divelab/Sys2Bench huggingface dataset:
Question: When ticket sales began, Pat was the nth customer in line for a ticket, and customers purchased their tickets at the rate of y customers per minute. Of the following, which best approximates the time, in minutes, that Pat had to wait in line from the moment ticket sales began?
Options:
A)(n - 1) y
B)n + y –1
C)(n-1)/y
D)y/(n-1)
E)n/(y-1)
Rationale: C. (n - 1) / y
Answer: C
Question: If D is the product of all positive integers less than 31, than what is the greatest integer k for which D/18^k is an integer?
Options:
A)3
B)6
C)7
D)14
E)26
Rationale: 30! D must be divisible by (3*3*2)^k.
As I will find a lot of 2's among 30!'s factors I will focus on the 3's (that also occurs twice instead of only once as a factor in 18).
Every multiple of 3 will provide me with atleast one factor of 3. There aren't that many so I list them quickly.
3 6 9*
12 15 18*
21 24 27**
30
The stars are marked as they are multiples of 9* or 27** and thus provides two or three 3's respectively.
3=3 (occurs 10 times) +10
3*3=9 (occurs 3 times) +3(adding just one additional three each as they were not counted for in the multiples of 3)
3*3*3=27 (occurs 1 time) +1 (again, adding just one as they were previously not counted)
Total: 14.
For every k we add two 3's. So we must divide 14 by 2 to get the highest integer K before we receive a non-integer result.
Answer: 7 -> Answer choice: C.
Answer: C
Question: What is the sum of the greatest common factor and the lowest common multiple of 45 and 125?
Options:
A)1920
B)2201
C)3240
D)1130
E)3840
Rationale: Prime factorization of the given numbers
45= 3^2
125= 5^3
Greatest common factor =5
Lowest common multiple = 3^2*5^2 *5 =1125
Sum = 5+ 1125 = 1130
Answer D
Answer: D
Question: Two concentric circles form a ring. The inner and outer circumference of the ring are 352/7 m and 528/7m respectively.Find the width of the ring.
Options:
A)2
B)4
C)5
D)6
E)78
Rationale: Explanation:
let the inner and outer radii be r and R meters
then, \inline {\color{Black}2\prod r} = 352/7
=> r = (352/7) * (7/22) * (1/2) = 8m
\inline {\color{Black}2\prod R} = 528/7
=> R= (528/7) * (7/22) * (1/2)= 12m
width of the ring = R-r = 12-8 = 4m
Answer: B) 4
Answer: B
Question: Length of a rectangular plot is 20 mtr more than its breadth. If the cost of fencin gthe plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr?
Options:
A)30 m
B)60 m
C)65 m
D)70 m
E)90 m
Rationale: Let breadth = x metres.
Then, length = (x + 20) metres.
Perimeter = 5300 m = 200 m.
26.50
2[(x + 20) + x] = 200
2x + 20 = 100
2x = 80
x = 40.
Hence, length = x + 20 = 60 m
B
Answer: B
Question: The present ages of A,B and C are in proportions 4:7:9. Eight years ago, the sum of their ages was 56. What are their present ages (in years)?
Options:
A)20, 25 and 35
B)21, 18 and 36
C)18, 21 and 34
D)12, 14 and 18
E)16, 28 and 36
Rationale: Sum of their present ages =56+3×8=80
Present age of A =80×420=16
Present age of B =80×720=28
Present age of C =80×920=36
Answer is E.
Answer: E
Question: If n is the smallest positive integer for which 2^n is a factor of 10!, then n =?
Options:
A)2
B)4
C)6
D)8
E)10
Rationale: 10! = 3628800
A. 2^2 = 4 (3628800/4) - this is a factor of 10!
A is answer
Answer: A
Question: A company has 540 employees, 40% of whom are employed part time. If it hires 30 new employees, 20% of whom are employed part time, what will be the percent increase in part time employees?
