mathewhe/aqua_rat huggingface dataset:
Question: A clock loses a minute every three hours for 4 days and gains 1% in the subsequent 6 days. If it was set right on Friday at 12 AM, what will be the time at the end of 10 days?
(A) 12:54:40 AM
(B) 12:56:24 AM
(C) 01:16:40 PM
(D) 12:54:24 AM
(E) 01:06:36 PM
Rationale: Loses 8 minutes each day.
so total loss = 4×8 = 32min
subsequent 6 days = 6×24×60 minutes
1% gain = ( 6×24×60)/100 = 86.4 minutes
so, total gain = 86.4 - 32 = 54.4 min = 54 + 0.4 min = 54 minutes + 0.4 × 60 seconds = 54min + 24seconds
10 days later the clock should be 54 min and 24seconds fast.
so time , 12:54:24 am (Answer D)
Answer: (D) 12:54:24 AM
Question: A certain farmer pays $30 per acre per month to rent farmland. How much does the farmer pay per month to rent a rectangular plot of farmland that is 1080 feet by 605 feet? (43,560 square feet = 1 acre)
(A) $5,330
(B) $3,360
(C) $450
(D) $360
(E) $150
Rationale: Basically the question an error. 1 acre = 43,560 square feet and if it is then the answer is 450(C)
Answer: (C) $450
Question: 1,11,21,_ what comes in the next series.
(A) 1
(B) 11
(C) 21
(D) 31
(E) 41
Rationale: 1+10=11
11+10=21
21+10=31
ANSWER:D
Answer: (D) 31
Question: One week, a certain truck rental lot had a total of 26 trucks, all of which were on the lot Monday morning. If 50% of the trucks that were rented out during the week were returned to the lot on or before Saturday morning of that week, and if there were at least 14 trucks on the lot that Saturday morning, what is the greatest number of different trucks that could have been rented out during the week?
(A) 18
(B) 16
(C) 12
(D) 24
(E) 4
Rationale: N - Not rented trucks; R - Rented trucks
N + R = 26
N + R/2 = 14
R = 24
D
Answer: (D) 24
Question: By selling an article for $225 a person gains $75. What is the gain %?
(A) 25%
(B) 30%
(C) 50%
(D) 20%
(E) 10%
Rationale: S.P. = $225
Gain = $75
C.P. = 225-75 = 150
Gain% = 75/150 * 100 = 50%
Answer is C
Answer: (C) 50%
Question: Triangle XYZ is an isosceles right triangle. If side XY is longer than side YZ, and the area of the triangle is 49, what is the measure of side XY?
(A) 4
(B) 4√2
(C) 14
(D) 8√2
(E) Cannot be determined from the information provided
Rationale: ans C ..14..
xy being larger means it is the hyp..
area =(1/2)*(yz)^2=4 or yz=7*\sqrt{2}..
therefore hyp=xy=14
Answer: (C) 14
Question: The regular price per can of a certain brand of soda is $0.40. If the regular price per can is discounted 15 percent when the soda is purchased in 24-can cases, what is the price of 100 cans of this brand of soda purchased in 24-can cases?
(A) $16.32
(B) $18.00
(C) $21.60
(D) $34
(E) $28.80
Rationale: The discounted price of one can of soda is (0.85)($0.40), or $0.34. Therefore, the price of 72 cans of soda at the discounted price would be (100)($0.34)= 34
Answer: D.
Answer: (D) $34
Question: Out of 40 applicants to a law school, 15 majored in political science, 20 had a grade point average higher than 3.0, and 10 did not major in political science and had a GPA equal to or lower than 3.0. How many T applicants majored in political science and had a GPA higher than 3.0?
(A) 5
(B) 10
(C) 15
(D) 25
(E) 35
Rationale: Total applicants = 40
Political science = 15 and Non political science = 40 - 15 = 25
GPA > 3.0 = 20 and GPA <= 3.0 = 20
10 Non political science students had GPA <= 3.0 --> 15 Non political science students had GPA > 3.0
GPA > 3.0 in political science = Total - (GPA > 3.0 in non political science) T= 20 - 15 = 5
Answer: A
Answer: (A) 5
Question: How many inches are in 2000 millimeters? (round your answer to the nearest hundredth of of an inch).
