all the four bulbs are defective.
(A) 1/126
(B) 1/127
(C) 1/26
(D) 1/129
(E) 1/261
Rationale: Out of nine, five are good and four are defective.
Required probability = â´Câ‚„/â¹Câ‚„ = 1/126
Answer: A
Answer: (A) 1/126
Question: How many seconds will a 700 metre long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
(A) 25
(B) 30
(C) 42
(D) 45
(E) 50
Rationale: Relative speed of the train=63-3=60kmph=60*5/18=50/3 m/sec
t=700*3/50=42sec
ANSWER:C
Answer: (C) 42
Question: A soft drink company had 6000 small and 15000 big bottles in storage. If 11% of small 12% of big bottles have been sold, then the total bottles remaining in storage is
(A) 15360
(B) 16010
(C) 15060
(D) 14930
(E) 18540
Rationale: 6000 + 15000 - (0.11*6000 + 0.12*15000) = 18540.
Answer: E.
Answer: (E) 18540
Question: 60 is to be divided into two parts such that the sum of 10 times the first and 22 times the second is 780. The bigger part is :
(A) 33
(B) 45
(C) 26
(D) 28
(E) 19
Rationale: Explanation:
Let the two parts be (60 - x) and x.
Then, 10 (60 - x) + 22x = 780
=> 12x = 180
=> x = 15.
Bigger part = (60- x) = 45.
Answer: B) 45
Answer: (B) 45
Question: John had a stock of 400 pens in his bookshop. He sold 50 on Monday, 25 on Tuesday, 80 on Wednesday, 100 on Thursday and 85 on Friday. What percentage of the pens were not sold?
(A) 15%
(B) 25%
(C) 86%
(D) 42%
(E) 55%
Rationale: Let N be the total number of pens sold. Hence
N = 50 + 25+ 80 +100 + 85= 340
Let M be the pens NOT sold
M = 400 - N = 400 - 340 = 798
Percentage
pens not sold / total number of books = 60/400= 0.15 = 15%
correct answer A
Answer: (A) 15%
Question: The ratio of 2 numbers is 2:7 and their H.C.F. is 18. Their L.C.M. is ?
(A) 252
(B) 243
(C) 521
(D) 361
(E) 600
Rationale: Let the numbers be 2x and 7x
Their H.C.F. = 18
so the numbers are 2*18 , 7*18 = 36,126
L.C.M. = 252
Answer is A
Answer: (A) 252
Question: In a certain group of 9 members, 3 members teach only French and the rest teach only Spanish or German. If the group is to choose 5-member committee, which must have at least 1 member who teaches French, how many different committee can be chosen ?
(A) 80
(B) 90
(C) 120
(D) 110
(E) 100
Rationale: Case 1
1french 4either German or Spanish: 3C1 * 6C4 = 45
Case 2
2french 3either German or Spanish: 3C2 * 6C3 = 60
Case 3
3french 2either German or Spanish = 3C3 * 6C2 = 15
Answer is C = 120
Answer: (C) 120
Question: Sides of a rectangular park are in the ratio 3: 2 and its area is 2460sq m, the cost of fencing it at 50 ps per meter is?
(A) s.122
(B) s.129
(C) s.129.76
(D) s.120
(E) s.121
Rationale: 3x * 2x = 2460 => x = 20.24
2(79.76 + 50) = 259.52 m
259.52 * 1/2 = Rs.129.76
Answer:C
Answer: (C) s.129.76
Question: Rs.850 is divided so that 4 times the first share, twice the 2nd share and twice the third share amount to the same. What is the value of the first share?
(A) s400
(B) s500
(C) s850
(D) s540
(E) s170
Rationale: A+B+C = 850
4A = 2B = 2C = x
A:B:C = 1/4:1/2:1/2 = 1:2:2
1/5* 850 =Rs170
Answer:E
Answer: (E) s170
Question: If two dice are thrown simultaneously, then find the probability that the sum of numbers appeared on the dice is 4?
(A) 5/6
(B) 7/36
(C) 5/36
(D) 3/36
(E) 12/36
Rationale: The sum of numbers appeared is 4.
Therefore, the required probability = n(E)/n(S) = 3/36.