Options:
A)2 7/9 %
B)2 2/3 %
C)4 %
D)4 1/6 %
E)9 %
Rationale: Total employee = 540
Part time Empl = 540 * 40/100 =216
New part time empl = 30 * (20/100)
= 6
Total new part time Emp = 6+216= 222
Old part time Emp = 216
% increase = (new - old)*100/old
=6*100/216
= 2.777%
Ans-A
Answer: A
Question: Convert the 13/48 m/s into kilometers per hour?
Options:
A)1.5 kmph.
B)0.91 kmph.
C)1.2 kmph.
D)1.5 kmph.
E)0.98 kmph.
Rationale: 13/48 m/s = 13/48 * 18/5 = 49/50 = 0.98 kmph.
ANSWER:E
Answer: E
Question: A train 150 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?
Options:
A)13 km/hr
B)59 km/hr
C)17 km/hr
D)18 km/hr
E)12 km/hr
Rationale: Speed of the train relative to man = (150/10) m/sec
= (15) m/sec. [15) * (18/5)] km/hr
= 54 km/hr. Let the speed of the train be x km/hr. Then, relative speed
= (x - 5) km/hr. x - 5 = 54 ==> x
= 59 km/hr.
Answer:B
Answer: B
Question: Jimâ€™s Taxi Service charges an initial fee of $2.35 at the beginning of a trip and an additional charge of $0.35 for each 2/5 of a mile traveled. What is the total charge for a trip of 3.6 miles?
Options:
A)$3.15
B)$4.45
C)$4.80
D)$5.50
E)$5.40
Rationale: Let the fixed charge of Jimâ€™s Taxi Service = 2.35 $
and charge per 2/5 mile(.4 mile) = .35$
Total charge for a trip of 3.6 miles = 2.35 + (3.6/.4) * .35
= 2.35 + 9*.35
= 5.5 $
Answer D
Answer: D
Question: The average salary of workers in an industry is Rs.200 the average salary of technicians being Rs.400 and that of non-technicians being Rs.125. What is the total number of workers?
Options:
A)277
B)665
C)662
D)552
E)281
Rationale: 8 * 84 = 672 – 7 = 665
Answer:B
Answer: B
Question: The first three terms of a proportion are 5, 15 and 20. The fourth term is?
Options:
A)60
B)65
C)89
D)78
E)88
Rationale: (15*20)/5= 60
Answer:A
Answer: A
Question: A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 44 hrs and a machine of type S does the same job in 20 hours. If the company used the same number of each type of machine to do the job in 4 hours, how many machines of type R were used?
Options:
A)56/21
B)59/16
C)44/21
D)55/16
E)12/59
Rationale: Rate of machine R =1/44
Rate of machine S =1/20
since same no of machines used for R and S to do the same work in 4 hrs
So collective rate needed to finish the work in 4 hrs= 1/4
Let the no of machine be x
So, x/44 +x/20 =1/4
(5x+11x)/220=1/4
16x=55
x=55/16
So no of machine R is 55/16
Answer D
Answer: D
Question: If the remainder is 7 when positive integer n is divided by 10, what is the remainder when n is divided by 5?
Options:
A)0
B)1
C)2
D)3
E)2
Rationale: Assume x is quotient here,
n=10x+7 ----------(1)
and n=5x+ ?
We can also write equation (1) as:
n=(10x+5)+2.
ie 5(2x+1)+1 ie the first term is perfectly divisible by 5.
So,the remainder left is 2
So,answer (E) is right choice.
Answer: E
Question: If Leo gains 10 pounds, he will weigh 50% more than his sister Kendra. Currently their combined weight is 180 pounds. What is Leo's current weight?
Options:
A)80
B)86
C)92
D)98
E)104
Rationale: L+K = 180 and so K = 180-L
L+10 = 1.5K = 1.5(180-L)
2.5L = 260
L = 104
The answer is E.
Answer: E
Question: If a boy travels with 5/6th of usual his speed,he is late by 10 mins.What is the usual time taken to travel?