(A) 98.74 inches
(B) 78.74 inches
(C) 88.74 inches
(D) 58.74 inches
(E) 48.74 inches
Rationale: One inch is the same as 25.4 mm. Let x inches be the same as 1000 mm
x = 1 inch * 2000 mm / 25.4 mm = 78.74 inches
correct answer B
Answer: (B) 78.74 inches
Question: If it takes a machine 3⁄5 minute to produce one item, how many items will it produce in 2 hours?
(A) 1⁄3
(B) 4⁄3
(C) 80
(D) 200
(E) 180
Rationale: 1 item takes 3/5 min so it takes 120 min to produce x
3x/5=120 the x=200
Answer:D
Answer: (D) 200
Question: When the positive integer r is divided by 11, the quotient is s and the remainder 3. When r is divided by 19, the remainder is also 3. What is the remainder when s is divided by 19?
(A) 4
(B) 3
(C) 2
(D) 1
(E) 0
Rationale: Any Number which when divided by divisor d1,d2, etc. leaving same remainderrtakes the form ofK+r
where k = LCM (d1,d2)
In this case the divisors are 1119 and remainder is 3.
so LCM (11,19) = 209
So N= 209+3 = 212
Also r=d1q+3 ; which means d1q=209d1=11 therefore q=19
And ( s divided by 19)19/19 leaves remainder 0.
Answer is E
Answer: (E) 0
Question: A word is defined as a sequence of five dots arranged in a row. Each dot is colored either red, yellow, or blue. How many distinct words can be formed?
(A) 124
(B) 150
(C) 212
(D) 243
(E) 316
Rationale: 3^5 = 243
The answer is D.
Answer: (D) 243
Question: A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train?
(A) 297m
(B) 276m
(C) 267m
(D) 180m
(E) 287m
Rationale: Length of the train be ‘X’
X + 120/15 = X + 180/18
6X + 720 = 5X + 900
X = 180m
Answer: B
Answer: (B) 276m
Question: Based on this year's costs, a company budgets P dollars for hiring N new employees next year. If the average cost of hiring each employee were to decrease 20% from this year's cost, then the greatest number of employees could hire next year using P dollars would be:
(A) Equal to N
(B) 25% greater than N
(C) 20% greater than N
(D) 25% less than N
(E) 20% less than N
Rationale: Correct answer is (B).
This year, the price of an employee is price1=P/N.
If this price decreases by 20% it becomes Price2=P/N*0.8
Then with P dollars, you can hire P/Price2 employees i.e. P/(P/N*0.8) i.e. N/1.1 i.e. 1.25*N
Which is 25% greater than N.
Answer: (B) 25% greater than N
Question: There are a total of 15 numbers with an average of 11. The average of first seven numbers is 14 and the average of last seven numbers is 6. What is the middle number?
(A) 31
(B) 24
(C) 29
(D) 25
(E) 21
Rationale: The total of 15 numbers = 15X11 = 165
The total of first 7 and last 7 numbers is = 7 X 14+7 X 6 = 140
So, the middle number is (165 - 140 ) = 25
D
Answer: (D) 25
Question: (X^n - A^n) is completely divisible by (X - A), when
(A) n is any natural number
(B) n is an even natural number
(C) n is an odd natural number
(D) n is prime
(E) none of these
Rationale: For every natural number n, (X^n - A^n) is always divisible by (X - A)
Answer A.
Answer: (A) n is any natural number
Question: The average age of a group of n people is 15 years old. One more person aged 35 joins the group and the new average is 17 years old. What is the value of n?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
Rationale: 15n + 35 = 17(n+1)
2n = 18
n = 9
The answer is B.
Answer: (B) 9
Question: Can you please walk me through how to best approach this problem? Thanks
If #p# = ap^3+ bp – 1 where a and b are constants, and #-4# = 2, what is the value of #4#?