ANSWER:D
Answer: (D) 3/36
Question: Rani bought more apples than oranges. She sells apples at ₹23 apiece and makes 15% profit. She sells oranges at ₹10 apiece and makes 25% profit. If she gets ₹653 after selling all the apples and oranges, find her profit percentage Q.
(A) 16.8%
(B) 17.4%
(C) 17.9%
(D) 18.5%
(E) 19.1%
Rationale: Given: Selling price of an Apple = 23 --> Cost price = 23/1.15 = 20
Selling price of an orange = 10 --> Cost price = 10/1.25 = 8
A > O
23*(A) + 10*(O) = 653
653 - 23*(A) has to be divisible by 10 --> Units digit has to be 0
Values of A can be 1, 11, 21, 31, .... --> 1 cannot be the value
Between 11 and 21, If A = 11, O = 30 --> Not possible
If A = 21, O = 17 --> Possible
Cost price = 20*21 + 8*17 = 420 + 136 = 556
Profit = 653 - 556 = 97
Profit% Q= (97/556)*100 = 17.4%
Answer: B
Answer: (B) 17.4%
Question: Three candidates contested an election and received 3408, 22908 and 34884 votes respectively. What percentage of the total votes did the winning candidate get ?
(A) 57%
(B) 45%
(C) 75%
(D) 86%
(E) 95%
Rationale: Explanation :
Total number of votes polled = (3408 + 22908 + 34884)
= 61200.
Required percentage = (34884/ 61200100)%
= 57%.
Answer : A
Answer: (A) 57%
Question: Chuck's apple tree produces 4 apples for every 2 branches. There are 8 branches on his tree. how many apples will Chuck's tree produce?
(A) 16
(B) 8
(C) 2
(D) 4
(E) 32
Rationale: 4 apples for every 2 branches = 2 apples for every 1 branch
2 apples for 1 branch (8 branches) = 2 apples x 8 branches = 16 apples
Answer is 16
Answer: (A) 16
Question: Priya invested some money in 5% stock at 200.If David wants to invest in an equally good 20% stock ,he must purchase a stock worth of :
(A) Rs. 400
(B) Rs. 600
(C) Rs. 800
(D) Rs. 600
(E) Rs. 500
Rationale: Solution
For an income of Rs. 5, investment = Rs. 200
For an income of Rs. 20, investment = Rs.(200/5x20) = Rs. 800
Answer C
Answer: (C) Rs. 800
Question: How many odd 4-digit positive integers W that are multiples of 5 can be formed without using the digit 3?
(A) 648
(B) 729
(C) 900
(D) 1296
(E) 3240
Rationale: I choose A.
Possible n° of 1st digit: 8 (0 can't be the first number, or else it wouldn't have 4 digits. 3 is exlcuded)
Possible n° of 2nd digit: 9 (3 is excluded)
Possible n° of 3rd digit: 9 (3 is excluded)
Possible n° of 4th digit: 1 (a number is a multiple of 5 if it ends in 5 or 0, here we are asked for the odd numbers, hence the last digit can't be 0)
So, W=8*9*9*1=648 (A)
Answer: (A) 648
Question: A and B are running around a circular track of length 120 meters with speeds 12 m/s and 6 m/s in the same direction. When will they meet for the first time?
(A) A meets C
(B) A meets B
(C) A meets D
(D) A meets A
(E) A meets G
Rationale: A meets B when A covers one round more than B.
A's relative speed = (12 - 6) m/s. So he takes 120 / 6 seconds to gain one extra round.
So after 20 seconds A meets B.
Answer:B
Answer: (B) A meets B
Question: If W is the set of all the integers between 29 and 99, inclusive, that are either multiples of 3 or multiples of 2 or multiples of both, then W contains how many numbers?
(A) 26
(B) 32
(C) 33
(D) 34
(E) 47
Rationale: Multiples of 2 from 29 to 99=Multiples of 2 from 1 to 99-Multiples of 2 from 1 to 28=[99/2]-[28/2]=49-14=35
Multiples of 3 from 29 to 99=Multiples of 3 from 1 to 99-Multiples of 3 from 1 to 28=[99/3]-[28/3]=33-9=24
Multiples of2 and 3 bothi.e.6 from 29 to 99=Multiples of 6 from 1 to 99-Multiples of 6 from 1 to 28=[99/6]-[28/6]=16-4=12
These 8 Numbers have been counted twice in both the above calculation while calculating multiples of 2 and 3
i.e. Total Numbers in W = 35 + 24 - 12 = 47
Answer Option E
Answer: (E) 47
Question: If the sides of a triangle are 26 cm, 24 cm and 15 cm, what is its area?
