divelab/Sys2Bench huggingface dataset:
Question: If 36 men can do a piece of work in 5 hours, in how many hours will15 men do it?
Options:
A)12
B)38
C)60
D)88
E)72
Rationale: Explanation:
Let the required no of hours be x. Then
Less men , More hours (Indirect Proportion)
\inline \fn_jvn \therefore 15:36 ::5:x \inline \fn_jvn \Leftrightarrow (15 x X)=(36 x 5) \inline \fn_jvn \Leftrightarrow \inline \fn_jvn x=\frac{36\times 5}{15}=12
Hence, 15 men can do it in 12 hours.
Answer: A) 12
Answer: A
Question: In the formula X = 1/(2y+1)^2, if y is halved, then X is multiplied by
Options:
A)25/9
B)25
C)1/9
D)1/25
E)9
Rationale: Say y=2 => X1 = 1/25
when y=1; X2 = 1/9
X2 = 25/9*X1.
Answer : A
Answer: A
Question: If y ¤ d = y^(2d) for all positive integers, then (3 ¤ 4) ¤ 2 =
Options:
A)3^8
B)3^12
C)3^16
D)3^24
E)3^32
Rationale: y ¤ d = y^(2d)
3 ¤ 4 = 3^(8)
(3 ¤ 4) ¤ 2 = (3^8) ¤ 2 = (3^8)^4 = 3^32
Correct Option: E
Answer: E
Question: A man can row a boat at 20 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 78 km downstream?
Options:
A)3 hours
B)33/13 hours
C)31/13 hours
D)30/13 hours
E)30/14 hours
Rationale: Speed downstream = 20 + 6 = 26 kmph.
Time required to cover 78 km downstream = d/s = 78/26
= 3 hours.
Answer:A
Answer: A
Question: A person borrows Rs. 5000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 6 p.a for 2 years. Find his gain in the transaction per year.
Options:
A)100 rs
B)150 rs
C)160 rs
D)180 rs
E)200 rs
Rationale: Gain in 2 years =
[(5000*6*2)/100]-[(5000*4*2)/100]
600-400=200
Gain in 1 year =(200/2)=100 rs
ANSWER:A
Answer: A
Question: Tickets for all but 100 seats in a 10,000-seat stadium were sold. Of the tickets sold, 35% were sold at half price and the remaining tickets were sold at the full price of $2. What was the total revenue from ticket sales?
Options:
A)$15,840
B)$17,820
C)$16,335
D)$19,800
E)$21,780
Rationale: 10000 seats --> Full Price : Half Price = 6500 : 3500
Price when all seats are filled = 13000 + 3500 = 16500
100 seats are unsold --> Loss due to unfilled seats = 35 + 2*65 = 165
Revenue = 16500 - 165 = 16335
Answer: C
Answer: C
Question: If -1 < a < 0, which of the following must be true? I. a^9 < a^4 II. a^3 < 1 – a III. a^6 < a^3
Options:
A)I only
B)III only
C)I,II,III only
D)II only
E)I,III only
Rationale: Answer : C
Answer: C
Question: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is?
Options:
A)65 km/hr
B)17 km/hr
C)76 km/hr
D)50 km/hr
E)15 km/hr
Rationale: Speed of the train relative to man = 125/10 = 25/2 m/sec.
= 25/2 * 18/5 = 45 km/hr
Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.
x - 5 = 45 => x = 50 km/hr.
Answer: D
Answer: D
Question: In a class of 50 students, 20 play Baseball, 15 play Cricket and 11 play Football. 7 play both Baseball and Cricket, 4 play Cricket and Football and 5 play Baseball and football. If 18 students do not play any of these given sports, how many students play exactly two of these sports?
Options:
A)10
B)46
C)67
D)68
E)446
Rationale: Notice that7 play both Baseball and Cricket does not mean that out of those 7, some does not play Football too. The same for Cricket/Football and Baseball/Football.
