divelab/Sys2Bench huggingface dataset:
Question: There are 6 people at a party sitting at a round table with 6 seats: A, B, C, D, E and F. A CANNOT sit next to either D or F. How many ways can the 6 people be seated?
Options:
A)720
B)120
C)108
D)84
E)48
Rationale: A,B,C,D,E and F can sit in (6-1)! ways -- 120
Now consider this, when we take AD as one person all of them can sit in AD, B, C, D ,E --> (5-1)! --> 24
now, this calculation considers clockwise and anti clockwise as different, i.e AD is different from DA. Therefore we have to divide this figure by 2, because We do not want to distinguish between AD and DA.
Hence there are 12 cases when AD sit to each other ( irrespective of AD or DA )
Similarly, there are 12 cases when AF sit to each other.
Similarly, we can say ADF can also be clockwise and anticlockwise, but we have to realize that, when counting AD and AF we have counted DAF or FAD TWICE ( once for each ) therefore we need to deduct the arrangement for DAF only once.
If DAF were 1 person, possible number of arrangements -- ADF,B,C,E --> 3!
We will not count it twice because we need to deduct this only once from AD and AF combination !
Therefore total count
5! - (4!/2 + 4!/2 -3!) = 120 - (12 + 12 -12 ) = 108
ANS:C
Answer: C
Question: On a test consisting of 30 questions. No. of wrong answers is 50% less than number of right answers. Each answer was either right or wrong. What is the ratio of right answers to wrong answers?
Options:
A)1 : 3
B)2 : 3
C)2 : 1
D)3 : 1
E)4 : 5
Rationale: Sol. Let the number of wrong answer - x and number of right answer = 30-x x = 50/100 of (30-x) x = 10
Required ratio = 20 : 10 = 2 : 1
C
Answer: C
Question: The ages of Patrick and Michael are in the ratio of 3 : 5 and that of Michael and Monica are in the ratio of 3 : 4. If the sum of their ages is 132, what is the difference between the ages of Patrick and Monica?
Options:
A)27
B)48
C)45
D)72
E)33
Rationale: Ages of P and Mi=3x:5x
Ages of Mi and Mo=3x:4x
Rationalizing their ages. ratio of their ages will be 9x:15x:20x
Sum=44x=132
x=3
Difference if ages of Pa and Mo=20x-9x=11x=11*3=33
Answer E
Answer: E
Question: The lenght of a room is 5.5 m and width is 4 m. Find the cost of paving the floor by slabs at the rate of Rs. 700 per sq. metre.
Options:
A)s. 15,550
B)s. 15,400
C)s. 16,500
D)s. 17,600
E)s. 17,900
Rationale: Area of the floor = (5.5 Ã— 4) m2 = 22 m2.
Cost of paving = Rs. (800 Ã— 22) = Rs. 15400
Answer: Option B
Answer: B
Question: What will be the compound interest on a sum of Rs. 40,000 after 3 years at the rate of 12% p.a.?
Options:
A)s:10123.19
B)s:10123.29
C)s:10123.20
D)s:10123.28
E)s:16197.12
Rationale: Amount
= [40000 * (1 + 12/100)3]
= 40000 * 28/25 * 28/25 * 28/25
= Rs. 56197.12
C.I. = (56197.12 - 40000)
= Rs:16197.12
Answer: E
Answer: E
Question: speed of a bus is 54kmph and including stoppages, it is 45kmph. For how many minsdoes the bus stop per hour?
Options:
A)10 min
B)15 min
C)20 min
D)25 min
E)30 min
Rationale: speed of the bus excluding stoppages = 54 kmph
speed of the bus including stoppages = 45 kmph
Loss in speed when including stoppages = 54 - 45 = 9kmph
=> In 1 hour, bus covers 9 km less due to stoppages
Hence, time that the bus stop per hour = time taken to cover 9 km
=distancespeed=954 hour=16 hour = 606 min=10 min
A
Answer: A
Question: The probability that Alex will solve a problem is 1/5. What is the probability that he solves at least one problem out of 4 problems?
Options:
A)64/125
B)256/625
C)64/625
D)369/625
E)359/625
Rationale: The probability that Alex will not solve a problem = 4/5. The probability that Alex will not solve 10 problems = (4/5)4 = 256/625.
