mathewhe/aqua_rat huggingface dataset:
Question: The price of a jacket is reduced by 25%. During a special sale the price of the jacket is reduced another 15%. By approximately what percent must the price of the jacket now be increased in order to restore it to its original amount?
(A) 32.5
(B) 35
(C) 48
(D) 56.8
(E) 67.5
Rationale: 1) Let the price of jacket initially be $100.
2) Then it is decreased by 25% , therefore bringing down the price to $75.
3) Again it is further discounted by 10%, therefore bringing down the price to $63.75.
4) Now 63.75 has to be added byX %in order to equal the original price.
63.75 + ( X% ) 63.75 = 100.
Solving this eq for X, we get X = 56.8
Ans is D.
Answer: (D) 56.8
Question: A lady has fine gloves and hats in her closet- 25 blue, 7 red, and 9 yellow. The lights are
out and it is totally dark. In spite of the darkness, she can make out the difference between
a hat and a glove. She takes out an item out of the closet only if she is sure that if it is a
glove. How many gloves must she take out to make sure she has a pair of each color?
(A) 36
(B) 37
(C) 38
(D) 39
(E) 40
Rationale: since it is not given hw many hats so he has hance to take any so 25+7+depends on given answer if 36 is answer round off to 25+7+4=36
ANSWER:A
Answer: (A) 36
Question: If x is the sum of six consecutive integers, then x is divisible by which of the following:
I. 3
II. 4
III. 6
(A) I only
(B) II only
(C) III only
(D) I and III
(E) I, II, and III
Rationale: let the six numbers be k-2, k-1, k, k+1, k+2, k+3
then, there sum will be 6k+3
3(2k+1),which is clearly a multiple of 3. Also, 2k+1 will always be odd. thus the sum will never be divisible by 2.
hence option A
Answer: (A) I only
Question: he average of 5 numbers is zero. Of them, at the most, how many may be greater than zero?
(A) 0
(B) 4
(C) 10
(D) 19
(E) 8
Rationale: Average of 5 numbers = 0.
Sum of 5 numbers (0 x 5) = 0.
It is quite possible that 4 of these numbers may be positive and if their sum is a the 5th number is (-a).
Answer: Option C
Answer: (C) 10
Question: if a@b = a * b^(1/2) then 3@9 = ?
self made
(A) 2
(B) 6
(C) 3
(D) 8
(E) 9
Rationale: a@b = a * b^(1/2)
3@9 = 3*9^(1/2) = 3*3 = 9
Correct Option: E
Answer: (E) 9
Question: If we want to choose out of 6 consonants and 4 vowels, how many words of 3 consonants and 3 vowels can be formed?
(A) 12200
(B) 720
(C) 9002
(D) 57600
(E) 12130
Rationale: Required selection = select 3 consonants from 6 and 3 vowels frm 4
= 6C3 * 4C3
= 80
As we have to form 6 letter word the above combination of consonants and vowels can be done in 6! = 720 different ways
Required no. of ways = 80 * 720
= 57600
Ans - D
Answer: (D) 57600
Question: A train covers a distance in 50 minutes, if it runs at a speed of 48kmph on an average. Find the speed
at which the train must run to reduce the time of journey to 40 minutes
(A) 50 km/hr
(B) 60 km/hr
(C) 65 km/hr
(D) 70 km/hr
(E) None of these
Rationale: Explanation:
We are having time and speed given, so first we will calculate the distance. Then we can get new speed
for given time and distance.
Lets solve it.
Time = 50/60 hr = 5/6 hr
Speed = 48 mph
Distance = S*T = 48 * 5/6 = 40 km
New Ɵme will be 40 minutes so,
Time = 40/60 hr = 2/3 hr
Now we know,
Speed = Distance/Time
New speed = 40*3/2 kmph = 60kmph
Answer: B
Answer: (B) 60 km/hr
Question: If A:B=4:7 AND B:C=5:9,THEN A:C=?
