mathewhe/aqua_rat huggingface dataset:
Question: If [[x]] = x^2 + 2x + 4, what is the value of [[7]]?
(A) 3
(B) 9
(C) 15
(D) 67
(E) 25
Rationale: These functions questions might look intimidating, but they just test your knowledge about how well you can substitute values
[[x]] = x^2 + 2x + 4
[[7]] = 7^2 + 2*7 + 4 = 67. Option D
Answer: (D) 67
Question: The cost price of 13 articles is equal to the selling price of 11 articles. Find the profit percent?
(A) 18 2/19%
(B) 18 2/11%
(C) 18 2/91%
(D) 18 2/81%
(E) 18 2/121%
Rationale: 13 CP = 11 SP
11 --- 2 CP
100 --- ? =>18 2/11%
Answer: B
Answer: (B) 18 2/11%
Question: The price of 5 kilograms of premium fertilizer is the same as the price of 16 kilograms of regular fertilizer. If the price of premium fertilizer is y cents per kilogram more than the price of regular fertilizer, what is the price, in cents, per kilogram of premium fertilizer?
(A) y/30
(B) 5/6*y
(C) 6/5*y
(D) 5y
(E) 16y/11
Rationale: Usingpfor premium andrfor regular, I got two equations from the question stem:
5p = 16r and p = r+y
Substitute for p: 5(r+y) = 16r
Distribute: 5r + 5y = 16r
Subtract 5r from both sides: 5y = 11r
Plug back into the first equation: 5p = 16(5y/11)
Distribute: 5p = 80y/11
Divide both sides by 5: p = 16y/11
The answer is E.
Answer: (E) 16y/11
Question: A train 110 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
(A) 5
(B) 6
(C) 7
(D) 9
(E) 1
Rationale: Speed of train relative to man = (60 + 6) km/hr = 66 km/hr
[66 * 5/18] m/sec = [55/3] m/sec.
Time taken to pass the man = [110 * 3/55] sec = 6 sec.Answer: B
Answer: (B) 6
Question: Which of the following is greatest?
(A) 1/5
(B) 2/5
(C) 3/5
(D) 4/5
(E) 6/5
Rationale: A,B,C,D if we divide by 5 , we get the value <1. If we divide 6 by 5 we get the value >1
Answer : E
Answer: (E) 6/5
Question: A certain debt will be paid in 65 installments from January 1 to December 31 of a certain year. Each of the first 20 payments is to be $410; each of the remaining payments is to be $65 more than each of the first 20 payments. What is the average (arithmetic mean) payment that will be made on the debt for the year?
(A) 443
(B) 455
(C) 465
(D) 468
(E) 475
Rationale: Total number of installments = 65
Payment per installment for the first 20 installments = 410
Payment per installment for the remaining 45 installments = 410+65=475
Average = (20*410 + 45*475)/65 = 455
Answer B
Answer: (B) 455
Question: Circular gears L and R start to rotate at the same time at the same rate. Gear L makes 10 complete revolutions per minute and gear R makes 30 revolutions per minute. How many seconds after the gears start to rotate will gear R have made exactly 6 more revolutions than gear L?
(A) a) 6
(B) b) 8
(C) c) 10
(D) d) 12
(E) e) 18
Rationale: Gear L -- 10 rotations per 60 seconds -- 1 rotation per 6 seconds.
Gear R -- 40 rotations per 60 seconds -- 3 rotations per 6 seconds.
First 6 seconds -- Gear L makes 1 rotation. -- Gear R makes 4 rotations -- Net difference --2 rotations
Hence every 6 seconds the difference between the number of rotations of R and L gear is 2 units.
Required net difference should be 6 rotations => 3 (6 seconds later) ==> 18 seconds.
Answer: E
Answer: (E) e) 18
Question: For any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum s of all the even integers between 99 and 301?
(A) 10,100
(B) 20,200
(C) 22,650
(D) 40,200
(E) 45,150
Rationale: I would solve it in a different way.