Hence, the probability that Alex will solve at least one problem
= 1 - 256/625 = 369/625.
ANSWER:D
Answer: D
Question: Ajay can ride 50km in 1 hour. In how many hours he can ride 750km?
Options:
A)10hrs
B)15hrs
C)20hrs
D)25hrs
E)18hrs
Rationale: 1 hour he ride 50km
he ride 750km in = 750/50 * 1 = 15hours
Answer is B
Answer: B
Question: The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 507 sq m, then what is the breadth of the rectangular plot?
Options:
A)16
B)17
C)13
D)19
E)14
Rationale: Let the breadth of the plot be b m.
Length of the plot = 3 b m
(3b)(b) = 507
3b2 = 507
b2 = 169
b = 13 m.
Answer: Option C
Answer: C
Question: Pujara has a certain average of runs for his 8 matches in Border Gavaskar Trophy. In the ninth match he scores 100 runs and thereby increases his average by 9 runs. His new average of runs is:
Options:
A)28
B)29
C)30
D)31
E)32
Rationale: let his average run in 8 matches be x
total runs for 8 matches = 8x
total runs for 9 matches = 8x+100
average runs for 9 matches = (8x+100)/9
(8x+100)/9 = x + 9
8x+100 = 9x + 81
x= 19
new average = 19+9 = 28
ANSWER:A
Answer: A
Question: A father said to his son, “I was as old as you are at present at the time of your birth”.If the father’s age is 38 years now,the son’s age five years back was :
Options:
A)14 years
B)19 years
C)33 years
D)38 years
E)39 years
Rationale: Solution
Let the son's present age be x years.Then,(38-x)=x ⇔ 2x = 38 ⇔ x = 19.
∴ Son's age 5 years back = (19 - 5) years =14 years. Answer B
Answer: B
Question: The average of seven numbers is 18. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number?
Options:
A)27
B)30
C)31
D)33
E)34
Rationale: The total of seven numbers = 7X18 = 126
The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99
So, the middle number is (126 - 99 ) = 27
A
Answer: A
Question: 12500 shares, of par value Rs. 20 each, are purchased from Ram by Mohan at a price of Rs. 25 each. Find the amount required to purchase the shares.
Options:
A)312000
B)313000
C)314000
D)315000
E)312500
Rationale: Face value of each share = Rs.20
Market value of each share = Rs.25
Number of shares = 12500
Amount required to purchase the shares = 12500 × 25 = 312500
Answer is E.
Answer: E
Question: The annual birth and death rate in a country per 1000 are 39.4 and 19.4 respectively . the number of years X in which the population would be doubled assuming there is no emigration or immigration is
Options:
A)20
B)X=25
C)X=30
D)X=35
E)40
Rationale: Suppose the population of the country in current year is 1000.
So annual increase is 1000 + 39.4 - 19.4=1020
Hence every year there is an increase of 2%.
2000= 1000(1+(2/100))^n
n=35 Answer is D.
Answer: D
Question: Two stations A and B are 110 km apart on a straight line. One train starts from A at 5 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
Options:
A)15 a.m
B)8 a.m
C)12 a.m
D)02 a.m
E)05 a.m
Rationale: Suppose they meet x hours after 5 a.m.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x - 1) hours = 25(x - 1) km.
Therefore 20x + 25(x - 1) = 110
45x = 135
x = 3.
So, they meet at 8 a.m.
Answer:B
Answer: B
Question: If in a company the female employees is 80% of male employees. What is the percentage of male employees in terms of female employees?
Options:
A)125%
B)112%
C)60%
D)12%
E)8%
Rationale: The female employees is 80% of male employees
If male employees=10
female employees=8
We are asked to find the percentage of male employees in terms of female employees
M/F=10/8=10 1/8=1.25=125%
Answer is A
Answer: A
Question: Three integers are at random chosen between 0 and 9 inclusive. What is the probability R that each number is different ?
Options:
A)A.18/25
B)B.4/5
C)C.81/100
D)D.9/10
E)E.1
Rationale: Number of ways of choosing the 3 integers without restriction = 10 * 10 * 10
Number of ways of choosing the 3 integers so that the 3 integers are different = 10 * 9 * 8
Probability R= 10 * 9 * 8/10 * 10 * 10 = 72/100 = 18/25
Answer: A
Answer: A
Question: The number of timeshare condos available at Sunset Beach is 2/5 the number of timeshare condos available at Playa del Mar. If the total number of timeshare condos available at the two beaches combined is 210, what is the difference between the number of condos available at Sunset Beach and the number of condos available at Playa del Mar?