(A) 28:37
(B) 18:37
(C) 16:53
(D) 20:63
(E) 15:48
Rationale: A/B=4/7 AND B/c=5/9
A/B*B/C=4/7*5/9=20/63
SO A/C=20/63
20:63
ANSWER D
Answer: (D) 20:63
Question: A car started running at a speed of 28 km/hr and the speed of the car was increased by 2 km/hr at the end of every hour. Find the total distance covered by the car in the first 10 hours of the journey.
(A) 37 km
(B) 76 km
(C) 25 km
(D) 15 km
(E) 30 km
Rationale: A
37 km
The total distance covered by the car in the first 10 hours = 28 + 30 + 32 + 34 + 36 + 38 + 40 + 42 + 44 + 46 = sum of 10 terms in AP whose first term is 28 and last term is 46 = 10/2 [28 + 46] = 370 km.
Answer: (A) 37 km
Question: A farmer has an apple orchard consisting of Fuji and Gala apple trees. Due to high winds this year 10% of his trees cross pollinated. The number of his trees that are pure Fuji plus the cross-pollinated ones totals 153, while 3/4 of all his trees are pure Fuji. How many of his trees are pure Gala?
(A) 22
(B) 33
(C) 55
(D) 27
(E) 88
Rationale: Let f = pure fuji , g = pure gala and c - cross pollinated.
c = 10% of x where x is total trees.
c = .1x
also 3x/4 = f and c+f = 153 => .1x + 3/4x = 153=> x = 180
180 - 153 = pure gala = 27.
D
Answer: (D) 27
Question: Three consecutive odd integers are in increasing order such that the sum of the last two integers is 19 more than the first integer. Find the three integers?
(A) 7, 9, 29
(B) 7, 2, 10
(C) 7, 9, 10
(D) 7, 9, 11
(E) 13,15,17
Rationale: Explanation:
Let the three consecutive odd integers be x, x + 2 and x + 4 respectively.
x + 4 + x + 2 = x + 19 => x = 13
Hence three consecutive odd integers are 13, 15 and 17.
Answer:E
Answer: (E) 13,15,17
Question: The standard deviation of a normal distribution of data is 2, and 3 standard deviations below the mean is greater than 46. What is a possible value for the mean of the distribution?
(A) 46
(B) 52
(C) 48
(D) 49
(E) 50
Rationale: The standard deviation ({SD}) = 2;
3 standard deviations below the mean is greater than 46:
{Mean} - 3*{SD} > 46;
{Mean} - 6 > 46;
{Mean} > 52.
Answer: B.
Answer: (B) 52
Question: Health insurance Plan P requires the insured person to pay $500 but then the insurance pays 80% of the cost over $500. Plan Q requires the insured to pay the initial $300, but then pays 60% of the cost over $300. Which of the following is a cost level for which both insurance plans pay out the same amount?
(A) $1100
(B) $1600
(C) $2200
(D) $2800
(E) $3300
Rationale: 0.8(x-500)=0.6(x-300)
0.2x=400-180
x=1100
The answer is A.
Answer: (A) $1100
Question: The contents of a certain box consist of 14 apples and 25 oranges. How many oranges must be removed from the box so that 70 percent of the pieces of fruit in the box will be apples?
(A) 3
(B) 6
(C) 14
(D) 19
(E) 20
Rationale: The objective here is that 70% of the fruit in the box should be apples.
Now, there are 14 apples at start and there is no talk of removing any apples, so number of apples should remain 14 and they should constitute 70% of total fruit, so total fruit = 14/0.7 = 20
So we should have 20-14 = 6 oranges.
Right now, there are 25 oranges, so to get to 6 oranges, we should remove 25 - 6 = 19 oranges.
Answer D
Answer: (D) 19
Question: What is the tens digit of 7^545?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 0
Rationale: 7^1 = 7
7^2 = 49
7^3 = 343
7^4 = 2401
7^5 = 16807
7^6 = 117649
We should see this as pattern recognition . We have a cycle of 4 . (We can multiply the last 2 digits only as we care about ten's digit )
0 , 4 , 4 , 0 .