(A) -4
(B) 0
(C) -2
(D) -3
(E) -4
Rationale: #p# = ap^3 + bp - 1
#-4# = 2
putting p = -4 in above equation
-64a -(4b +1) = 2 or
#-4# = (64a+4b+1) = -2
therefore 64a+4b = -3 .....(1
now putting p = 4
#4# = 64 a+4b - 1
using equation 1(64a+4b = -3)
#4# = -3-1 = -4
hence A
Answer: (A) -4
Question: A, B and C invested Rs.6600, Rs.4400 and Rs.11000 respectively, in a partnership business. Find the share of A in profit of Rs.12100 after a year?
(A) Rs.3300
(B) Rs.3100
(C) Rs.3500
(D) Rs.4200
(E) Rs.3400
Rationale: 6600:4400:11000
3:2:5
3/10 * 11000
= Rs.3300
AnswerA
Answer: (A) Rs.3300
Question: In an election between two candidates, 20% of votes are were declares invalid. First candidate got 480 votes which were 60% of the total valid votes . The total number of votes enrolled in that election was:
(A) 2000 votes
(B) 2500 votes
(C) 3000 votes
(D) 4000 votes
(E) 4200 votes
Rationale: Answer: Option 'B'
(100%-20%=80%
48%-32%=16%
16% = 16×30 = 480
100% =100×30 =3000 votes)
C
Answer: (C) 3000 votes
Question: A man gets a simple interest of Rs.400 on a certain principal at the rate of 5% p.a in two years. Find the compound interest the man will get on twice the principal in two years at the same rate?
(A) s.550
(B) s.556
(C) s.656
(D) s.750
(E) s.820
Rationale: Let the principal be Rs.P
S.I at 5% p.a in 8 years on Rs.P = Rs.400
(P)(8)(5)/100 = 400
P = 4000
C.I on Rs.2P i.e., Rs.8000 at 5% p.a in two years
=8000{ [1 + 5/100]^2 - 1}
= 8000(41/400)
= Rs. 820
Answer:E
Answer: (E) s.820
Question: A train is 460 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length
(A) 20 seconds
(B) 30 seconds
(C) 40 seconds
(D) 48 seconds
(E) None of these
Rationale: Explanation:
Speed = 45 Km/hr = 45*(5/18) m/sec
= 25/2 m/sec
Total distance = 460+140 = 600 meter
Time = Distance/speed
=600∗2/25=48seconds
Option D
Answer: (D) 48 seconds
Question: If (1/2)^23 (1/81)^k = 1/18^23, then k =
(A) 8
(B) 12
(C) 16
(D) 24
(E) 46/4
Rationale: I'm going to focus on denominator only..
(2^23) . ((3^4)^k = 18^23
(2^23) . ((3^4k) = (2. 3^2)^23
(2^23) . ((3^4k) = (2^23) . (3^2)^23
hence
4k = 46
k = 46/4
answer E
I hope it's quite clear
Answer: (E) 46/4
Question: The number 133 is equal to the sum of the cubes of two integers. What is the product of those integers?
(A) 8
(B) 15
(C) 21
(D) 27
(E) 10
Rationale: 2^3 + 5^3= 133 the number is 2*5=10
E
Answer: (E) 10
Question: (x + 6) is a factor in x^2 - mx - 42. What is the value of m?
(A) 2
(B) 2.2
(C) 1
(D) 4
(E) 5
Rationale: I solved the second degree equation and found it like this:
x^2 - mx - 42 = 0
(x-7)(x+6) = 0
x=7 or x= -6
Substituting both values for x in the equation we find:
x^2 - mx -42
=> (-6)^2 - m(-6) = 42
=> 36+ 6m= 42
=> 6m = 42-36=6
=> m = 1
And with 7, using a similar process we end up with:
(7)^2 - m(7) =42
-7m = 42-49= -7
m=-1
Ao,ANS C
Answer: (C) 1
Question: A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12100 after a year?
(A) 3630
(B) 2890
(C) 2707
(D) 2700
(E) 2772
Rationale: 6300:4200:10500
3:2:5
3/10 * 12100
= 3630
Answer:A
Answer: (A) 3630
Question: How many 1 1/4 foot pieces of cable can be cut out of a piece that is 30 feet long?
(A) a.10
(B) b.16
(C) c.17
(D) d.24
(E) e. 20
Rationale: Pretty Simple..the answer is choice (D) 24.