[color=#ffff00]{Total}={Baseball}+{Cricket}+{Football}-{HC+CH+HF}+{All three}+{Neither}For more checkADVANCED OVERLAPPING SETS PROBLEMS
[/color]
50=20+15+11-(7+4+5)+{All three}+18 --> {All three}=2;
Those who play ONLY Baseball and Cricket are 7-2=5;
Those who play ONLY Cricket and Football are 4-2=2;
Those who play ONLY Baseball and Football are 5-2=3;
Hence, 5+2+3=10 students play exactly two of these sports.
Answer: A.
Answer: A
Question: The average age of three boys is 15 years and their ages are in proportion 3:5:7. What is the age in years of the eldest boy?
Options:
A)6
B)9
C)16
D)4
E)21
Rationale: 3x + 5x + 7x = 45
x =3
7x = 21
Answer:E
Answer: E
Question: A cricketer whose bowling average is 12.4 runs per wicket takes 5 wickets for 26 runs and there by decreases his average by 0.4. The number age of the family now is:
Options:
A)18
B)17
C)76
D)85
E)86
Rationale: Let the number of wickets taken till the last match be x. Then,
(12.4x + 26)/(x + 5) = 12
= 12.4x + 26 = 12x + 60
= 0.4x = 34
= x = 340/4 = 85.
Answer: D
Answer: D
Question: The salary of a person was reduced by 10%. By what percent should his
reduced salary be raised so as to bring it at par with his original salary?
Options:
A)100/9
B)100
C)110
D)98
E)100/11
Rationale: Let the original salary be $100. New salary = $90.
Increase on 90=10 , Increase on 100=((10/90)*100)%
= (100/9)%
Answer A)100/9
Answer: A
Question: the hiker walking at a constant rate of 5 miles per hour is passed by a cyclist traveling in the same direction along the same path at 20 miles per hour. the cyclist stops to wait for the hiker 5 minutes after passing her, while the hiker continues to walk at her constant rate, how many minutes must the cyclist wait until the hiker catches up?
Options:
A)15
B)10
C)20
D)30
E)35
Rationale: After passing the hiker the cyclist travels for 5 minutes at a rate of 20 miles/hour.
In those 5 mins the cyclist travels a distance of 5/3 miles.
In those 5 mins the hiker travels a distance of 5/12 miles.
So the hiker still has to cover 15/12 miles to meet the waiting cyclist.
The hiker will need 1/4 hours or 15 mins to cover the remaining 15/12 miles.
So the answer is A.
Answer: A
Question: An insect leaps 60 centimeters in 1.5 seconds. What is its speed?
Options:
A)9 centimeters per second
B)0.9 meters per second
C)4 meters per second
D)0.4 meters per second
E)4.4 centimeters per second
Rationale: 60 / 1.5 = 40 cm/s = 0.4 m/s
The answer is D.
Answer: D
Question: (1^2+2^2+3^2+.....+10^2)=?
Options:
A)330
B)345
C)365
D)385
E)None of them
Rationale: formula is (1^2+2^2+3^2+....+n^2=1/6 n(n+1)(2n+1)
n=10
=(1/6x10x11x21)
=385
Answer is D.
Answer: D
Question: Jill works as a waitress at the local diner where she earns an hourly wage of $5.00 per hour and a standard tip rate of 25% of the cost of the orders she serves. If she worked four 9-hour shifts this week and averaged $40 in orders per hour, how much did Jill earn this week?
Options:
A)280
B)300
C)540
D)350
E)400
Rationale: Jill earns 5 dollars/hour and the hourly tip is (1/4)*40.
Jill thus earns 5*9+9*10 per day(or 5(9)+10(9)=15(9)=135).
Jill has worked for 4 days -> 135*4=540.
This matches answer choice C.
Answer: C
Question: The result when a number subtracted from 100 is the same as the number added to 40. what is the number?
Options:
A)70
B)65
C)80
D)140
E)60
Rationale: Answer
Let the number be x.
Then, x - 40= 100- x
â‡’ 2x = 100+ 40= 140
â‡’ 2x = 140
âˆ´ x = 70
Correct Option: A
Answer: A
Question: In how many different number of ways 4 boys and 2 girls can sit on a bench such that girls always sit together.
