divelab/Sys2Bench huggingface dataset:
Question: Rectangular tile each of size 20cm by 30cm must be laid horizontally on a rectangular floor of size 100cm by 150cm,such that the tiles do not overlap and they are placed with edges jutting against each other on all edges. A tile can be placed in any orientation so long as its edges are parallel to the edges of floor. No tile should overshoot any edge of the floor. The maximum number of tiles that can be accommodated on the floor is:
Options:
A)40
B)15
C)25
D)32
E)45
Rationale: Area of tile = 20*30 = 600
Area of floor = 100*150 = 15000
No of tiles = 15000/600 =25
So, the no of tile =25
ANSWER:C
Answer: C
Question: How many integers between 300 and 1200 are there such that their unit digit is odd?
Options:
A)250
B)350
C)450
D)550
E)650
Rationale: There are 900 numbers from 301 to 1200 (inclusive).
Half of the numbers are odd, so there are 450 odd numbers.
The answer is C.
Answer: C
Question: A merchant gets a 5% discount on each meter of fabric he buys after the first 2,000 meters and a 7% discount on every meter after the next 1,500 meters. The price, before discount, of one meter of fabric is $2, what is the total amount of money the merchant spends on 7,000 meters of fabric?
Options:
A)$13,360
B)$14,450
C)$15,720
D)$16,780
E)$17,240
Rationale: For first 2000 meters he does not get any discount.
The price is 2*2000 = $4000
For next 1500 meters, he gets a 5% discount.
The price is 1.9*1500 = $2850
For the next 1500 meters, he gets a 7% discount.
The price is 1.86*3500 = $6510
The total price is $4000 + $2850 + $6510 = $13,360
The answer is A.
Answer: A
Question: 8 men can do a piece of work in 12 days. 4 women can do it in 48 days and 10 children can do it in 24 days. In how many days can 10 men, 4 women and 30 children together complete the piece of work?
Options:
A)5 days
B)15 days
C)28 days
D)4 days
E)7 days
Rationale: Explanation:
1 man’s 1 day’s work = 1/8 × 12 = 1/96
10 men’s 1 day’s work = 1 × 10/96 = 5/48
1 woman’s 1 day’s work = 1/192
4 women’s 1 day’s work = 1/192 × 4 = 1/48
1 child’s 1 day’s work = 1/240
30 children’s 1 day’s work = 1/8
Therefore, (10 men + 4 women + 30 children)’s 1 day’s work = 5/48 + 1/48 + 1/8
=1/4
The required No. of days = 4 days
Answer: Option D
Answer: D
Question: Abi decided to save a certain amount of her monthly salary each month and her salary was unchanged from month to month. If abi's savings by the end of the year from these monthly savings were six times the amount she spent per month, what should be the fraction of her salary that she spent each month?
Options:
A)6/9
B)5/3
C)2/3
D)4/3
E)5/3
Rationale: Let Abi 's monthly savings = S
Abi 's monthly pay = P
Abi 's monthly expenditure = P-S
Abi 's savings by the end of the year from these monthly savings were six times the amount she spent per month
12S = 6*(P-S)
=>2S = P-S
=> P = 3S
Abi 's monthly expenditure = P-S = 3S-S = 2S
fraction of her salary that Abi spent each month = 2S / 3S=P-S/P = 2/3. Answer is C
Answer: C
Question: A present value of a machine is $148000. Its value depletiation rate is 25% per annum then find the machine value after 3 years?
Options:
A)A)$54000
B)B)$48000
C)C)$36520
D)D)$62437.5
E)E)$42500
Rationale: P= $148000
R = 25%
T = 3 years
Machine value after 3years = P/(1-R/100)^T
=148000*3/4 * 3/4 * 3/4
=$62437.5
Answer is D
Answer: D
Question: A boat with speed 15 km/hr in standing water goes 30 km downstream and returns in a total of 4.5 hours. What is the speed of current?