(A) 120
(B) 772
(C) 180
(D) 266
(E) 2848
Rationale: The triangle with sides 26 cm, 24 cm and 15 cm is right angled, where the hypotenuse is 26 cm.
Area of the triangle = 1/2 * 24 * 15 = 180 cm2
Answer: C
Answer: (C) 180
Question: A student was asked to find 4/5 of a number. But the student divided the number by 4/5, thus the student got 45 more than the correct answer. Find the number.
(A) 60
(B) 80
(C) 100
(D) 120
(E) 140
Rationale: Let the number be x.
(5/4) * x = (4/5)*x + 45
25x = 16x + 900
9x = 900
x = 100
The answer is C.
Answer: (C) 100
Question: From the salary of Rahul, 20% is deducted as house rent, 10% of the rest he spends on children’s education and 10% of the balance, he spends on clothes. After this expenditure he is left with Rs 1,377. His salary is?
(A) Rs 2,125
(B) Rs 2,040
(C) Rs 2,100
(D) Rs 2,200
(E) Rs 3,200
Rationale: Suppose that his salary = Rs 100
House rent = Rs 20, balance = Rs 80
Expenditure on education = Rs (10 x 80)/100 = Rs 8
Balance = Rs 72
Expenditure on clothes Rs (10 x 72)/100 = Rs 7.2
Balance now = Rs 64.8
If balance is Rs 64.8, salary = Rs 100
If balance is Rs 1,377, salary
= Rs (100 x 1377) / 64.8
Rs 2,125
ANSWER:A
Answer: (A) Rs 2,125
Question: A father said to his son, "I was as old as you are at present at the time of your birth." If the father's age is 38 years now, the son's age five years back was
(A) 14 years.
(B) 19 years
(C) 33 years
(D) 38 years
(E) None
Rationale: Solution
Let the son's present age be x years.
Then	(38-x)=x
2x=38
x=19.
Therefore son's age 5 years back	=(19-5) years
= 14 years.
Answer A
Answer: (A) 14 years.
Question: The length of a rectangle is twice its breadth. If its length is decreased by 5 cm and breadth is increased by 5 cm, the area of the rectangle is increased by 75 sq.cm. What is the length of the rectangle?
(A) 18 CM
(B) 16 CM
(C) 40 CM
(D) 20 CM
(E) 50 CM
Rationale: LET BRESDTH X CM
LENGTH = 2X CM
NEW L = (2X-5) CM
NEW BREADTH = (X + 5)
NEW AREA = (2X - 5 ) SQ CM
= (2X - 5 ) (X + 5 ) = 2X2+75
X = 20 CM
L = 2X - 2 = 2 * 20 = 40 CM
ANSWER C
Answer: (C) 40 CM
Question: The speed of a boat in still water is 60kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
(A) 29
(B) 40
(C) 99
(D) 28
(E) 12
Rationale: Speed downstream = 60 + 20 = 80 kmph
Speed upstream = 60 - 20
= 40 kmph
Answer: B
Answer: (B) 40
Question: In a village there are 150 men and 90 women in present time.if in next year population will be P=(a^2 +b^2)^1/2 , and in every year men are reduces 12%.what is population of after 2 year.
(A) 139
(B) 141
(C) 142
(D) 143
(E) 144
Rationale: next year total population=[150^2+90^2]^.5=174.92=175
man decreased by 11% so total man =150*.88=132
women will be= 175-132=43
so population after two years= [135^2+43^2]^.5=138.8=139
so population after two year= 139
ANSWER:A
Answer: (A) 139
Question: 8 identical machines, working alone and at their constant rates, take 6 hours to complete a job lot. How long would it take for 6 such machines to perform the same job?
(A) 2.25 hours
(B) 8 hours
(C) 12 hours
(D) 14.25 hours
(E) 16 hours
Rationale: Let each machine do 1 unit of work for 1 hour
8 machines --> 8 units of work in 1 hour
For 6 hours = 8*6 = 48 Units of total work is done.