Options:
A)60
B)90
C)120
D)150
E)240
Rationale: Let x be the number of timeshare condos available at Playa del Mar.
Then number of timeshare condos available at Sunset Beach = 3/5x
We know, x + 2/5 x = 210
Hence, x = 150. So, number of timeshare condos available at Playa del Mar = 150
the difference between the number of condos available at Sunset Beach and the number of condos available at Playa del Mar = x - 2/5x = 2/5x = 3/5(150) = 90
The correct answer is B
Answer: B
Question: 3 men and 8 women complete a task in same time as 6 men and 2 women do. How much fraction of work will be finished in same time if 3 men and 2 women will do that task.
Options:
A)4/7
B)3/10
C)3/18
D)13/16
E)4/11
Rationale: 3 m + 8 w = 6 m + 2 w
3 m = 6 w
1 m = 2 w
Therefore 3 m + 8 w = 14 w
3 m + 2 w =8 w
Answer is 8/14 = 4/7
Answer: A
Answer: A
Question: Four barrels of water have an average capacity of 8 gallons. What is the maximum possible capacity of the smallest barrel H if the median is 10 gallons?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: Suppose 4 barrels are B1, B2, B3, B4 in ascending capacity.
(B1+B2+B3+B4)/4 = 8
B1+B2+B3+B4=32
median is 10 ....... as the no. of terms are even i.e 4, median = (B2+B3)/2
==> B2+B3 = 20
now we have B1+B4 = 32-20 =12
Only the following possible cases can be there :
1,9,11,11
1,10,10,11
2,10,10,10
Max value of smallest barrel H= 2
Answer: B
Question: Two employees M and N are paid a total of Rs. 550 per week by their employer. If M is paid 120 percent of the sum paid to N, how much is N paid per week?
Options:
A)Rs.200
B)Rs.230
C)Rs.250
D)Rs.300
E)Rs.320
Rationale: Let the amount paid to M per week = x
and the amount paid to N per week = y
Then x + y = 550
But x = 120% of y = 120y/100 = 12y/10
∴12y/10 + y = 550
⇒ y[12/10 + 1] = 550
⇒ 22y/10 = 550
⇒ 22y = 5500
⇒ y = 5500/22 = 500/2 = Rs.250
C)
Answer: C
Question: . A car covers a distance of 624 km in 6 ½ hours. Find its speed?
Options:
A)104
B)55
C)66
D)288
E)2761
Rationale: 624/6 = 104 kmph
Answer: A
Answer: A
Question: Alfred buys an old scooter for $4700 and spends $800 on its repairs. If he sells the scooter for $5800, his gain percent is?
Options:
A)5.45%
B)6.23%
C)7%
D)8.12%
E)10%
Rationale: C.P. = 4700+800 = $5500
S.P. = $5800
Gain = 5800-5500 = $300
Gain% = 300/5500 * 100 = 5.45%
Answer is A
Answer: A
Question: A train 200 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 20 seconds. The speed of the train is?
Options:
A)36
B)50
C)88
D)66
E)23
Rationale: Speed of the train relative to man
= (200/20) m/sec = 5 m/sec. [5 * (18/5)] km/hr
= 18 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5
= 18 ==> x
= 23 km/hr.
Answer:E
Answer: E
Question: Find the perimeter and area of the rectangle of length 15 cm and breadth 11 cm.
Options:
A)71 cm2
B)121 cm2
C)165 cm2
D)171 cm2
E)221 cm2
Rationale: length = 15 cm, breadth = 11 cm
Perimeter of rectangle = 2 (length + breadth)
= 2 (15 + 11) cm
= 2 × 26 cm
= 52 cm
We know that the area of rectangle = length × breadth
= (15 × 11) cm22
= 165 cm2
ANSWER : C
Answer: C
Question: The length of rectangle is thrice its breadth and its perimeter is 96 m, find the area of the rectangle?
Options:
A)432
B)288
C)376
D)397
E)592
Rationale: 2(3x + x) = 96
l = 36 b = 12
lb = 36 * 12 = 432
Answer: A
Answer: A
Question: If 5 is 10 percent of 25 percent of a certain number, what is the number?