Options:
A)8kmph
B)6kmph
C)4kmph
D)5 kmph
E)1kmph
Rationale: Explanation:
Speed of the boat in still water: 15 km/hr
Speed of boat downstream: (15+x)km/hr where x is speed of the current.
The boat travels 30 km downstream and then 30 km upstream and takes 9/2 hours.
Total time= Time taken to travel downstream + Time taken to travel upstream
=> 4/5= (30/(15+x))+(30/(15-x))
=>x= 5
ANSWER:D
Answer: D
Question: How long will a train 100m long travelling at 72kmph take to overtake another train 200m long travelling at 54kmph ?
Options:
A)60 sec
B)70 sec
C)80 sec
D)50 sec
E)90 sec
Rationale: 72 kmph=72*5/18 mps=20mps.
54 kmph=54*5/18 mps=15 mps.
The train has to travel (200+100)m=300m to overtake the other one.
Resultant velocity=(20-15)mps=5 mps
time it takes to travel 300m at a velocity of 5 mps is 60 sec..
Ans 60 sec.
ANSWER:A
Answer: A
Question: 3,6,13,26,33,66,?
Options:
A)70
B)71
C)72
D)73
E)74
Rationale: 3*2=6
6+7=13
13*2=26
26+7=33
33*2=66
so next will be
66+7=73
ANSWER:D
Answer: D
Question: An accurate clock shows 8 o'clock in the morning. Through how may degrees will the hour hand rotate when the clock shows 2 o'clock in the afternoon?
Options:
A)180°
B)154°
C)160°
D)170°
E)150°
Rationale: We know that angle traced by hour hand in 12 hrs = 360°
From 8 to 2, there are 6 hours.
Angle traced by the hour hand in 6 hours = 6×36012=180°
Answer is A.
Answer: A
Question: Find the slope of the line perpendicular to the line y = x - 7
Options:
A)1
B)2
C)-1
D)4
E)5
Rationale: Two lines are perpendicular if the product of their slopes is equal to -1. The slope of the given line is equal to 1. If m is the slope of the line perpendicular to the given line, then
m × 1 = -1
Solve for m
m = - 1
correct answer C) -1
Answer: C
Question: In one alloy there is 12% chromium while in another alloy it is 8%. 35 kg of the first alloy was melted together with 40 kg of the second one to form a third alloy. Find the percentage of chromium in the new alloy.
Options:
A)8.8%
B)9.75%
C)9.2%
D)8.6%
E)8.4%
Rationale: The amount of chromium in the new 35+45=80 kg alloy is 0.12*35+0.08*45=7.8 kg, so the percentage is 7.8/80*100=9.75%.
Answer: B.
Answer: B
Question: Look at this series: 55, 55, 40, 40, 25, 25, ... What number should come next?
Options:
A)14
B)15
C)17
D)10
E)11
Rationale: In this series, each number is repeated, then 15 is subtracted to arrive at the next number.
The next number should be 10
Answer : D
Answer: D
Question: In order to obtain an income of Rs. 1250 from 10% stock at Rs. 210, one must make an investment of
Options:
A)5363
B)26250
C)28678
D)29002
E)2732
Rationale: To obtain Rs. 10, investment
= Rs. 210.
To obtain Rs. 1250, investment =
= Rs. 26250.
Answer: B
Answer: B
Question: In a certain city each of 17 Girl Scout troops is represented by a colored flag. Each flag consists of either a single color or a pair of two different colors. If each troop has a different flag, what is the minimum number of colors needed for the flags. (Assume that the order of colors in a pair on a flag does not matter.)
Options:
A)5
B)10
C)6
D)20
E)40
Rationale: B.6:
if we have 5 colors we can choose pairs in 5C2 ways = 10 and single color flags are 5. Therefore total number of flags = 15. This is less than the number of girl scout groups.
if we have 6 colors we can choose pairs in 6C2 ways = 15 and single color flags are 6. Therefore total number of flags = 21.