All that one has to do is :
1: Convert 1 1/4 into an improper fraction (5/4) or a decimal (1.25)
2: Divide 30 by 5/4 (or 1.25)
Answer =24 (D)
Answer: (D) d.24
Question: In how many ways can 4 black and 5 white chess pieces be arranged in a row such that they occupy alternate places? Assume that the pieces are distinct.
(A) 20
(B) 1440
(C) 120
(D) 2880
(E) 720
Rationale: 4 black chess pieces can be arranged in 4! ways and 5 white pieces can be arranged in 5 ! ways.
W_W_W_W
Number of ways = 4!*5! = 24 * 120 = 2880
Answer D
Answer: (D) 2880
Question: If an integer x is to be selected at random from 1 to 200, inclusive, what is probability x(x+1) will be divisible by 4?
(A) 0.5
(B) 1
(C) 0.25
(D) 0.75
(E) 1.25
Rationale: because x(x+1) is always an even product of even*odd or odd*even factors,
there is a probability of 1 that that it will be divisible by 2,
and, thus, a probability of 1/2 that it will be divisible by 4
1*1/2=1/2 =0.5
Answer : A
Answer: (A) 0.5
Question: To be undaunted is to be impervious, undisturbed and ‘fearless’.
(A) 2
(B) HH
(C) 28
(D) 28J
(E) 9J
Rationale: Answer:D
Answer: (D) 28J
Question: In a company, 50 percent of the employees are men. If 60 percent of the employees are unionized and 70 percent of these are men, what percent of the non-union employees are women?
(A) 85%
(B) 80%
(C) 75%
(D) 70%
(E) 65%
Rationale: The percent of employees who are unionized and men is 0.7*0.6 = 42%
The percent of employees who are unionized and women is 60 - 42 = 18%
50% of all employees are women, so non-union women are 50%-18% = 32%
40% of all employees are non-union.
The percent of non-union employees who are women is 32%/40% = 80%
The answer is B.
Answer: (B) 80%
Question: The average salary of all the workers in a workshop is Rs. 9000. The average salary of 7 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is?
(A) A)23
(B) B)21
(C) C)52
(D) D)56
(E) E)14
Rationale: Let the total number of workers be x. Then,
9000x = (12000 * 7) + 6000(x - 7)
=> 3000x = 42000
= x =14.
Answer:E
Answer: (E) E)14
Question: a right triangle has three sides (F, G, H). If F=5, G=8.66, and H=10, which angle is 90 degrees
(A) FG
(B) HG
(C) HF
(D) n/a
(E) n/a
Rationale: A) the angle FG is a right angle. HF, and HG are acute.
Answer: (A) FG
Question: A positive number x is multiplied by 5, and this product is then divided by 3. If the positive square root of the result of these two operations equals x, what is the value of x ?
(A)  9/4
(B)  3/2
(C)  4/3
(D)  5/3
(E)  1/2
Rationale: sq rt(5x/3) = x
=> 5x/3 = x^2
=> x = 5/3
Ans - D
Answer: (D)  5/3
Question: Students in Class I and II of a school are in the ratio of 3 : 5. Had 15 students leave the school from each class, the ratio would have become 1 : 2. How many total students were there in the beginning?
(A) 120
(B) 64
(C) 96
(D) 80
(E) None
Rationale: class 1 have 3x student and class 2 have 5x student.
3x-15/5x-15=1/2,6x-30=5x-15,x=15
45+75=120 student
answer A
Answer: (A) 120
Question: The maximum number of students among them 848 pens and 630 pencils can be distributed in such a way that each student get the same number of pens and same number of pencils?