First of all, total number of even integers between 99 and 301 are, (301-99)/2 = 202/2=101
Average = (301+99)/2 = 400/2 = 200
Sum s= Average*total count = 200*101 = 20,200
Answer is B
Answer: (B) 20,200
Question: Find out the number of ways in which 6 rings of different types can be worn in 3 fingers?
(A) 216
(B) 125
(C) 729
(D) 316
(E) 452
Rationale: The first ring can be worn in any of the 3 fingers (3 ways).
Similarly each of the remaining 5 rings also can be worn in 3 ways.
Hence total number of ways
=3×3×3×3×3×3=36=729
Ans: C
Answer: (C) 729
Question: There are some pigeons and hares in a zoo. If heads are counted, there are 200. If legs are counted, there are 580. The number of hares in the zoo is?
(A) 91
(B) 87
(C) 90
(D) 17
(E) 19
Rationale: 200*2 = 400
580
-----
180
1----2
?----180 = 90
Answer: C
Answer: (C) 90
Question: Which of the following lines is perpendicular to y = − 2x + 3 and has the same y-intercept as y = 2x − 7?
(A) y = -1/2*x + 3
(B) y = 1/2*x - 7
(C) y = 1/2*x + 3
(D) y = 2x + 3
(E) y = 2x − 3
Rationale: Since our line has to perpendicular to y = − 2x + 3
Slope of this line , m = -2
Slope will be required line L = 1/2 ( Product of slope of perpendicular lines = -1)
y-intercept of line L is same as y intercept of line y = 2x − 7
y - intercept of line L = -7
Required line = 1/2* x - 7
Answer B
Answer: (B) y = 1/2*x - 7
Question: In some quantity of ghee, 60% is pure ghee and 40% is vanaspati. If 10 kg of pure ghee is added, then the strength of vanaspati ghee becomes 20%. The original quantity was :
(A) 10
(B) 27
(C) 87
(D) 23
(E) 93
Rationale: Explanation:
Let the original quantity be x kg. Vanaspati ghee in x kg = (40x / 100 )kg = (2x / 5) kg.
Now, (2x/5)/(x + 10) = 20/100 <=> 2x / (5x + 50) = 1/5 <=> 5x = 50 <=> x = 10.
Answer: A) 10 kg
Answer: (A) 10
Question: Drum X is 1/2 full of oil and drum Y, which has twice the capacity of drum X, is 1/3 full of oil. If all of the oil in drum X is poured into drum Y, then drum Y will be filled to what capacity?
(A) 2/3
(B) 5/6
(C) 7/12
(D) 11/12
(E) 17/24
Rationale: (1/2)X = (1/4)Y
(1/4)Y + (1/3)Y = (7/12)Y
The answer is C.
Answer: (C) 7/12
Question: The sum of two numbers is 73 and their difference is 28. Find the difference between their squares.
(A) 101
(B) 45
(C) 2044
(D) 2048
(E) 2064
Rationale: Explanation:
Let x and y be the two given numbers
(x + y) = 73; (x – y) = 28
(x2 – y2) = (x + y) (x – y) = 73*28 = 2044
ANSWER:C
Answer: (C) 2044
Question: A man invested Rs.1552 in a stock at 97 to obtain an income of Rs.128. What is the dividend from the stock?
(A) 4
(B) 8
(C) 6
(D) 10
(E) 12
Rationale: By investing Rs.1552, income = Rs.128
By investing Rs.97, income = 128×97/1552=8
ie, dividend = 8%
Answer is B.
Answer: (B) 8
Question: Krishnakumar, Raghunandan, Chinnan and Aibak had an interesting discussion on the following:
Find the range of real values of x not satisfying even one of the inequalities 6x - 8 > 40 and 9x - 19 > 80"
(A) x greater than 8
(B) x lesser than or equal to 8
(C) x lesser to 8
(D) x greater than or equal to 8
(E) None of these
Rationale: 6x – 8 > 40 => 6x >48 => x > 8 ...(1)
And 9x – 19 > 80 = > 9x >99 => x >11 ...(2)
For both the inequalities to hold true, x should be greater than 11, and for values of x greater than 8, at least the first inequality (1) will be satisfied.