ANS C.
Answer: C
Question: A tank can supply water to a village for 60 days. If a leak at the bottom of the tank drains out 10 liters per day, the supply lasts for 45 days only. For how many days will the supply last if the leak drains out 20 liters per day?
Options:
A)15
B)18
C)20
D)24
E)36
Rationale: Losing 10 liters per day results in a loss of 450 liters in 45 days. So, those 450 liters were for 15 days, making daily consumption of the village 30 liters per day. Thus the capacity of the tank is 30*60 = 1800 liters.
Losing 20 liters plus 30 liters gives 50 liters per day. At this rate the supply will last 1800/50 = 36 days.
The answer is E.
Answer: E
Question: Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 36 kmph. Of how many minutes does the train stop per hour?
Options:
A)11
B)8
C)12
D)99
E)17
Rationale: T = 9/45 * 60
= 12
Answer: C
Answer: C
Question: If the price of gold increases by 50%, find by how much the quantity of ornaments must be reduced, so that the expenditure may remain the same as before?
Options:
A)331/8%
B)331/3%
C)338/3%
D)391/3%
E)311/3%
Rationale: 100
150
------
150-------50
100-------? => 331/3%
Answer: B
Answer: B
Question: In a group of ducks and cows, the total number of legs are 48 more than twice the no. of heads. Find the total no.of buffaloes.
Options:
A)28
B)12
C)24
D)16
E)19
Rationale: Let the number of buffaloes be x and the number of ducks be y
=> 4x + 2y = 2 (x + y) + 48
=> 2x = 48 => x = 24
C
Answer: C
Question: 66 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be :
Options:
A)84 m
B)88 m
C)120 m
D)137 m
E)None
Rationale: Sol.
Let the length of the wire b h.
Radius = 1/2 mm = 1/20 cm. Then,
22/7 * 1/20 * 1/20 * h = 66 ⇔ = [66 * 20 * 20 * 7 / 22] = 8400cm = 84 m.
Answer A
Answer: A
Question: Calculate the effect changes in dimension of a rectangle will have on its area, if length is increased by 15% and its breadth is decreased by 10%?
Options:
A)3.5 percent increase
B)9.5 percent increase
C)1.5 percent increase
D)3.9 percent increase
E)3.5 percent increase
Rationale: let L and B be 100 each
100 * 100 = 10000
L increase by 15% = 115
B decrease by 10% = 90
115 * 90 = 10350
3.5 percent increase
ANSWER:E
Answer: E
Question: Which of the following is equal to 10^-(-2)^2?
Options:
A)1/(10^6)
B)1/(10^7)
C)1/(10^8)
D)1/(10^9)
E)1/(10^4)
Rationale: 10^-(-2)^2 => 10^-(-2^2) => 10^-(4) = 1/(10^4)
Answer : E
Answer: E
Question: A credit card number has 6 digits (between 1 to 9). The first two digits are 12 in that order, the third digit is bigger than 6, the forth is divisible by 4 and the fifth digit is 3 times the sixth. How many different credit card numbers exist?
Options:
A)27
B)36
C)72
D)18
E)422
Rationale: {1}{2}{greater than 6}{divisible by 4}{3x}{x}:
The third digit can take 3 values: 7, 8, or 9.
The fourth digit can take 2 values: 4, or 8.
The fifth and sixth digits can take 3 values: 31, 62, or 93.
Total = 3*2*3 = 18.
Answer: D.
Answer: D
Question: Karen places a bet with Tom that she will beat Tom in a car race by 4 miles even if Karen starts 4 minutes late. Assuming that Karen drives at an average speed of 60 mph and Tom drives at an average speed of 45 mph, how many H miles will Tom drive before Karen wins the bet?