Options:
A)A)720
B)B)240
C)C)740
D)D)780
E)E)790
Rationale: 240
Option 'B'
Answer: B
Question: What is the units' digit of the following expression (10)^5*(12)^5*(18)^5?
Options:
A)0
B)1
C)3
D)5
E)9
Rationale: We do not have to do any calculations or find units digit of remaining numbers...
all three terms - 10,12,18 - are EVEN and since the PRODUCT contains 0, the units digit of the product will remain 0
A
Answer: A
Question: The length of a rectangle is one- sixth of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1296 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?
Options:
A)560 sq.units
B)360 sq.units
C)260 sq.units
D)460 sq.units
E)160 sq.units
Rationale: Given that the area of the square = 1225 sq.units
=> Side of square = √1296 = 36units
The radius of the circle = side of the square = 35 units Length of the rectangle = 2/5 * 35 = 14 units
Given that breadth = 10 units
Area of the rectangle = lb = 36 * 10 = 360 sq.units
Answer:B
Answer: B
Question: Each child has 5 stickers and 8 candies. If there are 7 children, how many stickers are there in total?
Options:
A)12
B)38
C)48
D)21
E)35
Rationale: 5*7=35.Answer is E.
Answer: E
Question: If r and s are two different prime numbers, which of the following cannot be true?
Options:
A)rs is odd.
B)r + s is even.
C)r + s is odd.
D)rs is even.
E)r/s is an integer
Rationale: A prime number is a positive integer with exactly two distinct positive divisors: 1 and itself. So, a prime number cannot be a multiple of another prime number. Which makes option E not possible (r/s=integer means that r is a multiple of s).
.
All other options are possible:
A. rs is odd --> r=3 and s=5;
B. r + s is even --> r=3 and s=5;
C. r + s is odd --> r=2 and s=3;
D. rs is even --> r=2 and s=3;
Answer: E
Answer: E
Question: Dan read that an average snowfall of 10 inches yields 1 inch of water when melted. Very wet
snow will measure 5 inches for one inch of water, and very dry snow may measure 20 inches for an
inch of water. He made measurements for a storm that started with 5.3 inches of average snowfall.
The precipitation changed to wet snow and dropped another 4.1 inches. The weather continued to
warm up, and the storm finished with 1.5 inches of rain. What was the actual amount of water that fell
during the storm? Round your answer to tenths.
Options:
A)2.9" of water
B)3.9" of water
C)4.9" of water
D)7.9" of water
E)8.9" of water
Rationale: 5.3 ÷ 10 = .53" water from average snow
4.1 ÷ 5 = .82" water from wet snow
If you are unsure whether to multiply or divide, check your answer to see if it makes
sense. The actual snowfall in each case was less than what was needed to make
an inch of water, so division yields a sensible answer.
.53 + .82 + 1.5 = 2.85" rounds to 2.9" of water
correct answer A
Answer: A
Question: The diagonals of two squares are in the ratio of 2:5 then find the ratio of its areas?
Options:
A)2:12
B)4:25
C)5:31
D)2:19
E)3:17
Rationale: Let the diagonals of the squares be 2x and 5x
Ratio of their areas = 1/2 (2x)^2 : 1/2 (5x)^2 = 4x^2 : 25x^2 = 4:25
Answer is B
Answer: B
Question: 20 people are there, they are shaking hands together, how many hand shakes possible, if they are in pair of cyclic sequence.
Options:
A)21
B)20
C)40
D)42
E)19
Rationale: n for cyclic hand shake and n-1 for linear handshake.
so here no of hand shake is 20.
ANSWER:B
Answer: B
Question: X starts a business with Rs.45000. Y joins in the business after 2 months with Rs.30000. What will be the ratio in which they should share the profit at the end of the year?
Options:
A)1:2
B)9:5
C)1:5
D)3:1
E)1:1
Rationale: Explanation:
Ratio in which they should share the profit
= Ratio of the investments multiplied by the time period
=45000Ã—12:30000Ã—10
=45Ã—12:30Ã—10
=3Ã—12:2Ã—10
=9:5
Answer: Option B
Answer: B
Question: If x is an integer and (x)(x^2)(x^3)(x^8) is positive, which of the following could be negative?