Options:
A)44min
B)46min
C)48min
D)50min
E)52min
Rationale: speed=5/6*x
time=6/5t becz speed inversely proportional to time
6t/5-t=10
t=50min
ANSWER:D
Answer: D
Question: Sum of the squares of 3 no. is 138 and the sum of their products taken two at a time is 131. Find the sum?
Options:
A)20
B)21
C)25
D)26
E)27
Rationale: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 138 + 2* 131
a + b + c = √400 = 20
A
Answer: A
Question: A trader marked the price of his commodity so as to include a profit of 25%. He allowed discount of 16% on the marked price. His actual profit was :
Options:
A)4
B)5
C)10
D)12
E)None
Rationale: Sol.
Let C.P. be Rs. 100. Then, marked price = Rs. 125.
S.P. = 84% of Rs. 125 = Rs. [84 /100 * 125] = Rs. 105.
∴ Profit% = (105 - 100)% = 5%.
Answer B
Answer: B
Question: In a store, the total price for 20 shirts is $360 and the total price for 45 sweaters is $900. By how much does the average (arithmetic mean) price of a sweater exceed that of a shirt in this store?
Options:
A)$1
B)$2
C)$3
D)$4
E)$5
Rationale: The average price of a shirt is: $360 / 20 = $18.
The average price of a sweater is: $900 / 45 = $20.
The difference in price is: $20 - $18 = $2.
The answer is B.
Answer: B
Question: In a business school case competition, the top three teams receive cash prizes of $5,000, $3,000, and $2,000, respectively, while the remaining teams are not ranked and do not receive any prizes. There are 6 participating teams, named Team A, Team B, Team C, Team D, Team E, and Team F. If Team A wins one of the prizes, Team B will also win one of the prizes. How many outcomes Q of the competition are possible?
Options:
A)18
B)20
C)54
D)84
E)120
Rationale: the ways the three teams can be selected is..
i) A is selected, B is also selected, third can be any of the remaining 4.. so total ways 4.. they can be arranged in 4*3!=24 ways..
ii) A is not selected. threee teams can be selected from remaining 5 so total arrangements =5C3*3!=60
total Q=84 outcomes
D
Answer: D
Question: P can do a work in the same time in which Q and R together can do it. If P and Q work together, the work can be completed in 10 days. R alone needs 20 days to complete the same work. then Q alone can do it in
Options:
A)20
B)22
C)25
D)27
E)40
Rationale: Work done by P and Q in 1 day = 1/10
Work done by R in 1 day = 1/20
Work done by P, Q and R in 1 day = 1/10 + 1/20 = 3/20
But Work done by P in 1 day = Work done by Q and R in 1 day . Hence the above equation can be written as Work done by P in 1 day Ã— 2 = 3/20
=> Work done by P in 1 day = 3/40
=> Work done by Q and R in 1 day = 3/40
Hence work done by Q in 1 day = 3/40 â€“ 1/20 = 1/40
So Q alone can do the work in 40 days
Answer is E.
Answer: E
Question: January 1, 2008 is Tuesday. What day of the week lies on Jan 1, 2009?
Options:
A)sunday
B)friday
C)monday
D)wednesday
E)thursday
Rationale: The year 2008 is a leap year. So, it has 2 odd days.
1st day of the year 2008 is Tuesday (Given)
So, 1st day of the year 2009 is 2 days beyond Tuesday.
Hence, it will be Thursday.
Answer: E) thursday
Answer: E
Question: The profit earned by selling an article for Rs. 832 is equal to the loss incurred when the same article is sold for Rs. 448. What should be the sale price for making 50% profit?
Options:
A)277
B)960
C)277
D)266
E)121
Rationale: Let C.P. = Rs. x.
Then, 832 - x = x - 448
2x = 1280 => x = 640
Required S.P. = 150% of Rs. 640 = 150/100 * 640 = Rs. 960.
Answer: B
Answer: B
Question: Find the odd man out.
1, 5, 2, 3, 6, 11, 13
Options:
A)6
B)5
C)1
D)13
E)11
Rationale: Explanation:
Each of the numbers except 6 is a prime number.