For x not to satisfy both the inequalities, it has to be equal to or lesser than 8.
Therefore, our answer is x lesser than or equal to 8
ANSWER:C
Answer: (C) x lesser to 8
Question: If x < y < 0, which of the following must be true?
(A) 2x+y is a negative integer
(B) 2xy is a negative integer
(C) x-y is a positive integer
(D) (-x)+ (-y) is positive integer
(E) x/y is a negative integer
Rationale: Given x, y are less than 0. So both will be negative integers
negative + negative = negative
negative * negative = positive
negative / negative = positive
x-y is false since xSo, option D is true , because if we multiple negative number with negative it becomes positive(x, y are negative numbers)
Answer : D
Answer: (D) (-x)+ (-y) is positive integer
Question: If x is a positive integer, then the least value of x for which x! is divisible by 10,000 is?
Can someone please explain intuitively what the question is asking?
(A) 5
(B) 9
(C) 12
(D) 15
(E) 20
Rationale: In order x! to be divisible by 1,000, it should have at least 3 trailing zeros. A trailing 0 in factorial of a number is produced by 2 and 5 in it: 2*5 = 10. So, we need 10 to be in x! at least in power of 3.
5! = 120 has 1 trailing zeros.
10! will have 2 trailing zeros.
15! will have 3 trailing zeros.
20! will have 5 trailing zeros.
Answer: E.
Answer: (E) 20
Question: Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
A.
B.
C.
D.
E.
(A) 210
(B) 1050
(C) 25200
(D) 21400
(E) 42800
Rationale: 7C3 * 4C2 * 5!
(7 * 6 * 5)/3! * 4!/2!2! * 120
35 * 6 * 120
= 210 * 120
= 25200
ANSWER:C
Answer: (C) 25200
Question: For any real number x, the operatoris defined as:
(x) = x(2 − x)
If p + 1 =(p + 1), then p =
(A) 5
(B) 0
(C) 1
(D) 2
(E) 3
Rationale: (x) = x(2 − x)
(p + 1) = (p + 1)(2 - p - 1) = (1-p)(p+1)
We are given that p + 1 =(p + 1)
Therefore (1-p)(p+1) = (p + 1)
Or (p + 1) + (p-1)(p+1) = 0
(p + 1)(p-1) = 0
p = -1,p=1
Option C
Answer: (C) 1
Question: 9 people decided to split the restaurant bill evenly. If the bill was $514.16 dollars, how much money did they 1 cent is the smallest unit?
(A) $514.16
(B) $514.17
(C) $514.18
(D) $514.19
(E) $514.20
Rationale: This is equivalent to finding the first number that is divisible by 9 that occurs after 51416.
In order to divide the sum in 9 parts, the amount must be divisible by 9
Divisibility rule of 9: The sum of the digits must be divisible by 9
Sum of digits of 51416 = 17 and 18 is divisible by 9.
Hence, we need to add 1 to this number for it to be divisible by 9
Correct Option: B
Answer: (B) $514.17
Question: A man bought a horse and a cart. If he sold the horse at 10 % loss and the cart at 20 % gain, he would not lose anything; but if he sold the horse at 5% loss and the cart at 5% gain, he would lose Rs. 10 in the bargain. The amount paid by him was Rs.­­­­_______ for the horse and Rs.________ for the cart
(A) 400 & 300
(B) 400 & 500
(C) 400 & 200
(D) 300 & 200
(E) 500 & 200
Rationale: let cp of horse be x
and cp of cart be y
then
horse sp=90*x/100=9x/10
cart sp=120*y/100=6y/5
now he say thru these no loss no gain mean cp of both equal to sp of both
=> x+y=(9x/10)+(6y/5)-----(1)
again
horse sp=95*x/100=19x/20
cart sp=105*y/100=21y/20
now at this time he suffer loss of 10 rs mean
cp=sp+10
x+y=19x/20+21y/20+10-----(2)
solving eq 1 and 2 u will get the ans x=400 & y=200
ANSWER:C
Answer: (C) 400 & 200
Question: Two boys starts from the same place walking at the rate of 4.5 kmph and 5.5 kmph respectively in the same direction. What time will they take to be 9.5 km apart?