Options:
A)x^4
B)(x)(x^3)
C)(x)(x)
D)x + x^9
E)3x^2
Rationale: A) X^4 - always positive (or 0).
B) X(X^3) = X^4 - Again always positive (or 0).
C) (x)(x) = X^2 - Again always positive (or 0).
D) x+x^9 - Could be -ve if x is -ve.
E) 3X^2 - again always positive (or 0)
Answer D.
Answer: D
Question: A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is:
Options:
A)720
B)900
C)1200
D)1800
E)None of these
Rationale: Explanation:
2(15 + 12) × h = 2(15 × 12)
=> h = (180/27)m = 20/3 m.
Volume = (15 × 12 × (20/3)) m3 = 1200 m3
Answer: C
Answer: C
Question: Two trains T1 and T2 start simultaneously from two stations X and Y respectively towards each other. If
they are 50 km apart both 3 and 6 hours after start, then find the distance between the two stations.
Options:
A)190km
B)200km
C)220km
D)180km
E)150km
Rationale: In first 3 hours T1 travels R km and T2 travels S km.
After 6 hours they traveled R+S+50+ 50
2(R+S ) = R+S +100
R+S = 100
Hence distance between XY is R+S+ 50 = 100 +50 =150
Answer : E
Answer: E
Question: A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour?
Options:
A)7.9
B)7.3
C)7.8
D)7.2
E)7.1
Rationale: distance = 600 meter
time = 5 minutes = 5 x 60 seconds = 300 seconds
Speed = distancetime=600300=2m/s=2×185 km/hr=365 km/hr=7.2 km/hr
Answer :D
Answer: D
Question: On a certain date, Pat invested $10,000 at x percent annual interest, compounded annually. If the total value of the investment plus interest at the end of 12 years will be $40,000, in how many years, the total value of the investment plus interest will increase to $320,000?
Options:
A)30
B)16
C)18
D)20
E)24
Rationale: if i were to choose during the test, would go for 18 or 20. probably 18 cuz it wont take too long to get the value doubled....
I found a method: Rule of 72.
Given an x% return, it takes 10,000 to quadralope 12 years.
So according to the rule: 72/x is the no of years 10,000.00 took to double 20,000.00.
Again, 20,000.00 took to double 40,000.00 same (72/x) no of years.
72/x+ 72/x = 12
x = 12% (though rate here is not very much required).
Again, 40,000.00 takes the same (72/x) no of years to double 320,000.00.
72/x = 6 years.
So altogather:
10,000 - 20,000 = 6 years
20,000 - 40,000 = 6 years
40,000 - 80,000 = 6 years
80,000 - 160,000 = 6 years
160,000 - 320,000 = 6 years
total 30 years.
Answer: A
Question: A and B undertake to do a piece of work for Rs. 600. A alone can do it in 6 days while B alone can do it in 8 days. With the help of C, they finish it in 3 days. Find the share of A
Options:
A)300
B)450
C)750
D)800
E)None of them
Rationale: C's 1 day's work = 1/3-(1/6+1/8)=24
A : B : C = Ratio of their 1 day's work = 1/6:1/8:1/24= 4 : 3 : 1.
A’s share = Rs. (600 *4/8) = Rs.300, B's share = Rs. (600 *3/8) = Rs. 225.
C's share = Rs. [600 - (300 + 225») = Rs. 75.
Answer is A
Answer: A
Question: What percent is 120 of 80?
Options:
A)150 %
B)134 1/3 %
C)135 1/3 %
D)140 1/3 %
E)143 1/3 %
Rationale: 120/80 = 3/2
3/2 × 100 = 300/2 = 150 %
A
Answer: A
Question: Pomes can eat 25 marshmallows is 20 minutes. Dylan can eat 25 in one hour. In how much time will the two eat 150 marshmallows?
Options:
A)40 minutes.
B)1 hour and 30 minutes.
C)1 hour.