(A) 10
(B) 4
(C) 2
(D) 14
(E) 16
Rationale: number of pens = 848
number of pencils = 630
Required number of students = H.C.F. of 848 and 630 = 2
Answer is C
Answer: (C) 2
Question: The average monthly salary of 8 workers and one supervisor in a factory was 430.@SSWhen@SSthe@SSsupervisor@CC@SSwhose@SSsalary@SSwas@SS430.@SSWhen@SSthe@SSsupervisor@CC@SSwhose@SSsalary@SSwas@SS430.Whenthesupervisor,whosesalarywas430. When the supervisor, whose salary was 870 per month, retired, a new person was appointed and then the average salary of 9 people was $$390 per month. The salary of the new supervisor is:
(A) 233
(B) 600
(C) 510
(D) 771
(E) 191
Rationale: Explanation:
Total salary of 8 workers and supervisor together = 9 Ã— 430 = 3870
Now total salary of 8 workers = 3870 âˆ’ 870 = 3000
Total salary of 9 workers including the new supervisor = 9 Ã— 390 = 3510
Salary of the new supervisor = 3510 âˆ’ 3000 = 510
Answer: C
Answer: (C) 510
Question: How long will a boy take to run round a square field of side 35 meters, If he runs at the rate of 9 km/hr?
(A) 22
(B) 38
(C) 37
(D) 56
(E) 28
Rationale: Answer: D) 56 sec
Answer: (D) 56
Question: A man covers a distance on scooter. Had he moved 3kmph faster he would have taken 40 min less. If he had moved 2kmph slower, he would have taken 40min more. The distance is.
(A) 30 km
(B) 60 km
(C) 80 km
(D) 20 km
(E) 40 km
Rationale: E
40 km
Let distance = x m
Usual rate = y kmph
x/y – x/y+3 = 40/60 hr
2y(y+3) = 9x ---------------------------------(1)
x/y-2 – x/y = 40/60 hr y(y-2) = 3x -----------(2)
divide 1 & 2 equations
by solving we get x = 40 km
Answer: (E) 40 km
Question: 12 spheres of the same size are made from melting a solid cylinder of 8 cm diameter and 1 cm height. What is the diameter of each sphere?
(A) 2 cm
(B) 4 cm
(C) 8 cm
(D) 10 cm
(E) 12 cm
Rationale: Volume of cylinder = pi*r^2*h
Volume of a sphere = 4*pi*R^3 / 3
12*4*pi*R^3 / 3 = pi*r^2*h
R^3 = r^2*h / 16 = 1 cm^3
R = 1 cm
D = 2 cm
The answer is A.
Answer: (A) 2 cm
Question: A small company is planning to rent either computer A or computer B to print customer mailing lists. Both computer A and computer B must be rented on an hourly basis. The rental fee is based only on the amount of time the computer is turned on. It will cost 40 percent more per hour to rent computer A than to rent computer B. Computer B would, however, require 20 hours more than computer A to do the job. If either computer A, or computer B were rented the total cost to rent the computer would be $850.00. What would be the approximate hourly charge to rent computer B?
(A) $9.40
(B) $11.30
(C) $12.14
(D) $17.80
(E) $22.10
Rationale: Pa = price of A
Pb = price of B
Ta = time for A to complete the job
Tb = time for B to complete the job
Given
Pa = 1.4 Pb
Ta+20 = Tb
Pa*Ta = Pb*Tb=850
1.4Pb * (Tb-20) = Pb*Tb
1.4 Pb Tb - Pb Tb = 1.4 Pb * 20
0.4PbTb = 28Pb
Tb = 28/0.4 = 70
Pb=850/70 ~ 12.14
C
Answer: (C) $12.14
Question: The owner of a furniture shop charges his customer 60% more than the cost price. If a customer paid Rs. 2000 for a computer table, then what was the cost price of the computer table?
(A) 2789
(B) 2772
(C) 1250
(D) 6725
(E) 2099
Rationale: CP = SP * (100/(100 + profit%))
= 1250(100/160) = Rs. 1250.
Answer: C
Answer: (C) 1250
Question: Tom spent six lucky days in Las Vegas. On his first day he won a net amount of only $20, but on each of the following days, the daily net amount he won grew by d dollars. If Tom won a total net amount of $1620 during his stay in Las Vegas, how much did he win on the last day?
(A) 330
(B) 500
(C) 520
(D) 540
(E) 620
Rationale: I drew a diagram:
1 - $20
2 -
3 -
4 - $320
5 -
6 -
Total: $1,620
Between 1 and 6 are 5 days where he won $1,600. This means he averaged $320 per day (1600/5). You can put $320 by 4 because it's the middle number. Now you just find the two points betwenn $20 and $320 (320-20 = 300 / 3 = 100). So each day, he earned $100 more. This means on day 6, tom earned$520. Answer choice C.