Answer: A) 6
Answer: A
Question: If 45% of a number is 36, then the number is
Options:
A)number is 60
B)number is 70
C)number is 90
D)number is 80
E)None of these
Rationale: Solution:
Let "a" be the number we seek. We get
45% × a = 36
2 × 45% × a = 2 × 36 = 72
90% × a = 72
10% × a = 72 : 9 = 8
100% × a = 8 × 10 = 80
a = 80
Answer D
Answer: D
Question: A special municipal payroll tax charges not tax on a payroll less than $200,000 and only 0.2% on a company’s payroll above $200,000. If Belfried Industries paid $400 in this special municipal payroll tax, then they must have had a payroll of
Options:
A)$180,000
B)$400,000
C)$220,000
D)$402,000
E)$2,200,000
Rationale: ANSWER : B , ( with different approach) :
The 400 paid is 0.2% of the additional amount above 200,000. Let it be X
Now 0.2% of X = 400
Therefore X= 200,000
Total = 200,000 + X= 400,000
Answer: B
Question: If a * b = 2a – 3b + ab, then 5 * 7 + 7 * 5 is equal to:
Options:
A)34
B)18
C)72
D)78
E)82
Rationale: 5 * 7 + 7 * 5 = (2 * 5 – 5 * 7 + 5* 7) + (2 * 7 – 5 * 5 + 7 * 5)
= (10 + 14 – 25 + 35) = 34.
ANSWER:A
Answer: A
Question: The average monthly salary of 24 employees in an organisation is Rs. 1500. If the manager's salary is added, then the average salary increases by Rs. 400. What is the manager's monthly salary ?
Options:
A)Rs. 11,300
B)Rs. 11,500
C)Rs. 11,302
D)Rs. 11,301
E)Rs. 11,303
Rationale: Explanation:
Manager's monthly salary
= Rs. (1900 x 25 - 1500 x 24) = Rs. 11,500
Answer:B
Answer: B
Question: How many four letter words are formed using the letters of the word PROBLEM?
Options:
A)760
B)800
C)840
D)880
E)920
Rationale: The number of letters in the given word is seven.
The number of four letter words that can be formed using these seven letters is 7P4
= 7 * 6 * 5 * 4 = 840.
Answer: C
Answer: C
Question: A batsman scored 120 runs whichincluded 3 boundaries and 8sixes. What % of his total score did he make by running between the wickets
Options:
A)40%
B)50%
C)55%
D)65%
E)70%
Rationale: Number of runs made by running = 110 - (3 x 4 + 8 x 6)
= 120 - (60)
= 60
Now, we need to calculate 60 is what percent of 120.
=> 60/120 * 100 = 50%
B
Answer: B
Question: A began business with 12500 and is joined afterwards by B with 50000. When did B join, if the profits at the end of the year are divided equally?
Options:
A)3 months
B)9 months
C)10 months
D)7 months
E)None of these
Rationale: Let B join after x months of the start of the business so that B’s money is invested for (12 – x) months.
∴ Profit ratio is 12 × 12500 : (12 – x) × 50000
or 12 : 4(12 – x)
Since profit is equally divided so
12 = 4(12 – x) or x = 3. Thus B joined after 8 months.
Answer A
Answer: A
Question: Working together, Wayne and his son can shovel the entire driveway in three hours. If Wayne can shovel eight times as fast as his son can, how many hours would it take for his son to shovel the entire driveway on his own?
Options:
A)4
B)6
C)8
D)9
E)12
Rationale: W: the time for Wyane to do the job
S: the time for his son to do the job
We have 1/W + 1/S = 1/8 and W = 8S
Then we have 1/(8*S) + 1/S = 1/8 <=> 9/(8*S) = 1/8 <=> S = 9
ANS: D
Answer: D
Question: a, b are positive integers. The remainder of a to be divided by 8 is 5 and the remainder of b to be divided by 6 is 2.
Which is possible to be the remainder of a*b to be divided by 48
Options:
A)a) 10
B)b) 6
C)c) 8
D)d) 12
E)e) 20
Rationale: Two ways to do it...
a=8x+5..
b=6y+2..