D)1 hour and 40 minutes.
E)2 hours and 15 minutes.
Rationale: Rate =Output/Time
Pomes Rate=25/20=5/4
Dylan Rate=25/60=5/12
Combined rate = 5/4+5/12= 20/12
CombinedRate*CombinedTime= CombinedOutput
20/12*t=150
t=90 mins => 1 hr 30 min
Answer: C
Question: Which of the following must be subtracted from 2^72 so that the resulting integer will be a multiple of 3?
Options:
A)5
B)4
C)1
D)3
E)2
Rationale: {4^1} / 3 =4/3 remainder 1
{4^2} / 3 = 16/3 remainder 1
{4^3} / 3 = 64/3 remainder 1
{4^4} / 3 = 256/3 remainder 1
Actually the same remainder keeps repeating .....
Try with a diff no, say 2
{2^1}/3 = remainder 2
{2^2}/3 = remainder 1
{2^3}/3 = remainder 2
{2^4}/3 = remainder 1
Answer : C
Answer: C
Question: A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3600. With the help of C, they completed the work in 3 days. How much is to be paid to C?
Options:
A)s. 375
B)s. 450
C)s. 600
D)s. 800
E)s. 850
Rationale: C's 1 day's work = 1/3 - (1/6 + 1/8) = 1/3 - 7/24 = 1/24
A's wages : B's wages : C's wages = 1/6 : 1/8 : 1/24 = 4: 3 : 1
C's share (for 3 days) = Rs.	(3 * 1/24 * 3600) =Rs.450
Answer = B
Answer: B
Question: Bag A contains red, white and blue marbles such that the red to white marble ratio is 1:3 and the white to blue marble ratio is 2:3. Bag B contains red and white marbles in the ratio of 1:4. Together, the two bags contain 24 white marbles. How many red marbles could be in bag A?
Options:
A)1
B)3
C)4
D)6
E)7
Rationale: # of Red marbles in Bag A can be either 2 or 6. No 2 in the choices, so 6. D.
Bag A:
R:W:B = 2:6:9
Bag B
R:W = 1:4
6X + 4Y = 24 i.e 3X + 2Y = 12
X has to be odd to make an odd sum from the eq.
X = 2 , Y = 3 OR X = 4, Y = 0
So R can be 2X i.e 4 or 8.
Answer C
Answer: C
Question: A man buys an article for rs.27.50 and sells it for rs.28.50. find his gain percentage.
Options:
A)4
B)2
C)1
D)3
E)None of them
Rationale: cost price=rs27.50, sp=rs 28.50
gain=rs(28.50 –27.50)=rs1.10
so gain%={(1.10/27.50)*100}=4%
Answer is A.
Answer: A
Question: How many different ways are possible to arrange the letters of the word “MACHINE” so that the vowels may occupy only the odd positions?
Options:
A)800
B)125
C)348
D)576
E)None of these
Rationale: Solution
MACHINE has 4 consonants and 3 vowels.The vowels can be placed in position no. 1, 3, 5, 7
⇒ Total number of ways possible = 4P3 = 24.
For each of these 24 ways the 4 consonants can occupy the other 4 places in 4P4 ways
⇒ Total = 24 × 24 = 576. Answer D
Answer: D
Question: The distance between a book store and a coffee shop is approximately 5.3 x 10^4 inches. Which of the following is closest to the distance between the book store and a coffee shop, in kilometers? (1 kilometer is approximately 3.9 x 10^4 inches.)
Options:
A)1.4
B)2.2
C)1.9
D)2.5
E)2.9
Rationale: We know that 1 kilometer = 3.9x10^4 inches. Therefore, we now have a ratio of (1 kilometer/3.9x10^4 inches).
We also know that the distance between the book store and a coffee shop is approximately 5.3 x 10^4 inches. To convert inches to kilometers, we need to multiply 5.3 x 10^4 inches by the ratio we just found out.
kilometers = 5.3 x 10^4 inches x (1 kilometer/3.9x10^4 inches) [note: "inches" cancel out, leaving us with just km]
km = 5.3x10^5/3.9x10^4 km
km = 1.36 = 1.4 km
Therefore, we can see that the closest answer is A.