Answer: (C) 520
Question: The average of first nine prime numbers which are odd is?
(A) 16.1
(B) 15.1
(C) 14.1
(D) 17.1
(E) 13.1
Rationale: Explanation:
Sum of first 9 prime no. which are odd = 158
Average = 127/9 = 14.1
Answer:C
Answer: (C) 14.1
Question: If two sides of a triangle are 12 and 6, which of the following could be the area of triangle?
1. 35
2. 48
3. 56
(A) a) 1 only
(B) b) 1 and 2 only
(C) c) 1 and 3 only
(D) d) 2 and 3 only
(E) e) 1, 2 and 3 only
Rationale: when two sides of a triangle are known , the maximum area occurs when the angle between those two sides is 90.
lets say base = 12 , height =8 (angle = 90)
maximum area = (1/2)*12*8 = 48 ( this is the same maximum area even when base is 8 and height is 12).
if we fix the base and keep lowering the angle, it will result in a lower height . hence the resulting area will always be < 48.
C,D and E are ruled out.
3 and 2 are possible areas as their areas are less than 48.
Hence the answer is D.
Answer: (D) d) 2 and 3 only
Question: An error 2% in excess is made while measuring the side of a square. What is the percentage of error in the calculated area of the square?
(A) 4.05%
(B) 4.02%
(C) 4%
(D) 3%
(E) 2%
Rationale: Percentage error in calculated area
=(2+2+(2×2)/100)%
=4.04%
ANSWER:A
Answer: (A) 4.05%
Question: Joan and Karl each bought a bicycle and the sum of their purchases was $800. If twice of what Joan paid was $40 more than what Karl paid, what did Joan pay for her bicycle?
(A) $280
(B) $300
(C) $320
(D) $340
(E) $360
Rationale: J+K=800 so K=800-J
2J=K+40
2J=(800-J)+40
3J=840
J=280
The answer is A.
Answer: (A) $280
Question: When positive integer n is divided by 3, the remainder is 1. When n is divided by 7, the remainder is 5. What is the smallest positive integer k such that k+n is a multiple of 21?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Rationale: n = 3p + 1 = 7q + 5
n+2 = 3p + 3 = 7q + 7
n+2 is a multiple of 3 and 7, so it is a multiple of 21.
The answer is A.
Answer: (A) 2
Question: Find the principle on a certain sum of money at 9% per annum for 2 2/5 years if the amount being Rs.1120?
(A) 1000
(B) 912.88
(C) 927.78
(D) 926.82
(E) 921.05
Rationale: 1120 = P [1 + (9*12/5)/100]
P= 921.05
Answer: E
Answer: (E) 921.05
Question: In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was :
(A) 2500
(B) 2600
(C) 2700
(D) 2900
(E) 3200
Rationale: Total number of votes = 7500
Given that 20% of Percentage votes were invalid
Valid votes = 80%
Total valid votes = 7500x (80/100)
1st candidate got 55% of the total valid votes.
Hence the 2nd candidate should have got 45% of the total valid votes
Valid votes that 2nd candidate got = total valid votes x 45/100
7500x (80/100)x45/100= 2700
answer :C
Answer: (C) 2700
Question: Which of the following equivalent to (1/125)^2?
(A) (0.03)^5
(B) (0.04)^3
(C) (0.05)^6
(D) (0.06)^3
(E) (0.07)^2
Rationale: (1/125)^2 = (1/5^3)^2 = (1/5)^6 = (1/25)^3 = (0.04)^3
Answer: Option B
Answer: (B) (0.04)^3
Question: In how many ways can 5 boysand 2 girls be arranged at a table if 2 girls are never together?