546= 4*136 + 1
The ten's digit will be 0 .
Answer E
Answer: (E) 0
Question: Working together, printer A and printer B would finish the task in 24 minutes. Printer A alone would finish the task in 60 minutes. How many pages does the task contain if printer B prints 6 pages a minute more than printer A ?
(A) 600
(B) 800
(C) 1000
(D) 720
(E) 1500
Rationale: Answer: D.
Answer: (D) 720
Question: The sector of a circle has radius of 20 cm and central angle 135o. Find its perimeter?
(A) 91.5
(B) 87.1
(C) 91.7
(D) 91.3
(E) 91.1
Rationale: Perimeter of the sector = length of the arc + 2(radius)
= (135/360 * 2 * 22/7 * 20) + 2(20)
= 47.1 + 40 = 87.1 cm
Answer:B
Answer: (B) 87.1
Question: If books bought at prices ranging from Rs. 250 to Rs. 350 are sold at prices ranging from Rs. 300 to Rs. 425, what is the greatest possible profit that might be made in selling eight books ?
(A) 23267
(B) 1400
(C) 1800
(D) 2778
(E) 76611
Rationale: Explanation:
Least Cost Price = Rs. (250 * 8) = Rs. 2000.
Greatest Selling Price = Rs. (425 * 8) = Rs. 3400.
Required profit = Rs. (3400 - 2000) = Rs. 1400.
Answer: B) 1400
Answer: (B) 1400
Question: If A lends Rs.3500 to B at 10% per annum and B lends the same sum to C at 12% per annum then the gain of B in a period of 3 years is?
(A) 200
(B) 210
(C) 220
(D) 225
(E) 230
Rationale: (3500*2*3)/100 => 210
Answer: B
Answer: (B) 210
Question: Ten years ago, P was half of Q in age. If the ratio of their present ages is 3:4, what will be the total of their present ages
(A) 35
(B) 34
(C) 45
(D) 25
(E) 65
Rationale: Explanation:
Let the present age of P and Q be 3x and 4x respectively.
Ten years ago, P was half of Q in age
=> 2(3x – 10) = (4x – 10)
=> 6x – 20 = 4x – 10
=> 2x = 10
=> x = 5
Option A
Answer: (A) 35
Question: There are 40 doors marked with numbers 1 to 40. And there are 40 individuals marked 1 to 40.
An operation on a door is defined as changing the status of the door from open to closed or vice versa. All doors are closed to start with.
Now one at a time one randomly picked individual goes and operates the doors. The individual however operates only those doors which are a multiple of the number he/she is carrying. For e.g. individual marked with number 5 operates the doors marked with the following numbers: 5, 10, 15,... and 40.
If every individual in the group get one turn then how many doors are open at the end?
(A) 0
(B) 1
(C) 2
(D) 4
(E) 6
Rationale: Let us start with 1.
When 1 goes, all the doors are open since every number is a multiple of 1.
Also 1 will remain opened since 1 is not a multiple of any number.
Prime numbers can only be operated by people with prime numbers.
So 2,3,5,7,11,13,17,19,23,29,31,37 will be closed when people with respective numbers perform operations on them.
Our numbers left are 4,6,8,9,10,12,14,15,16,18,20,21,22,24,...28 and
From these numbers, only those numbers will remain opened on which even number of operations are performed including the operation performed by number 1.
This is possible only for perfect squares which are 4,9,16,25 and 36.
So our numbers are 1,4,9, 16,25 and 36.
Answer:- E
Answer: (E) 6
Question: If x/y =1/4, then (x-y)/x?
(A) -1/2
(B) -1
(C) -3
(D) 1/2
(E) 4
Rationale: we have this law of fraction:
a/b=c/d= (a-c)/(b-d)
x/y=1/4 ---> x/1=y/4= (x-y)/(1-4)=(x-y)/(-3) ---> (x-y)/x= -3
Answer: C
Answer: (C) -3
Question: A positive integer n is a perfect number provided that the sum of all the positive factors of n, including 1 and n, is equal to 2n. What is the sum of the reciprocals of all the positive factors of the perfect number 28?