1) convenient way..
Take x and y as 0, and you will get a*b as 5*2=10
Answer : A
Answer: A
Question: A and B complete a work in 8 days. A alone can do it in 14 days. If both together can do the work in how many days?
Options:
A)5 days
B)8 days
C)6 days
D)3.15 days
E)2.75 days
Rationale: 1/8 + 1/14 = 11/56
56/11 = 5 days
Answer: A
Answer: A
Question: Here the sum of the series is 4+8+12+16+….. =612. find how many terms are there in the series?
Options:
A)15
B)19
C)17
D)14
E)13
Rationale: Solution: This is an A.P. in which a=4, d=4 and Sn=612
Then, n/2[2a+(n-1)d]=612 => n/2[2*4+(n-1)*4]=612
=> 4n/2(n+1)=612
=> n(n+1)=306
=> n^2+n-306=0
=> n^2+18n-17n-306=0
=> n(n+18)-17(n+18)=0
=> (n+18)(n-17)=0
=> n=17.
Number of terms=17.
Answer C
Answer: C
Question: If a man crosses a 600 m long street in 5 minutes. What is his speed?
Options:
A)7 km/hr
B)7.1 km/hr
C)7.2 km/hr
D)8 km/hr
E)9.2 km/hr
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
C
Answer: C
Question: P beats Q by 125 meter in a kilometer race. Find Q's speed if P's speed is 40 meter/sec.
Options:
A)21 meter/sec
B)7 meter/sec
C)14 meter/sec
D)18 meter/sec
E)35 meter/sec
Rationale: P's speed =40 m/s
P's distance = 1000m (as it is a km race)
t = 1000/16 =25 sec
Q's distance = 1000-125= 875m
Q's time to complete this distance is also 62.5 sec.
Q's speed = dist/time = 875/25 = 35 m/s
Hence E is the answer.
Answer: E
Question: I have two 10 paise coins. If 4 If 4/5 of what I have is 8is 8/9 of what you have, how much do you have?
Options:
A)13
B)17
C)11
D)18
E)11
Rationale: D
18 paise.
Answer: D
Question: The amount of electrical current that flows through a wire is inversely proportional to the resistance in that wire. A wire originally carries 4 amperes of electrical current. Then the resistance is reduced to one-seventh of its original value. How many amperes of electrical current will flow through the wire?
Options:
A)4/7
B)7
C)14
D)28
E)35
Rationale: Given that, I∝1/R, I*R is a constant value.
I1*R1 = I2*R2
I1*R1 = I2*R1/7
I2 = 7*I1 = 28 amperes
The answer is D.
Answer: D
Question: A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 12, the how old is B?
Options:
A)10 years
B)4 years
C)6 years
D)15 years
E)16 years
Rationale: Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years.
(2x + 2) + 2x + x = 12
5x = 10
x = 2.
Hence, B's age = 2x = 4 years.
B)
Answer: B
Question: In how many different ways can the letters of the word "LEADING" be arranged in such a way that the vowels always come together.
Options:
A)W8
B)789
C)279
D)277
E)191
Rationale: Answer:D
Answer: D
Question: A car salesman earns a base salary of $800 per month plus a commission of $200 for each car he sells. If the car salesman earned $1600 in May, how many cars does he need to sell in June in order to double his May earnings?
Options:
A)10
B)11
C)12
D)13
E)14
Rationale: 800+200x=3200
x=12 cars.
The answer is C.
Answer: C
Question: A dishonest dealer professes to sell his goods at Cost Price but still gets 20% profit by using a false weight. What weight does he substitute for a kilogram?
Options:
A)833 1/0
B)833 1/3
C)833 1/21
D)833 1/2
E)833 1/3
Rationale: If the cost price is Rs.100, then to get a profit of 20%, the selling price should be Rs.120.
If 120kg are to be sold, and the dealer gives only 100kg, to get a profit of 20%.
How many grams he has to give instead of one kilogram(1000 gm).