Options:
A)15
B)18
C)21
D)24
E)27
Rationale: Let K and T be the speeds of Karen and Tom respectively.
t be the time that Karen will travel ----> t+4/60 will be the total time Tom will travel by the time the distance between Karen and Tom is 4 miles.
Thus, per the question , K(t) - T(t+4/60) = 4 ---> t = 7/15 hours
Thus the distance traveled by Tom when Karen is 4 miles ahead of him H: T*(t+4/60) = 45 (7/15+4/60) = 24 miles. D is the correct answer.
Answer: D
Question: Lucy invested $10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 5 percent during the second year, and decreased by 25 percent during the third year. What is the value of the account today?
Options:
A)$10,350
B)$8,662.50
C)$10,500
D)$11,500
E)$12,705
Rationale: Value after 1 year: 10,000 * 1.1 = 11,000
Value after 2 years: 11,000 * 1.05 = 11,550
Value today: 11,550 * 0.75 = 10,395
Answer B is correct.
Answer: B
Question: Markov bought shares for a total value of $1000. Next day, the price of shares is reduced by 10%. With the same $1000, he could now buy 10 more shares. Which of the following is closest to the original price per share?
Options:
A)$10
B)$11
C)$12
D)$13
E)$14
Rationale: From the given information,we can conclude that Markov bought x number of shares for $1000. With a 10% reduction in price, he could buy the same x number of shares for 1000*.90 = $900 . With the remaining money ($1000 - $900 = $100), he can buy 10 more shares. So, the reduced price per share = $100/10 = $10.
Therefore, if the reduced price of $10 equals the original price * 9/10, then the original price is approximately $11=B
Answer: B
Question: The first three terms of a proportion are 3, 9 and 12. The fourth term is?
Options:
A)33
B)20
C)28
D)36
E)11
Rationale: (9*12)/3 = 36
Answer: D
Answer: D
Question: Out of 15 consecutive numbers, 2 are chosen at random. The probability that they are both odds or both primes is?
Options:
A)1/8
B)1/7
C)1/0
D)1/6
E)1/1
Rationale: A leap year has 52 weeks and two days
Total number of cases = 7
Number of favourable cases = 1
i.e., {Saturday, Sunday}
Required Probability = 1/7
Answer: B
Answer: B
Question: Five boys picked up 30 mangoes .In how many ways can they divide them if all mangoes be identical?
Options:
A)A)5^30
B)B)2^30
C)C)1^30
D)D)3^30
E)E)6^30
Rationale: Each Mango can be given to any one of the five people or in other words..1 mango can be divided into 5 ways...so all 30 can be divided in 5^30 ways
ANS:A
Answer: A
Question: The value of x + x(xx) when x = 2 is:
Options:
A)8
B)10
C)12
D)14
E)16
Rationale: x + x(xx)
Put the value of x = 2 in the above expression we get,
2 + 2(22)
= 2 + 2(2 × 2)
= 2 + 2(4)
= 2 + 8
= 10
ANSWER : (B) +10
Answer: B
Question: It takes Jim three hours to wash the gym and it takes Julia two hours to wash the gym. Working together, how many minutes will it take them to wash the gym?
Options:
A)70
B)72
C)74
D)76
E)78
Rationale: Jim can wash (1/3) of the gym per hour.
Julia can wash (1/2) gym per hour.
Together they can wash 1/3+1/2=5/6 of the gym per hour.
1 gym / (5/6) of the gym per hour = 6/5 hours = 72 minutes.
The answer is B.
Answer: B
Question: If a card is drawn from a well shuffled pack of cards, the probability of drawing a spade or a king is
Options:
A)4/15
B)4/18
C)4/16
D)4/13
E)4/11
Rationale: P(SᴜK) = P(S) + P(K) - P(S∩K), where S denotes spade and K denotes king.
P(SᴜK) = 13/52 + 4/52 - 1/52
= 4/13
Answer: D
Answer: D
Question: Three 6 faced dice are thrown together. The probability that all the three show the same number on them is ?