(A) 1/4
(B) 56/27
(C) 2
(D) 3
(E) 4
Rationale: Soln:
28 = 1*28
2*14
4*7
sum of reciprocals = 1+1/28+1/2+1/14+1/4+1/7=56/28=2
ANSWER:C
Answer: (C) 2
Question: what is the least number. which should be added to 0.0282 to make it a perfect square?
(A) 0.0007
(B) 0.0042
(C) 0.0002
(D) 0.0003
(E) 0.0004
Rationale: 0.0282+0.0007=0.0289
(0.17)^2
ANSWER:A
Answer: (A) 0.0007
Question: Given that 2x + 17 > 5 and 5x - 13 < 7, all values of x must be between which of the following pairs of integers?
(A) -4 and -1
(B) -1 and 4
(C) -4 and 1
(D) -6 and 4
(E) 2 and 5
Rationale: 2x + 17 > 5
i.e 2x >5-17
i.e. 2x > -12
i.e. x > -6
Also, 5x - 13 < 7
i.e. 5x <7+13
i.e 5x < 20
i.e x < 4
i.e. -6 < x < 4
Answer: Option D
Answer: (D) -6 and 4
Question: For the positive numbers, n, n + 2, n + 4, n + 6, and n + 8, the mean is how much greater than the median?
(A) n+l
(B) 1
(C) 0
(D) n+2
(E) n+3
Rationale: Let’s first calculate the mean (arithmetic average).
mean = sum/quantity
mean = (n + n + 2 + n + 4 + n + 6 + n + 8)/5
mean = (5n + 20)/5
mean = n + 4
Next, we determine the median. The median is the middle value when the terms are ordered from least to greatest. The terms ordered from least to greatest are as follows:
n, n + 2, n + 4, n + 6, n + 8
The median is n + 4.
Finally we are asked how much greater the mean is than the median. To determine the difference we can subtract the smaller value (the median) from the larger value (the mean) and we get:
n + 4 – (n + 4) = n + 4 – n – 4 = 0
The answer is C
Answer: (C) 0
Question: if 7v passes to that wire and a current of 260mA then find the resistance
(A) 26.9
(B) 27.9
(C) 28.9
(D) 29.9
(E) 30.9
Rationale: V=IR
=> R=V/I = 7 V / 260 mA = 7 V / 260*10^(-3) A = 26.92 ohm
ANSWER:A
Answer: (A) 26.9
Question: Every digit of a number written in binary is either 0 or 1. To translate a number from binary, multiply the nth digit (reading from right to left) by 2^(n-1)
What is the largest prime number (written in binary) that is a factor of both 100010000 and 1000100000 ?
(A) 10
(B) 11
(C) 101
(D) 1011
(E) 10001
Rationale: Starting from right count the positions of 1 s
100010000=(1*2^8) + (1*2^4)=(2^8 + 2^4)
similarly,
1000100000=(1*2^9)+(1*2^5)=(2^9 + 2^5)
Lets simplify them further,
(2^8 + 2^4)=2^4(2^4 +1)=2^4(16+1)=2^4(17)
(2^9 + 2^5)=2^5(2^4 +1)=2^5(16+1)=2^5(17)
The prime numbers common in both are 2 and 17, and the largest one is 17.
from the options, (E) 10001=1*2^4+1*2^0=16+1=17
Hence answer (E).
Answer: (E) 10001
Question: An urn contains 5 red, 6 blue and 8 green balls. 4 balls are randomly selected from the urn, find the probability that the drawn ball are 1 blue and 2 red and 1 green balls ?