120 gm ------ 100 gm
1000 gm ------ ?
(1000 * 100)/120 = 2500/3 = 833 1/3 grams.
Answer: B
Answer: B
Question: In an election between two candidates, 10% of votes are were declares invalid. First candidate got 9000 votes which were 60% of the total valid votes . The total number of votes enrolled in that election was:
Options:
A)9000
B)98000
C)50000
D)11000
E)12000
Rationale: 100 % - 10 % = 90 %
54%-36%=18%
18% ------> 9000 ( 18 × 500 = 9000)
100% -------> 50000 votes (100 × 500 = 50000)
C
Answer: C
Question: Reeya obtained 40, 60, 70, 80 and 80 out of 100 in different subjects, What will be the average
Options:
A)66
B)75
C)80
D)85
E)90
Rationale: Explanation:
(40+60+70+80+80 / 5)=66
Option A
Answer: A
Question: Convert 0.38 in to a vulgar fraction ?
Options:
A)18/50
B)16/50
C)17/50
D)19/50
E)None
Rationale: Answer
0.38 = 38/100 = 19/50
Correct Option: D
Answer: D
Question: A worker is paid x rupees for painting every 25 metres of a wall and y rupees for painting every extra metre. During one week, he painted 25 metres on Monday, 50 metres on Tuesday, 25 metres on Wednesday, 45 metres on Thursday and 25 metres on Friday. What is his average daily earning rupees for the five day week?
Options:
A)x + (8/5)y
B)(5x + 9y)/5
C)x + 9y
D)None of these
E)Cannot be determined
Rationale: Explanation :
On Monday, the payment = Rs x
On Tuesday, the payment = Rs (x + 25y)
On Wednesday, the payment = Rs x
On Thursday, the payment = Rs (x +20y)
On Friday, the payment = Rs x
Average daily earning during the five-day week = (5x + 45y)/5
= x + 9y
Answer : C
Answer: C
Question: A brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 25 m * 2 m * 0.75 m?
Options:
A)24000
B)23000
C)22000
D)25000
E)26000
Rationale: 25 * 2 * 0.75 = 20/100 * 10/100 * 7.5/100 * x
25 = 1/100 * x => x = 25000
ANSWER:D
Answer: D
Question: If there are 200 questions in a 3 hr examination. Among these questions are 20 type A problems, which requires twice as much as time be spent than the rest of the type B problems. How many minutes should be spent on type A problems?
Options:
A)72 min
B)62 min
C)70 min
D)32.72727 min
E)76 min
Rationale: x=time for type B prolems
2x=time for type A problem
total time=3hrs=180min
180x+20*2x=180
x=180/220
x=0.818182
time taken for type A problem=20*2*0.818182=32.72727min
ANSWER:D
Answer: D
Question: A runs twice as fast as B and gives B a start of 42m.How long should the racecourse be so that A and B might reach in the same time?
Options:
A)75 m.
B)80 m.
C)84 m.
D)100 m.
E)None of the above
Rationale: ratio of speeds of a and b is 2:1
b is 42m away from a but we know that a covers 1 meter(2-1) more in every second than b
the time taken for a to cover 42m is 42/1=42m
so the total time taken by a and b to reach =2*42=84m
ANSWER:C
Answer: C
Question: The speed of a boat in still water in 22 km/hr and the rate of current is 5 km/hr. The distance travelled downstream in 24 minutes is:
Options:
A)10.6
B)10.2
C)10.8
D)10.4
E)10.0
Rationale: Speed downstream = (22 + 5) = 27 kmph
Time = 24 minutes =24/60 hour = 2/5 hour
Distance travelled = Time × speed =2/5×27 = 10.8 km
Answer is C.
Answer: C
Question: A car that has an original value of $52,500 depricates $10000 in the first year and there original cost per year. What is its value after 8 years?
Options:
A)$12100
B)$13100
C)$14100
D)$15100
E)$16100
Rationale: 1st year depreciation amount = 10000
next 7 year's depreciation amount = 7 * 8% original cost price
= 7*8/100 * 52500
=29400
Total depreciation amount = 39400
Value after 8 years = $13100
ANSWER:B
Answer: B
Question: Which of the following is an integer?