(A) 9.5
(B) 5.5
(C) 8.5
(D) 9.6
(E) 9.7
Rationale: Explanation:
Relative speed = 5.5 - 4.5 = 1 kmph (because they walk in the same direction)
distance = 9.5 km
time = distance / speed=9.5/1=9.5 hr
Answer :A
Answer: (A) 9.5
Question: A and B walk around a circular track. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. If they start at 8 a.m. from the same point in opposite directions, how many times shall they cross each other before 9.00 a.m.?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 23
Rationale: Relative speed = Speed of A + Speed of B (? they walk in opposite directions)
= 2 + 3 = 5 rounds per hour
=> They cross each other 5 times in 1 hour
Time duration from 8 am to 9 am = 1 hour
Hence they cross each other 5 times before 9 am
Answer is A
Answer: (A) 5
Question: Find the largest number of four digits which is exactly divisible by 27,18,12,21
(A) 9700
(B) 9710
(C) 9828
(D) 9830
(E) 9740
Rationale: Explanation:
LCM of 27-18-12-21 is 756.
After dividing 9999 by 756 we get 171 remainder.
So answer will be 9999-171 = 9828
Option C
Answer: (C) 9828
Question: IF 2+7=57 ; 3+6=63 ; 5+9=206 Then 5+8=?
(A) 185
(B) 186
(C) 177
(D) 168
(E) 189
Rationale: 2^3 + 7^2= 57
3^3 + 6^2=63
5^3 + 9^2=206
and
5^3 + 8^2=189
ANSWER:E
Answer: (E) 189
Question: A train running at the speed of 52 km/hr crosses a pole in 9 seconds. Find the length of the train?
(A) 130
(B) 272
(C) 278
(D) 277
(E) 112
Rationale: Speed = 52*(5/18) m/sec = 130/9 m/sec
Length of Train (Distance) = Speed * Time
(130/9) * 9
= 130 meter
Answer: A
Answer: (A) 130
Question: Every person in a certain group is either a Lakers fan or a Warriors fan, but not both. The ratio of Lakers fans to Warriors fans is 9 to 4. If 40 Lakers fans change teams to become Warriors fans, the ratio of Warriors fans to Lakers fans will be 1 to 1. How many people are in the group?
(A) 260
(B) 52
(C) 182
(D) 169
(E) 12
Rationale: By checking the answer choices:
Since we have an initial ratio of 9:4, the total count should be divisible by 13.
A. 260/13=20, Lakers Fan = 180, Warriors Fan = 100, and 180-40 = 100+40. This is the Correct Answer
B. 52/13=4, Lakers Fan = 36, Warriors Fan = 16, Since 36-40 is not equal to 16+40 this as well can not be the answer.
C. 182/13=14, Lakers Fan = 126, Warriors Fan = 56, Since 126-40 is not equal to 56+40 this as well can not be the answer.
D. 169/13=13, Lakers Fan = 117, Warriors Fan = 52, Since 117-40 is not equal to 52+40 this as well can not be the answer.
E. Out, since not divisible by 13.
A is the correct answer.
Answer: (A) 260
Question: If Jesse flips a coin 7 times in a row, what is the probability that the result will be 2 heads and 2 tails at all the times ?
(A) 21/128
(B) 29/128
(C) 35/128
(D) 1/16
(E) 1/4
Rationale: In a flip of a coin seven times in a row, heads and tails 2 each at all times means,
Heads = exact 2 heads
The total outcome of flip is = 2^7 = 128
For any Coins problem write the ask in the shown format.
HHTT
Once you have written in the above mentioned format the answer is pretty straight.
HHTT = [7!]/[5!] [2!]= 21
Sum = 21
Answer = 21/128
Answer - A
Answer: (A) 21/128
Question: The area of the square formed on the diagonal of a rectangle as its side is 108 1/3 % more than the area of the rectangle. If the perimeter of the rectangle is 28 units, find the difference between the sides of the rectangle?