Now this 48 Units of total work must be done by 6 machines
6units of work(6 machines) ---> 1 hour
for 48 Units of work
6*8 ---> 1*8 hours
B 8 hours
Answer: (B) 8 hours
Question: A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 78000, then the share of A is?
(A) s.42028
(B) s.42000
(C) s.42003
(D) s.42029
(E) s.24029
Rationale: Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6
Total profit = Rs. 78000
Share of B = 7/13 (78000) = Rs.42000
Answer: B
Answer: (B) s.42000
Question: ?% of 360 = 108
(A) 30
(B) 36
(C) 64
(D) 72
(E) None of these
Rationale: ?% of 360 = 108
or, ? = 108×100/360=30
Answer A
Answer: (A) 30
Question: Find smallest prime number is:
(A) 6
(B) 18
(C) 7
(D) 15
(E) 11
Rationale: C
7
Answer: (C) 7
Question: Simplify: 8888 + 888 + 88 + 8
(A) 9872
(B) 9782
(C) 9827
(D) 9287
(E) None of them
Rationale: 8888
888
88
8
-------
9872
Answer is A.
Answer: (A) 9872
Question: Aphid and Ladybug are investors in a pineapple farm. Aphid owns a 30% stake in it, and Ladybug owns the remaining 70%. The profits this year in pineapples and pineapple byproducts total five million zenny (the national currency of their land). How much zenny should Aphid receive?
(A) 50000 zenny
(B) 100000 zenny
(C) 150000 zenny
(D) 200000 zenny
(E) 250000 zenny
Rationale: A = 30
B = 70
A share 3 parts & B share 7 parts
Total 10 parts -----> 5000000
----> 1 part -------> 500000
A share = 3 parts -----> 150000
C
Answer: (C) 150000 zenny
Question: The product of 4 consecutive even numbers is always divisible by:
(A) 384
(B) 350
(C) 400
(D) 200
(E) 250
Rationale: The product of 4 consecutive numbers is always divisible by 4!.
Since, we have 4 even numbers, we have an additional 2 available with each number.
Now, using both the facts, we can say that the product of 4 consecutive even numbers is always divisible by,
2^4 * 4!
16 * 24 = 384
ANSWER A
Answer: (A) 384
Question: Walking across campus, a student interviewed a group of students. 20% of the students took a finance class last semester, 50% took a marketing class last semester, and 40% took neither a finance nor a marketing class last semester. What percent of the students in the group took both a finance and a marketing class?
(A) 60%
(B) 50%
(C) 25%
(D) 15%
(E) 10%
Rationale: {Total} = {finance} + {marketing} - {both} + {neither}
100 = 20 + 50 - {both} + 40
{both} = 10%.
The answer is E.
Answer: (E) 10%
Question: In a candy dish the ratio of red to yellow candies is 2:5, the ratio of red to green candies is 3:8, and the ratio of yellow ot blue candies is 9:2.what is the maximum total number R of yellow and green candies combined if the maximum combined number of red and blue candies is fewer than 85?
(A) 144
(B) 189
(C) 234
(D) 279
(E) 309
Rationale: Given that Red is to yellow is 2:5, Red is to green is 3:8 and Yellow is to blue is 9:2.
Therefore, the total number of red, yellow, blue and green balls will be 18x, 45x, 10x and 48x respectively, where x is a constant.
If the combined number of red and blue balls is fewer than 85, i.e. max 84 balls, then the maximum number of yellow and green balls will be 279.
(10x+18x) < 85.
28x < 85, i.e. 28x <= 84 (Since number of balls cannot be in fraction). Thus, x<=3.
(45x+48x) = 93x.
Max (93x) R= 279.
Answer is D.
Answer: (D) 279
Question: How many diagonals does a polygon with 23 sides have, if one of its vertices does not connect to any diagonal?
(A) 201
(B) 159
(C) 179
(D) 189
(E) 209
Rationale: If I calculate it using the formulae, #diagonals = n (n-3)/2Each vertex sends of n-3 diagonals
n= 23-1 then 22*(22-3)/2 = 209
Correct Option:E
Answer: (E) 209
Question: The difference between a five digit number and the number formed by reversing its digit is not a multiple of
(A) 2
(B) 4
(C) 3
(D) 1749
(E) 5
Rationale: Another approach is to TEST a number.