I. 13! / 6!
II. 13! / 8!
III. 13! / 7!5!
Options:
A)I only
B)II only
C)III only
D)I and II only
E)I, II and III
Rationale: 13!/6! = 13*12*11*10*9*8*7 which is an integer.
13!/8! = 13*12*11*10*9 which is an integer.
13!/7!5! = 13*12*11*10*9*8 / 5*4*3*2 = 13*12*11*3*2 which is an integer.
The answer is E.
Answer: E
Question: If a computer program generates three-digit odd numbers using the numbers 9, 7, 0, 6, and 1, and the digits can be repeated, what is the probability that the number formed from the program is a multiple of three?
Options:
A)1/3
B)1/4
C)1/5
D)1/6
E)1/7
Rationale: A
Answer: A
Question: Last year the range of the annual sales of the 100 lamps at Company X was $30,000. If the annual sale of each of the 100 lamps this year is 10 percent greater than it was last year, what is the range of the annual sales of the 100 lamps this year?
Options:
A) $27,000
B) $30,000
C) $33,000
D) $36,000
E) $63,000
Rationale: let the lowest sale be x.
Therefore, highest sale is x +30000.
Now sale of each lamp is increased by 10%.
Therefore the sale will remain arranged in the same order as before.
or Lowest sale = 1.1x and Highest = 1.1 * (x+30000)
or Range = highest - lowest = 1.1 * (x+30000) - 1.1x
= 33000, Hence, C
Answer: C
Question: A sum of 1200 lent at S.I at 10% will become twice in how many years?
Options:
A)12 years
B)14 years
C)10 years
D)8 years
E)6 years
Rationale: Explanation:
To become twice means S.I should be as much as initial sum i.e, 1200
(1200 x 10 x T)/100 = 1200
T = 10 years
Answer: Option C
Answer: C
Question: If the sum of two positive integers is 12 and the difference of their squares is 48, what is the product of the two integers?
Options:
A)32
B)119
C)128
D)135
E)143
Rationale: Let the 2 positive numbers x and y
x+ y = 12 -- 1
x^2 - y^2 = 48
=> (x+y)(x-y)=48 -- 2
Using equation 1 in 2 , we get
=> x-y = 4 -- 3
Solving equation 1 and 3 , we get
x= 8
y= 4
Product = 8*4 = 32
Answer A
Answer: A
Question: The output of a factory was increased by 15% to keep up with rising demand. To handle the holiday rush, this new output was increased by 20%. By approximately what percent would the output now have to be decreased in order to restore the original output?
Options:
A)20%
B)27%
C)30%
D)32%
E)79%
Rationale: The original output increases by 15% and then 20%.
Total % change = a + b + ab/100
Total % change = 15 + 20 + 15*20/100 = 38%
Now, you want to change it to 0, so,
0 = 38 + x + 38x/100
x = -38(100)/138 = 27% approximately
Answer is B
Answer: B
Question: In a certain archery competition, points were awarded as follows: the first place winner receives 11 points, the second place winner receives 7 points, the third place winner receives 5 points and the fourth place winner receives 2 points. No other points are awarded. John participated several times in the competition and finished first, second, third, or fourth each time. The product of all the points he received was 53900. How many times did he participate in the competition?
Options:
A)7
B)8
C)9
D)10
E)11
Rationale: 53900 = 2*2*5*5*7*7*11
John participated 7 times.
The answer is A.
Answer: A
Question: In 10 years, A will be twice as old as B was 10 years ago. If A is now 9 years older than B, the present age of B is
Options:
A)9 years
B)19 years
C)29 years
D)39 years
E)None
Rationale: Solution
Let B's present age	= x years.
Then, A's present age	‹=› (x + 9) years.
∴(x + 9) + 10 = 2 (x - 10)
‹=› x + 19 = 2x - 20
‹=› x = 39.
Answer D
Answer: D