(A) 6m
(B) 9m
(C) 5m
(D) 2m
(E) 3m
Rationale: Let the sides of the rectangle be l and b respectively.
From the given data,
(√l2 + b2) = (1 + 108 1/3 %)lb
=> l2 + b2 = (1 + 325/3 * 1/100)lb
= (1 + 13/12)lb
= 25/12 lb
=> (l2 + b2)/lb = 25/12
12(l2 + b2) = 25lb
Adding 24lb on both sides
12l2 + 12b2 + 24lb = 49lb
12(l2 + b2 + 2lb) = 49lb
but 2(l + b) = 28 => l + b = 14
12(l + b)2 = 49lb
=> 12(14)2 = 49lb
=> lb = 48
Since l + b = 14, l = 8 and b = 6
l - b = 8 - 6 =2m.
Answer:D
Answer: (D) 2m
Question: A certain car dealership sells economy cars, luxury cars, and sport utility vehicles. The ratio of economy to luxury cars is 3:1. The ratio of economy cars to sport utility vehicles is 4:3. What is the ratio of luxury cars to sport utility vehicles?
(A) 9:8
(B) 8:9
(C) 4:9
(D) 2:3
(E) 1:2
Rationale: The ratio of economy to luxury cars is 3:1 --> E:L = 3:1 = 12:4.
The ratio of economy cars to sport utility vehicles is 4:3 --> E:S = 4:3 = 12:9.
Thus, L:S = 4:9.
Answer: C.
Answer: (C) 4:9
Question: Bookman purchased 55 copies of a new book released recently, 10 of which are hardback and sold for $20 each, and rest are paperback and sold for $10 each. If 14 copies were sold and the total value of the remaining books was 460, how many paperback copies were sold?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 9
Rationale: The bookman had 10 hardback ad 55-10=45 paperback copies;
14 copies were sold, hence 55-14=41 copies were left. Let # of paperback copies left be p then 10p+20(41-p)=460 --> 10 p=360 --> p=36
# of paperback copies sold is 45-36=9
Answer: E
Answer: (E) 9
Question: If a car had increased its average speed for a 210 mile journey by 5 mph, the journey would have been completed in one hour less. What was the original speed of the car for the journey?
(A) 20 mph
(B) 10 mph
(C) 30 mph
(D) 40 mph
(E) 60 mph
Rationale: C
30 mph
Answer: (C) 30 mph
Question: A recycling facility is staffed by 10 floor workers and one manager. All of the floor workers are paid equal wages, but the manager is paid n times as much as a floor worker. If the manager’s wages account for 1/10 of all wages paid at the facility, what is the value of n?
(A) 5/4
(B) 10/9
(C) 3/2
(D) 5/3
(E) 5
Rationale: Say each floor worker is paid $x, then the manager is paid $xn.
Total salary would be 10x+xn and we are told that it equals to 10xn:
10x+xn=10xn --> reduce by x:10+n=10n -->9n= 10
n = 10/9
Answer: B
Answer: (B) 10/9
Question: If a car went the first third of the distance at 80 kmh, the second third at 24 kmh, and the last third at 44 kmh, what was the average speed of the car for the entire trip?
(A) 39 kmh
(B) 40 kmh
(C) 42 kmh
(D) 44 kmh
(E) 50 kmh
Rationale: Assume D/3 = 2640 (this number is convenient because it is divisible by 80, 24 and 44)
So:
2640 = 80*T1 = 33 hrs
2640 = 24*T2 = 110 hrs
2640 = 44*T3 = 60 hrs
T = T1 + T2 + T3 = 203 hrs
D = RT
(2640*3) = R*203
R = 39
ANSWER: A
Answer: (A) 39 kmh
Question: In a certain candy store, 22% of the customers are caught sampling the candy and are charged a small fine, but 20% of the customers who sample the candy are not caught. What is the total percent of all customers who sample candy?