(A) 230
(B) 240
(C) 254
(D) 260
(E) 480
Rationale: Total ways of arranging 7 person in a circle = 6! = 720 ways
If we consider two women as one, then we have 5+1=6 persons. Arranging these six persons in circle will take = 5! = 120 ways
And two women can arrange themselves in 2! ways
Total ways in which two women sit together in circle = 5!*2! = 240 ways
Total ways in which two women doesn’t sit together in circle = 6! - 5!*2! = 720 - 240 = 480 ways
E
Answer: (E) 480
Question: There are 7 magazines lying on a table; 3 are fashion magazines and the other 4 are sports magazines. If 3 magazines are to be selected at random from the 8 magazines, what is the probability that at least one of the fashion magazines will be selected?
(A) 1/2
(B) 7/8
(C) 32/35
(D) 11/12
(E) 13/14
Rationale: answer isB
Total probability=7C3=48
4C3 +4C2*4C1+4C1*4C2=4+24+24=42
therefore the probability that at least one of the fashion magazines will be selected= 42/48=7/8
B
Answer: (B) 7/8
Question: if x/4-x-3/6=1,then find the value of x.
(A) 6
(B) 4
(C) 5
(D) 1
(E) 2
Rationale: (x /4)-((x-3)/6)=1=> (3x-2(x-3) )/12 = 1 => 3x-2x+6=12 => x=6.
Answer is A
Answer: (A) 6
Question: Triathlete Dan runs along a 2-mile stretch of river and then swims back along the same route. If Dan runs at a rate of 8 miles per hour and swims at a rate of 6 miles per hour, what is his average rate for the entire trip in miles per minute?
(A) 1/9
(B) 2/15
(C) 3/15
(D) 1/4
(E) 3/8
Rationale: Dan travels 4 miles round trip.
Running part: (2/8 = 1/4*60 = 15 minutes)
Swimming Part: (2/6 = 1/3*60 = 20 minutes)
4 miles in (15+20) minutes
4/35 = 1/9 mile per minute
Answer: 1/9 mile per minute
Answer: (A) 1/9
Question: A man has only 20-paise and 25-paise coins in a bag. If he has 50 coins in all totaling to Rs.11.25, then the number of 20-paise coins is
(A) 28
(B) 27
(C) 26
(D) 25
(E) 24
Rationale: x=20p;y=25p;
x+y=50;
0.20x+0.25y=11.25;
25x+25y=1250;
20x+25y=1125;
=>x=25;
ANSWER:D
Answer: (D) 25
Question: A takes twice as much time as B or thrice as much time to finish a piece of work. Working together, they can finish the work in 2days. B can do the work alone in?
(A) 8
(B) 10
(C) 12
(D) 15
(E) 20
Rationale: Suppose A,B,C takes x,x/2,x/3 hours to finish the work
Then, 1/x + 2/x + 3/x = 1/2
6/x = 1/2
x = 12
Answer is C
Answer: (C) 12
Question: The cost of 2 books and 2 magazines is $26. The cost of 1 book and 3 magazines is $27. How much does 1 magazine cost?
(A) 8
(B) 5
(C) 7
(D) 4
(E) 6
Rationale: Let the cost of 1 book = x, let the cost of 1 magazine = y
2x + 2y = 26
x = (26 - 2y)/2
x = 13 - y
Again,
(13 - y) + 3y = 27
13 + 2y = 27
2y = 14
y = 7
Answer: C
Answer: (C) 7
Question: If 45-[28-{37-(15-*)}]= 57, then * is equal to:
(A) -29
(B) -19
(C) 18
(D) 29
(E) 39
Rationale: 45-[28-{37-(15-*)}]= 57 => 45-[28-{37-15+*}]=57
45-[28-37+15-*]=57 => 45[43-37-*]=57
45-[6-*]=57 => 45-6+*=57
39+*=57 => *=57-39
= 18
ANSWER:C
Answer: (C) 18
Question: Five different books (A, B, C, D and E) are to be arranged on a shelf. Books C,D and E are to be arranged first and second starting from the right of the shelf. The number of different orders in which books A, B and may be arranged is
(A) 1!
(B) 2!
(C) 5!
(D) 15!
(E) 24!
Rationale: Solution
Since books C,D and E are arranged first and second, only books A and B will change order. Therefore it an arrangement problem involving 2 items and the number of different order is given by
2!
Answer B
Answer: (B) 2!