Options:
A)1/39
B)1/36
C)1/35
D)1/34
E)1/32
Rationale: It all 3 numbers have to be same basically we want triplets. 111, 222, 333, 444, 555 and 666. Those are six in number. Further the three dice can fall in 6 * 6 * 6 = 216 ways.
Hence the probability is 6/216
= 1/36
Answer: B
Answer: B
Question: Elvin's monthly telephone bill is the sum of the charge for the calls he made during the month and a fixed monthly charge for Internet service. Elvin's total telephone bill for January was $52 and Elvin's total telephone bill for February was 76$. If Elvin's charge for the calls he made in February was twice the charge for the calls he made in January, what is Elvin's fixed monthly charge for Internet service?
Options:
A)$5
B)$10
C)$14
D)$28
E)$29
Rationale: Bill = Fixed Charge + Charge of Calls made
in Jan, Bill = Fixed Charge(Let, y) + Charge of calls made in Jan (Let, x) = $52
in Feb, Bill = Fixed Charge (Let, y) + Charge of calls made in Feb (Then, 2x) = $76
i.e. x+y = 52
and 2x+y = 76
Take the difference if two equations
i.e. (2x+y) - (x+y) = 76 - 52
i.e. x = 24
i.e. Fixed Monthly Charge, y = 28
Answer: Option
D
Answer: D
Question: If a sum of money doubles itself in 10 years at simple interest, the ratepercent per annum is
Options:
A)10
B)12.5
C)13
D)13.5
E)14
Rationale: Explanation:
Let sum = x then Simple Interest = x
Rate = (100 * x) / (x * 10) = 10
Option A
Answer: A
Question: A rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m?
Options:
A)3909
B)3907
C)3905
D)3900
E)3901
Rationale: Area = (l + b – d) d
(80 + 60 – 10)10 => 1300 m2
1300 * 3 = Rs.3900
25. The length of a rectangl.Answer:D
Answer: D
Question: What is the perimeter of a square with area 4p^2/9 ?
Options:
A)8p/3
B)3p^2/4
C)3p
D)3p^2
E)4p/3
Rationale: Area of square, (side)^2 = (2p/3)^2
Therefore side of the square = 2p/3
Perimeter of square = 4*side = 4* (2p/3) = 8p/3
Answer is A.
Answer: A
Question: For what value(s) of n is the following equation satisfied: 2n-6-n = 5n+6-4n
Options:
A)a. -5
B)b. 0 only
C)c. 5/2 only
D)d. No value
E)e. Any value
Rationale: 2n-6-n = 5n+6-4n
n - 6 = n + 6
-6 = 6, which is false.
So, no n satisfies given equation.
Answer: D.
Answer: D
Question: Ages of two persons differ by 4 years. If 3 years ago, the elder one was 3 times as old the younger one, find their present age
Options:
A)5,9
B)14,18
C)16,20
D)18,22
E)19,23
Rationale: Explanation:
Let the age of the younger person be x,
Then the elder person's age is (x+4)
=> 3(x-3) = (x+4-3) [3 years before]
=> 3x-9 = x+1
=> x = 5.
So the elder person's age is x + 4 = 9
Answer: Option A
Answer: A
Question: If the Average of 10 consecutive integers is 19.5 then the 10th integer is :-
Options:
A)15
B)20
C)23
D)24
E)25
Rationale: The average falls between the 5th and 6th integers,
integer 5 = 19, integer 6 = 20.
Counting up to the tenth integer
we get 24.
ANSWER:D
Answer: D
Question: Together, 15 type A machines and 7 type B machines can complete a certain job in 4 hours. Together 8 type B machines and 15 type C machines can complete the same job in 11 hours. How many W hours would it take one type A machine, one type B machine, and one type C machine working together to complete the job (assuming constant rates for each machine)?