Answer: A
Question: John's Ice Cream Shop sells ice cream at m cents a scoop. For an additional n cents, a customer can add 5 toppings to his or her sundae. How much would a sundae with 5 scoops and 5 toppings cost, in terms of m and n?
Options:
A)5m+5n
B)5m+2n
C)4m+n
D)5m+n
E)6m+n
Rationale: Answer D 5m+n
Answer: D
Question: A watch was sold at a loss of 10%. If the watch was sold for $32 more, there would have been a gain of 6%. What is the cost price?
Options:
A)$180
B)$200
C)$220
D)$240
E)$260
Rationale: 0.9x + 32 = 1.06x
0.16x = 32
x = 200
The answer is B.
Answer: B
Question: An error 17% in excess is made while measuring the side of a square. Now What is the percentage of error in the calculated area of the square?
Options:
A)6.64%
B)36.89%
C)15.64%
D)26.64%
E)10.64%
Rationale: Percentage error in calculated area
=(17+17+(17Ã—17)/100)%=36.89%
ANSWER:B
Answer: B
Question: A rectangular-shaped carpet that measures x feet by y feet is priced at $27. What is the cost of the carpet, in dollars per square yard? (1 square yard = 6 square feet)
Options:
A)xy/297
B)11xy/3
C)3xy/11
D)297/(xy)
E)162/(xy)
Rationale: The area of the carpet in feet is xy.
The area in square yards is xy / 6.
The price per square yard is 27 / (xy/6) = 162/(xy).
The answer is E.
Answer: E
Question: The fourth proportional to 12, 14 and 6 is?
Options:
A)2
B)6
C)7
D)8
E)9
Rationale: (14*6)/12 = 7
Answer: C
Answer: C
Question: In the City ,there are 40% of the population lived in the North side at the Beginning of the Year and the rest lived in the South side. During the Same Year, the population grew by 6%. If the population in the North grew by 2%, by how much did the population grow in the South side?
Options:
A)8.6%
B)7.28%
C)9.2%
D)10.0%
E)8%
Rationale: Ratio of population in City = North:South :: 40%:60% = 2:3
Mean growth = 6%
North side: 2%
South side = ??
North-------------Average--------------South
2 __(3n)_____6.0%_____(2n)_____??
Since:
2+3n=6
n=4/3
Therefore:
South=6+2n
South=6+2(4/3)
The population increased in the south grew by 8.6%
Answer: A
Question: In a division sum, the divisor is 10 times the quotient and 5 times the remainder. If the remainder is 46, what is the dividend ?
Options:
A)4236
B)4306
C)4336
D)5336
E)4510
Rationale: Divisor = (5 x 46) = 230
10 x Quotient = 230 =	230	= 23
10
Dividend = (Divisor x Quotient) + Remainder
= (230 x 23) + 46
= 5290 + 46
= 5336.
Option D
Answer: D
Question: Pipe P can drain the liquid from a tank in 4/4 the time that it takes pipe Q to drain it and in 2/3 the time that it takes pipe R to do it. If all 3 pipes operating simultaneously but independently are used to drain liquid from the tank, then pipe Q drains what portion of the liquid from the tank?
Options:
A)9/29
B)8/23
C)3/4
D)17/29
E)3/8
Rationale: Suppose Q can drain in 1 hr. So, rQ = 1/1 = 1
So, rP = 1/[(4/4)rQ] = 4/4 =1
Also, rP = rR/(2/3) => 1 = rR/(2/3) => rR = 2/3
Let H is the time it takes to drain by running all 3 pipes simultaneously
So combined rate = rC = 1/H = 1 + 1 + 2/3 = 8/3 = 1/(3/8)
Thus running simultaneously, Pipe Q will drain 3/8 of the liquid.
Thus answer = E.
Answer: E
Question: Vijay bought 160 shirts at the rate of Rs. 225 per shirt. The transport expenditure was Rs. 1400. He paid an octroi at the rate of Rs. 1.75 per shirt and labour charges were Rs. 320. What should be the selling price of one shirt, if he wants a profit of 10%?