(A) 20/323
(B) 40/323
(C) 60/273
(D) 50/373
(E) 40/373
Rationale: Sample space = no. of ways 4 balls were drawn from urn = 19C4 = 3876
No. ways 1 blue and 2 red and 1 green balls were drawn from bag = 6C1 * 5C2 * 8C1 = 480
Probability = 480 / 3876 = 40/323
Ans - B
Answer: (B) 40/323
Question: In a garden, trees are planted in rows. In each row there are as many trees as the number of rows in the garden. If the total number of trees in that garden is n, then :
(A) n is a perfect square
(B) n is an odd number
(C) n is an even number
(D) n is a perfect cube.
(E) none
Rationale: If there are, for example, 4 rows of trees, each row would have 4 trees. The total would be 4*4=16, which is a perfect square.
Answer: A
Answer: (A) n is a perfect square
Question: A glucose molecule contains 6 carbon, 12 hydrogen and 6 oxygen atoms. During photosynthesis, green plants create glucose daily. If, over a period of 15 days, an eucalyptus plant (a green plant) creates 15,000 molecules of glucose then approximately how many more atoms of hydrogen than carbon are created on average per day?
(A) 60,000
(B) 6,000
(C) 2,500
(D) 250
(E) 0
Rationale: Solution:
We know that 15,000 glucose molecules are created over a period of 15 days. Therefore 15,000/15 = 1,000 glucose molecules are created on average per day.
Each glucose molecule contains 6 carbon atoms and 12 hydrogen atoms. So 1,000 glucose molecules contain 6 × 1,000 = 6,000 carbon atoms and 12 × 1,000 = 12,000 hydrogen atoms. The difference is 12,000 – 6,000 = 6,000.
The correct answer is B.
Answer: (B) 6,000
Question: Sum of the squares of three numbers is 138 and the sum of their products taken two at a time is 131. Find the sum?
(A) 20
(B) 24
(C) 27
(D) 28
(E) 30
Rationale: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 138 + 2* 131
a + b + c = √400 = 20
A
Answer: (A) 20
Question: Which of the following leads to the correct mathematical solution for the number of ways that the letters of the word CAREER could be arranged to create a six-letter code?
(A) 6!
(B) 6! − (3! + 2!)
(C) 6! − (3! × 2!)
(D) 6!/(3! + 2!)
(E) 6!/(2! × 2!)
Rationale: Number of letters in word 'CAREER' = 6.
The letters 'R' and 'E' appear 2 times and 2 times respectively in the word 'CAREER'.
Therefore the mathematical solution for number of ways that the letters of the word CAREER can be arranged to create six-letter code
= 6!/(2!*2!)
Answer:E
Answer: (E) 6!/(2! × 2!)
Question: Out of 470 students of a school, 325 play football, 175 play cricket and 50 neither play football nor cricket. How many students play both football and cricket ?
(A) 80
(B) 150
(C) 100
(D) 180
(E) 220
Rationale: n(A)=325,n(B)=175,n(AuB)=470-50=420.
Required number = n(AnB)=n (A)+n (B)-n(AuB)=325+175-420=80.
Answer is A
Answer: (A) 80
Question: A meeting has to be conducted with 6 managers. Find the number of ways in which the managers may be selected from among 9 managers, if there are 2 managers who refuse to attend the meeting together.
(A) 36
(B) 40
(C) 42
(D) 45
(E) 49
Rationale: The total number of ways to choose 6 managers is 9C6 = 84
We need to subtract the number of groups which include the two managers, which is 7C4 = 35.
84 - 35 = 49
The answer is E.
Answer: (E) 49
Question: For 6-digit integer 46x,y12, when x and y are drawn at random from {3,5,8}, what is the probability T that the integer drawn is divisible by 8?
* A solution will be posted in two days.
(A) 1/6
(B) 1/3
(C) 1/2
(D) 2/3
(E) 5/6
Rationale: In general, the remainder divided by integer n is the same as the remainder that up to tens of n is divided by 8.
Thus, in order for 46,x,y12 to be divided by 8, y12 should be divided by 8.
Amongst 3,5,8, 3 and 5 can be divided by 8.
Therefore,T two out of three can be divided and the answer is D.