Options:
A) 22 hours
B) 30 hours
C) 44 hours
D) 60 hours
E) It cannot be determined from the information above.
Rationale: Say the rates of machines A, B and C are a, b, and c, respectively.
Together 15 type A machines and 7 type B machines can complete a certain job in 4 hours --> 15a + 7b = 1/4;
Together 8 type B machines and 15 type C machines can complete the same job in 11 hours --> 8b + 15c = 1/11.
Sum the above: 15a + 15b + 15c = 1/4 + 1/11 = 15/44 --> reduce by 15: a + b + c = 1/44 --> so, the combined rate of the three machines is 1/44 job/hour --> time is reciprocal of the rate, thus machines A, B and C can do the job W in 44 hours.
Answer: C.
Answer: C
Question: Evaluate: 40 - 12*3*2 = ?
Options:
A)62
B)52
C)32
D)12
E)22
Rationale: According to order of operations, 12?3?2 (division and multiplication) is done first from left to right
12**2 = 4* 2 = 8
Hence
40 - 12*3*2 = 40 - 8 = 32
correct answer C
Answer: C
Question: The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?
Options:
A)140 sq.units
B)556 sq.units
C)155 sq.units
D)146 sq.units
E)142 sq.units
Rationale: Given that the area of the square = 1225 sq.units
=> Side of square = √1225 = 35 units
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 = 14 * 10 = 140 sq.units
Answer:A
Answer: A
Question: The compound interest earned by Sunil on a certain amount at the end of two years at the rate of 8% p.a. was Rs.2828.80. Find the total amount that Sunil got back at the end of two years in the form of principal plus interest earned.
Options:
A)19828.89
B)19828.8
C)19828.37
D)19828.82
E)19828.87
Rationale: Let the sum be Rs.P
P{ [ 1 + 8/100]2 - 1 } = 2828.80
P(8/100)(2 + 8/100) = 2828.80 [a2 - b2
= (a - b) ( a + b)] P = 2828.80 / (0.08)(2.08)
= 1360/0.08 = 17000 Principal + Interest
= Rs.19828.80
Answer: B
Answer: B
Question: The average age of three boys is 12 years and their ages are in proportion 4:5:9. What is the age in years of the youngest boy?
Options:
A)6
B)9
C)8
D)4
E)2
Rationale: 4x + 5x + 9x = 36
x =2
4x = 8
Answer: C
Answer: C
Question: If f(a)=a^2 and a is a positive integer, which of the following CANNOT be the value of f(f(a))?
Options:
A)256
B)16
C)81
D)1
E)165
Rationale: f(a)=a^2
f(f(a)) = (a^2)^2 = a^4
Therefore f(f(a)) will be numbers that are 4th power of other numbers.
Checking the options:
1 = 1^$
16 = 2^4
81 = 3^4
165. This cannot be written as the 4th power of any number
256 = 4^4
Answer: E
Answer: E
Question: How many times in a day, the hands of a clock are straight?
Options:
A)22
B)24
C)44
D)48
E)46
Rationale: In 12 hours, the hands coincide or are in opposite direction 22 times.
In 24 hours, the hands coincide or are in opposite direction 44 times a day.
ANSWER:C
Answer: C
Question: The moon revolves around the earth at a speed of approximately 1.03 kilometers per second. This approximate speed is how many kilometers per hour?
Options:
A)60
B)61.2
C)62.5
D)3,708
E)3,672
Rationale: moon revolves around the earth at a speed of 1.02kilometers per second.
one hour equal to 60 minutes.
one minute equals to 60 seconds. so one hour equals to 3600seconds.
so one hour, speed= 1.03*3600=3708kilometers per hour.
Option D is correct
Answer: D
Question: The slant height of a cone is 12 cm and radius of the base is 4cm, find the curved surface of the cone.