Options:
A)282
B)229
C)277
D)285
E)261.25
Rationale: Total CP per shirt = 225 + 1400/160 + 1.75 + 320/160 = Rs. 237.5
SP = CP[(100 + profit%)/100]
= 237.5 * [(100 + 10)/100] = Rs. 261.25.
Answer:E
Answer: E
Question: Among the employees of a certain company, 53 percent of the employees are male and 47 percent are female. In this company 70 percent of the male employees are married and 50 percent of the female employees are married. If one employee in the company is randomly selected, approximately what is the probability that he or she is NOT married?
Options:
A) 0.3
B) 0.4
C) 0.5
D) 0.6
E) 0.7
Rationale: Much faster: draw 4 quadrants
______________Male (53%)_____Female (47%)
Married :__________70%____________50%
Not Married:_______30%____________50%
Therefore: the probability of picking one random person Not Married (he or she) is: 0,53 x 0,30 + 0,50 x 0,50 = 0,15 + 0,25 (approx.)
Solution: approx. 0,4 (answer B)
Answer: B
Question: (1/5)^r * (1/4)^18 = 1/(2(10)^35). What is r?
Options:
A)17
B)18
C)34
D)35
E)36
Rationale: We need to arrive at a common base. -->
(5)^(-r) * 2^(-36) = 2^(-36)*5^(-35)
5^(-r)=5^(-35)
-r=-35
r=35=D
Answer: D
Question: A dress on sale in a shop is marked at $D. During the discount sale its price is reduced by 15%. Staff are allowed a further 10% reduction on the discounted price. If a staff member buys the dress what will she have to pay in terms of D ?
Options:
A)0.965D
B)0.760D
C)0.765D
D)0.865D
E)4.765D
Rationale: Explanation:
If the price is reduced by 15 %, then the new price will be 0.85D
If this new price is further reduced by 10%, the discounted price will be 0.9 x 0.85D = 0.765D
Answer: C
Answer: C
Question: What is the least number which should be added to 5432 so that the sum is exactly divisible by 5, 6, 4, and 3?
Options:
A)16
B)22
C)28
D)34
E)40
Rationale: L.C.M. of 5, 6, 4 and 3 = 60.
When dividing 5432 by 60, the remainder is 32.
The number to be added = 60 - 32 = 28.
The answer is C.
Answer: C
Question: A , B , and C started a partnership business by investing $27,000 , $72,000 , and $81,000 respectively. At the end of the year , the profit was distributed among them. If C's share of profit is $27,000, what is the total profit?
Options:
A)$80,000
B)$90,000
C)$60,000
D)$120,000
E)$40,000
Rationale: A:B:C = 27000:72000:81000 which is a ratio of 3:8:9.
Let the total profit be x.
x * 9/20 = 27000
x = 27000*20/9 = 60,000.
The answer is C.
Answer: C
Question: What is the square root of 400, divided by 2?
Options:
A)9
B)36
C)122
D)6
E)10
Rationale: Square root is a number times itself
Square root of 400=20, 20/2=10
(E)1
Answer: E
Question: A child buy 18 pencil and pay 100 rs. He pay 1 rs more for white pencil than brown pencil. How many white pencil He buy? and what is price of one white pencil
Options:
A)4
B)5
C)6
D)7
E)8
Rationale: LET white pencil be x and brown be 18-x
let 1 brown pencil be y rs.
so, x(y+1)+(18-x)y=100
=>xy+x+18y-xy=100
=>x+18y=100
x=10 y=5
ans : 6
ANSWER:C
Answer: C
Question: If 1/(b – 2) = 1/(b + 2) + 1/(b – 1), which of the following is a possible value of b?
Options:
A)1
B)0
C)-1
D)-2
E)2
Rationale: Multiply by (b-2)*(b+2)*(b-1) throughout to get:
(b+2)*(b-1) = (b-2)*(b-1) + (b+2)(b-2)
Of the given options, only b=0 satisfies this.
Answer : B
Answer: B