Answer: (D) 2/3
Question: 8 people decided to split the restaurant bill evenly. If the bill was $314.12 dollars, how much money did they 1 cent is the smallest unit?
(A) $314.16
(B) $314.17
(C) $314.18
(D) $314.19
(E) $314.20
Rationale: If the last three digits of a whole number are divisible by 8, then the entire number is divisible by 8
the last 3 digit 412 not divisible by a
Hence, we need to add 4 to this number for it to be divisible by 8
Correct Option: A
Answer: (A) $314.16
Question: The sum Q of the arithmetic sequence a, a+d, a+2d,..., a+(n-1)d is give by Qn = (n/2)*(2a + n-1)d. What is the sum of the integers 1 to 100 inclusive, with the even integers between 25 and 63 omitted.
(A) 4345
(B) 4302
(C) 4258
(D) 4214
(E) 4170
Rationale: a method to do it under one minutes is to take advantage of the choices given...
lets work on the last digit as we have different units digit in each choice...
total sum of 1 to 100 inclusive will have 0 as the last digit..
this is so because the resultant will be 10*(sum of all single digits)... and since we are multiplying by 10,units digit will be 0...
now for single digit in sum Q of even number from 25 to 63..
25 to 65 will have 4 times sum of single digit even int, 4*(2+4+6+8+0)=4*20..
here too the units digit is 0, but 64 has to be excluded from the total..
two ways from here on..
1) we are subtracting 0 from 0
so units digit should be 0, but we have to add 64..
so last/units digit =4..
2)we subtract 64 from sum of even int..
so units digit=80-4=76..
or units digit =6...
so our answer should have units digit as 10-6=4..
only D has 4 as units digit..
ans D
Answer: (D) 4214
Question: A company hired a printer to produce a total of x + 1 envelopes. The job consisted of two types of envelopes, 4¢ envelopes and 7¢ envelopes. If the company requested 3 more 4¢ envelopes than 7¢ envelopes, which of the following expressions denotes the cost, in cents, of the total x + 1 envelopes ?
(A) (9x-12)/2
(B) 4x+13
(C) 3x+34
(D) 6x-4
(E) (7x+4)/2
Rationale: We can take
X+1 = 11
X= 10
So 4c envelopes will be 7
and 7c envelopes will be 4
So total cost will be 56
Then that is our target
Plug x =10 in answer choices
Only D works
Correct Answer :D
Answer: (D) 6x-4
Question: If six persons sit in a row, then the probability that three particular persons are always together is -
(A) 1/9
(B) 1/7
(C) 1/5
(D) 1/1
(E) 1/3
Rationale: Six persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes = 3!4! Required probability = 3!4!/6!
= 1/5
Answer: C
Answer: (C) 1/5
Question: A rower can row 6 km/h in still water. When the river is running at 1 km/h, it takes the rower 1 hour to row to Big Rock and back. How many kilometers is it to Big Rock?
(A) 2.66
(B) 2.78
(C) 2.8
(D) 2.87
(E) 2.92
Rationale: Let x be the distance to Big Rock.
time = x/5 + x/7 = 1
x = 35/12 = 2.92
The answer is E.
Answer: (E) 2.92
Question: A man is 24 years older than his son.In two years,his age will be twice the age of his son.The present age of the son is:
(A) 14 years
(B) 18 years
(C) 20 years
(D) 22 years
(E) None of these
Rationale: Solution
Let the son's present age be x years.Then,man's present age =(x + 24)years.
∴ (x + 24)+ 2 =2(x + 2) ⇔ x + 26 =2x + 4 ⇔ x =22. Answer D
Answer: (D) 22 years
Question: Sakshi can do a piece of work in 5 days.Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work :
(A) 4
(B) 16
(C) 18
(D) 25
(E) 10
Rationale: Solution
Ratio of times taken by Sakshi and Tanya = 125 : 100 = 5 : 4 .
Suppose Tanya taken x days to do the work.
5 : 4 : : 5 : x ⇒ x = (5x4/5) ⇒ x = 4 days.