(A) 22%
(B) 23%
(C) 24%
(D) 25%
(E) 27.5%
Rationale: Since 20% of the customers who sample the candyare notcaught, then 80% of the customers who sample the candyarecaught:
{% of customers who sample candy}*0.80 = 0.22;
{% of customers who sample candy} = 0.275
Answer: E.
Answer: (E) 27.5%
Question: For any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum z of all the even integers between 99 and 301?
(A) 10,100
(B) 20,200
(C) 22,650
(D) 40,200
(E) 45,150
Rationale: I would solve it in a different way.
First of all, total number of even integers between 99 and 301 are, (301-99)/2 = 202/2=101
Average = (301+99)/2 = 400/2 = 200
Sum z= Average*total count = 200*101 = 20,200
Answer is B
Answer: (B) 20,200
Question: Jhon's average (arithmetic mean) test score on 5 tests is 87. What must be the Jhon's score on a 6th test for the Jhon's average score on the 6 tests to be 85?
(A) 65
(B) 75
(C) 85
(D) 95
(E) 105
Rationale: (5*87+x)/6=85
x=(6*85)-(5*87)
x= 510 - 435
total score required 510 - 435=75
Correct answer is B
Answer: (B) 75
Question: A parking garage rents parking spaces for $10 per week or $42 per month. How much does a person save in a year by renting by the month rather than by the week?
(A)  $14
(B)  $16
(C)  $22
(D)  $24
(E)  $26
Rationale: 10$ per week!
An year has 52 weeks.
Annual charges per year = 52* 10 = 520$
30$ per month!
An year has 12 months.
Annual charges per year = 12 * 42 = 504$
520 - 504 = 16
Ans B
Answer: (B)  $16
Question: The distance that light travels in one year is approximately 5,870,000,000,000 miles. The distance light travels in 100 years is:
(A) 111 × 1827 miles
(B) 999× 1238 miles
(C) 346 × 1012 miles
(D) 247 × 1012 miles
(E) 587 × 1012 miles
Rationale: The distance of the light travels in 100 years is:
5,870,000,000,000 × 100 miles.
= 587,000,000,000,000 miles.
= 587 × 1012 miles.
Answer :E
Answer: (E) 587 × 1012 miles
Question: In how many different ways can the letters of the word FLUTE be arranged in such a way that the vowels occupy only the even positions?
(A) 8
(B) 12
(C) 18
(D) 24
(E) 32
Rationale: The 2 vowels can be arranged in even places in 2! ways.
The 3 consonants can be arranged in three odd places in 3! ways.
The number of arrangements with vowels in even positions = 2! Ã— 3! = 2 Ã— 6 = 12
The answer is B.
Answer: (B) 12
Question: The perimeters of two squares are 80 cm and 32 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares?
(A) 76 cm
(B) 24 cm
(C) 88 cm
(D) 55 cm
(E) 73.2 cm
Rationale: We know perimeter of square = 4(side)
So Side of first square = 80/4 = 20 cm
Side of second square = 32/4 = 8 cm
Area of third Square = 20*20 - 8*8
= 336 cm
So side of third square = 18.3 [because area of square = side*side]
Perimeter = 4*Side = 4*18.3 = 73.2 cm
Answer:E
Answer: (E) 73.2 cm
Question: N is one of the numbers below. N is such that when multiplied by 0.75 gives 1. Which number is equal to N?
(A) 3/2
(B) 5/3
(C) 1+1/3
(D) 1 1/2
(E) 1 1/3
Rationale: N is such that when multiplied by 0.75 gives 1" is written mathematically as
N * 0.75 = 1
Solve for N
N = 1/0.75 = 100/75 = (75 + 25) / 75 = 75/75 + 25/75 = 1+1/3
correct answer C
Answer: (C) 1+1/3
Question: The integer Q has a tens digit of 6 and a units digit of 7. The units digit of integer y is 8. The product of Q and y has a tens digit of 8. Which of the following is a possible tens digit of integer y?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Let Q be 67 and y be a8. Then the product of Q and y can be written as (60+7)*(10a+8)=600a + 480+70a+56=600a+536+70a. Since 600a dose not affect on the tens digit we can ignore 600a.