Let's say the original number is 12345
So, the REVERSED number is 54321
The DIFFERENCE = 54321-12345 =41976
No check the answer choices
41976 is a multiple of2,3,4,1749
5 is NOT a multiple of 41976
Answer:E
Answer: (E) 5
Question: Exactly 3/7 of the people in the room are under the age of 21, and exactly 5/14 of the people in the room are over the age of 65. If the total number of the people in the room is greater than 50 and less than 100, how many people in the room are under the age of 21?
(A) 21
(B) 35
(C) 39
(D) 42
(E) 65
Rationale: The total number of the people in the room must be a multiple of both 7 and 14 (in order 3/7 and 5/14 of the number to be an integer), thus the total number of the people must be a multiple of LCM of 7 and 14, which is 98.
Since, the total number of the people in the room is greater than 50 and less than 100, then there are 98 people in the room.
Therefore there are 3/7*98=42 people in the room under the age of 21.
Answer: D.
Answer: (D) 42
Question: A sum of money placed at C.I. interest doubles itself in 5 years. It will amount to eight times itself at the same rate of interest in?
(A) 11
(B) 88
(C) 15
(D) 27
(E) 20
Rationale: P(1 + R/100)5 = 2P => (1 + R/100)5 = 2
Let P(1 + R/100)n = 8P
=> (1 + R/100)n = 8 = 23 = {(1 + R/100)5}3
=> (1 + R/100)n = (1 + R/100)15 => n = 15 Required time = 15 years.
Answer: C
Answer: (C) 15
Question: Of all the students in a certain dormitory, 1/2 are first-year students and the rest are second-year students. If 4/5 of the first-year students have not declared a major and if the fraction of second-year students who have declared a major is 1/2 times the fraction of first-year students who have declared a major, what fraction of all the students in the dormitory are second-year students who have not declared a major?
(A) 1/15
(B) 1/5
(C) 9/20
(D) 1/3
(E) 2/5
Rationale: tot students=x
1st year student=x/2----> non majaor=4/5(x/2)-----> maj=1/5(x/2)
2nd year student=x/2---->maj=1/2(1/5(x/2))=1/20(x)--->non major=x/2-1/20(x)=9/20(x)
hence 9/20
C
Answer: (C) 9/20
Question: A television manufacturer produces 600 units of a certain model each month at a cost to the manufacturer of £90 per unit and all of the produced units are sold each month. What is the minimum selling price per unit that will ensure that the monthly profit (revenue from sales minus production costs) on the sales of these units will be at least £42,000?
(A) £110
(B) £120
(C) £140
(D) £160
(E) £180
Rationale: Explanation:
Let's say x is the amount that the manufacturer sells each unit for, then the profit per unit can be expressed as x-90. We also know that 600 units have been produced and that the total profit has to be at least £42,000.
600(x-90)≥42,000
x-90≥70
x≥160
Answer: Option D
Answer: (D) £160
Question: Find out the wrong number in the given sequence of numbers.
1, 2, 6, 15, 31, 55
(A) 55
(B) 6
(C) 15
(D) 31
(E) 91
Rationale: 1(result) + (1*1) = 2.
2(result) + (2*2) = 6.
6(result) + (3*3) = 15.
15(result) + (4*4) = 31.
31(result) + (5*5) = 56.
Now we are getting 56 not 55.. So 55 is the wrong number of the given.
answer : A
Answer: (A) 55
Question: The distance between A&B is 1540km. A person is traveling from A to B at 100km/hr started at 6AM and another person is traveling from B to A at 120km/hr and started at same time. Then at what time they meet together.
(A) 11AM
(B) 1PM
(C) 3PM
(D) 10AM
(E) 9AM
Rationale: Let x hours be they will meet together
distance covered by 1st person+distance covered by 2nd person = 1540km
100x+120x = 1540
x= 7 hr
They will meet = 6AM +7hr = 1PM
Answer is B
Answer: (B) 1PM
Question: Favid has d books, which is 3 times as many as Jeff and 1/2 as many as Paula. How many books do the three of them have altogether, in terms of d?
(A)  5/6*d
(B)  7/3*d
(C)  10/3*d
(D)  7/2*d
(E)  9/2*d
Rationale: Favid has d books;
Jeff has d/3 books;
Paula has 2d books;
Total = d+d/3+2d=10d/3.
Answer: C.
Answer: (C)  10/3*d