Hence,Tanya takes 16 days is complete the work.
Answer A
Answer: (A) 4
Question: A die is thrown twice and the sum of the numbers appearing is observed to be 6.
find the conditional probability that the number 4 has appeared at least once?
(A) 2/5
(B) 4/5
(C) 5/7
(D) 7/11
(E) 7/13
Rationale: Let E be the event that ‘number 4 appears at least once’ and F be
the event
that ‘the sum of the numbers appearing is 6’.
Then, E = {(4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (1,4), (2,4), (3,4),
(5,4), (6,4)}
and F = {(1,5), (2,4), (3,3), (4,2), (5,1)}
We have P(E) = 11/36
and P (F) = 5/36
Also EnF = {(2,4), (4,2)}
Therefore P(EnF) = 2/36
the required probability
P(E|F) = P(EnF)/P(F) = (2/36)/(5/36) = 2/5
A)
Answer: (A) 2/5
Question: Find the rate at Simple interest, at which a sum becomes four Ɵmes of itself in 15 years.
(A) 10%
(B) 20%
(C) 30%
(D) 40%
(E) 50%
Rationale: Explanation:
Let sum be x and rate be r%
then, (x*r*15)/100 = 3x [important to note here is that simple interest will be 3x not 4x, beause 3x+x =
4x]
=> r = 20%
Answer: B
Answer: (B) 20%
Question: One day a car rental agency rented 2/3 of its cars, including 3/5 of its cars with CD players. If 3/4 of its cars have CD players, what percent of the cars that were not rented had CD players?
(A) 10%
(B) 35%
(C) 45%
(D) 66.7%
(E) 90%
Rationale: Let us try to solve this by getting some number for total cars.
let there be 3,4 and 5 = 60 cars... ( we have taken denominators of 2/3,3/4 and 3/5 least common number).
2/3(60) = 40 cars ...total rented cars , then 1/3(60) = 20 cars were not rented.
3/4(60) = 45 cars with CD players...total CDP cars
now 3/5(3/4) = 3/5(45) = 27 CDP cars and these are cars that we rented.
Non rented CDP = Total CDP - rented CDP = 45 -27 = 18.
18/20 = 90%.
ANSWER:E
Answer: (E) 90%
Question: The average of seven numbers is 18. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number?
(A) 22
(B) 88
(C) 27
(D) 89
(E) 287
Rationale: The total of seven numbers = 7X18 = 126
The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99
So, the middle number is (126 - 99 ) = 27
Answer: C
Answer: (C) 27
Question: Find the least number of complete years in which a sum of money put out at 25% compound interest will be more than double of itself?
(A) 6 years
(B) 9 years
(C) 5 years
(D) 4 years
(E) 6 years
Rationale: 4 years
Answer: D
Answer: (D) 4 years
Question: Four rooms of the same type were advertised to be let in a locality. four men made separate applications for a house. What is the probability that each of them applied for the same house.
(A) 1/16
(B) 1/256
(C) 1/64
(D) 4/64
(E) 4/16
Rationale: Each men can choose any of the three houses, hence the total number of ways they can apply is 4^4 = 256.
Each of them to apply for the same house means each of them applying for house A, B or C,D.
P = 4/256 = 1/64.
Answer: C.
Answer: (C) 1/64
Question: A five-character password consists of two letter of the alphabet and three different digits between 0 and 9, inclusive. The letter must appear as the second or third character of the password. How many different passwords are possible?
(A) 915,040
(B) 918,720
(C) 926,000
(D) 937,440
(E) 973,440
Rationale: 5 character password: DLDLD
First digit can be chosen in 10 ways.
The letter can be chosen in 26 ways.
Next digit can be chosen in 9 ways.
Next digit can be chosen in 8 ways.
The letter can be chosen in 25 ways.
This gives us 10*26*9*25*8ways
Now, the letter can also be DDLLD so there will be another 10*9*26*25*8 ways
Total = 10*26*9*25*8*2 = 973,440 ways
E
Answer: (E) 973,440