Options:
A)48 pi cm2
B)30 pi cm2
C)35 pi cm2
D)40 pi cm2
E)45 pi cm2
Rationale: Ï€ * 12 * 4 = 48
ANSWER A
Answer: A
Question: A survey of employers found that during 1993 employment costs rose 3.5 percent, where employment costs consist of salary costs and fringe-benefit costs. If salary costs rose 3 percent and fringe-benefit costs rose 9.5 percent during 1993, then fringe-benefit costs represented what percent of employment costs at the beginning of 1993 ?
Options:
A) 16.5%
B) 8%
C) 35%
D) 55%
E) 65%
Rationale: The amount by which employment costs rose is equal to 0.035(salary costs + fringe benefit costs);
On the other hand the amount by which employment costs rose is equal to 0.03*salary costs + 0.095*fringe benefit costs;
So, 35(S+F) = 30S+95F --> S = F --> F/S = 1/12 --> F/(S+F) = 1/(1+12) = 1/13 = 0.08.
Answer: B.
Answer: B
Question: When positive integer N is divided by positive integer P, the quotient is 18, with a remainder of 7. When N is divided by (P + 2), the quotient is 15 and the remainder is 1. What is the value of N?
Options:
A)151
B)331
C)511
D)691
E)871
Rationale: Use the rule dividend = (integer quotient)*(divisor) + remainder to translate each sentence.
The first sentence becomes N = 18P + 7. The second equation becomes N = (P + 2)*15 + 1, which simplifies to N = 15P + 31. These are ordinary simultaneous equations Since they both equal N already, let’s set them equal and solve for P.
18P + 7 = 15P + 31
3P + 7 = 31
3P = 24
P = 8
Now that we know P = 8, we can just plug in. The product 15*8 is particularly easy to do, without a calculator, by using the “doubling and halving” trick. Double 15 to get 30, and take half of 8 to get 4 —- 15*8 = 30*4 = 120. So
N = 15(8) + 31 = 120 + 31 = 151
N = 151, answer = A.
Answer: A
Question: If P represents the product of the first 18 positive integers, then P is NOT a multiple of
Options:
A)99
B)84
C)72
D)65
E)95
Rationale: Answer is E.
Since prime factor of 95 is 5x19. 19 is a prime number and not part of the first 18 positive integers.
A) 9 x 11
B) 12 x 7
C) 12 x 6
D) 13 x 5
E) 3 x 19
Answer: E
Question: how many zeros are there in 50!
Options:
A)10
B)11
C)12
D)13
E)14
Rationale: To find the number of trailing zeroes in 50! factorial we must find the number of integral values in :
50/5 + 50/5^2 + 50/5^3 +.........
= 10+2+0+0....
=12
ANSWER:C
Answer: C
Question: There are two numbers. If 40% of the first number is added to the second number, then the second number increases to its five-fourth. Find the ratio of the first number to the second number?
Options:
A)8 : 25
B)25 : 8
C)8 : 5
D)5 : 8
E)None of these
Rationale: Let the two numbers be x and y.
40/100 * x + y = 5/4y
=> 2/5 x = 1/4 y => x/y = 5/8
ANSWER:D
Answer: D
Question: In 1995 a certain store had 1800 tools in stock that had been purchased for $30 each. If 1,000 of these tools were sold in 1995 for $50 each and the remaining 800 were sold in 1996 for $70 each, how many greater was the gross profit on the tools sold in 1996 than the gross profit on those sold in 1995?
Options:
A)$12,000
B)$6,000
C)$8,000
D)$32,000
E)$40,000
Rationale: The keyword here isGross Profit:
Gross Profit = (Selling Price - Original Price)*(# of Items Sold)
So lets figure out what the Gross Profit for 1995:
GP1995 = (50-30)*(1000) = 20000
And the Gross Profit for 1996:
GP1996 = (70-30)*(800) = 32000
So the difference would be:
32000-20000 = 12000
ANSWER: A 12000
Answer: A