So tens digit should be the unit of 3+7a. That means 3+7a =8, 18, 28, 38, 48 or 58 (since 3+7a<=3+7*9=66) --->7a=5, 15, 25, 35, 45, 55. So the only possibility is a=5.
So the answer is (C).
Answer: (C) 5
Question: In how many years will a sum of money doubles itself at 5% per annum on simple interest?
(A) 11%
(B) 20%
(C) 12%
(D) 19%
(E) 14%
Rationale: P = (P*5*R)/100
R = 20%
Answer:B
Answer: (B) 20%
Question: A saxophone player practices 2 hours a day Sunday through Saturday of one week, then Sunday through Friday of a second week. How many hours would she need to practice on Saturday and Sunday combined in order to have practiced an average (arithmetic mean) of 3 hours a day over the two week period?
(A) 10
(B) 12
(C) 14
(D) 16
(E) 18
Rationale: total number of hours practiced in the first week and through Friday of the second week: 7*2+5*2 = 14+10 = 24
total number of hours needed to be practiced over the two weeks if the average daily practice is 3 hours: 14*3 = 42
thus there are 42 - 24 = 18 hours still needed to be practiced on Saturday and Sunday of the second week
E
Answer: (E) 18
Question: Pat, kate and mark charged a total of 144 hours to a certain project . If pat charged twice as much time to the project as kate and 1/3 as much times as mark, how many more hours did mark charge to the project than kate.
(A) 18
(B) 36
(C) 80
(D) 90
(E) 108
Rationale: Let Kate charge for x hours,
then Pat charged for 2x and Mat - for 6x.
So, 2x+6x+x = 144 -total hours charged for,
x= 16.
Mat charged 6x-x or 5x for more hours than kate, or for 80 hours .
C is correct
Answer: (C) 80
Question: While working alone at their constant rates, computer X can process 240 files in 12 hours, and computer Y can process 240 files in 3 hours. If all files processed by these computers are the same size, how many hours would it take the two computers, working at the same time at their respective constant rates, to process a total of 240 files?
(A) 1.6
(B) 1.8
(C) 2
(D) 2.2
(E) 2.4
Rationale: Both computers together process files at a rate of 240/12 + 240/3 = 20+80 = 100 files per hour.
The time required to process 240 files is 240/100 = 2.4 hours
The answer is E.
Answer: (E) 2.4
Question: On one side of a coin there is the number 0 and on the other side the number 1. What is the probability that the sum of three coin tosses will be 2 if a 1 was the value of the first coin flip ?
(A) 1/8.
(B) 1/4.
(C) 1/5.
(D) 3/8.
(E) 1/3.
Rationale: Assume the coin is unbiased.
Possible sums from 3 tosses = 0,1,2,3
O and 3 are possible in only 1 case each. (0,0,0 or 1,1,1)
1 is possible in 3C1 = 3 cases. (1,0,0; 0,1,0 or 0,0,1) or
similarly, 2 is possible in 3C2=3 cases (1,0,1; 1,1,0; 0,1,1)
If 1 was the first flip you can only have (1,0,0) (1,1,1)(1,0,1) (1,1,0) only two of these have a value of 2
So answer will be 2/8 OR 1/4. Option B.
Answer: (B) 1/4.
Question: A number when divided by 3 leaves a remainder 1. When the quotient is divided by 2, it leaves a remainder 1. What will be the remainder when the number is divided by 6?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: Let n=3q+1 and let q= 2p+1. Then, n= 3(2p+1)+1= 6p+4
Therefore, the number when divided by 6, we get remainder= 4
ANSWER:C
Answer: (C) 4
Question: How much interest will $10,000 earn in 9 months at an annual rate of 3%?
(A) $250
(B) $350
(C) $450
(D) $550
(E) $225
Rationale: Soln:-
9 months = 3/4 of year;
3% = 3/100=3/100;
$10,000(principal)*3/100(interest rate)*3/4(time)=$225.
ANSWER:E
Answer: (E) $225