Options:
A)190
B)21
C)150
D)200
E)250
Rationale: Using elimination method to pick the correct option it will be discovered that option D i.e 200 is the correct option because 25% of 200 is 50 and 10% of 50 is 5.
ANSWER:D
Answer: D
Question: If the area of a square with sides of length 6 centimeters is equal to the area of a rectangle with a width of 4 centimeters, what is the length of the rectangle, in centimeters?
Options:
A)4
B)8
C)12
D)9
E)18
Rationale: Let length of rectangle = L
6^2 = L*4
=> L = 36/4 = 9
Answer D
Answer: D
Question: What is the remainder when 1250*1040*1057*1145 is divided by 32?
Options:
A)3
B)5
C)0
D)2
E)9
Rationale: OA is 'C'.
OE:
take the remainder from each of 1250/32, 1040/32 and so on..
1250/32 gives remainder = 2
1040/32 gives remainder = 16
1057/32 gives remainder = 1
1145/32 gives remainder = 25
the net remainder is the product of above individual remainders. i.e = 2*16*1*25
break them into pairs 2*16/32 gives remainder 0
and 1*25/32 gives remainder 25
so 0*25/32 gives remainder 0.
Answer: C
Answer: C
Question: 9 years ago I was five times as old as my eldest son. Today I am 3 times his age. How old am I now?
Options:
A)45
B)54
C)34
D)58
E)56
Rationale: x-9=5(y-9)
& x=3y
x-9=5x/3-45
x=54
ANSWER:B
Answer: B
Question: How many three-digit numbers satisfy this property.: The last digit (unit's digit) of the square of the two-digit number is 2 ?
Options:
A)8
B)0
C)6
D)10
E)12
Rationale: A number ending with 2 can never be a perfect square.
Answer: B
Answer: B
Question: A train covers a distance of 10 km in 12 minutes. If its speed is decreased by 5 km/hr, the time taken by it to cover the same distance will be?
Options:
A)13min 20sec
B)10min
C)11min 30sec
D)12min 15sec
E)15min 15sec
Rationale: Speed = 10*60/12 = 50 km/hr
new speed = 50-5 = 45 km/hr
time taken = 10/45 = 60*2/9 = 13 min 20 sec
Answer is A
Answer: A
Question: A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?
Options:
A)121 m
B)128 m
C)125 m
D)120 m
E)198 m
Rationale: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.
Length of the train = 20 * 6 = 120 m.
Answer:D
Answer: D
Question: In one hour, a boat goes 11 km/hr along the stream and 5 km/hr against the stream. The speed of the boat in still water (in km/hr) is:
Options:
A)6
B)7
C)8
D)9
E)5
Rationale: Speed in still water =	1	(11 + 5)/2 kmph = 8 kmph.
Answer:C
Answer: C
Question: The smallest value of n, for which 2n + 1 is not a prime number is
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: Sol.
= (2 × 1 + 1) = 3,
= (2 × 3 + 1) = 7,
= (2 × 4 + 1) = 9, which is not prime.
Therefore n = 4.
Answer B
Answer: B
Question: Calculate how many men are needed to finish a specific task in 10 days if it will take 30 men to complete the same task in 60 days?
Options:
A)180
B)185
C)170
D)280
E)182
Rationale: men required to finish the work in 10 days = 30*60/10 = 180
Answer is A
Answer: A
Question: A train 320 m in length crosses a telegraph post in 12 seconds. The speed of the train is?
Options:
A)77 kmph
B)95 kmph
C)94 kmph
D)98 kmph
E)96 kmph
Rationale: S = 320/12 * 18/5
= 96 kmph
Answer: E
Answer: E
Question: The C.I. on a certain sum for 2 years Rs.41 and the simple interest is Rs.40. What is the rate percent?
Options:
A)2%
B)5%
C)3%
D)4%
E)8%
Rationale: SI = 20 + 20
CI = 20 + 21
20 ---- 1
100 ---- ? => 5%
Answer: B
Answer: B
Question: If g(x) = ax^5 + bx^3 + 6, and g(5) = 10, then g(–5) =?
Options:
A) – 10
B) – 8
C) – 6
D) 0
E) 2
Rationale: g(5) = 10
or, 5^5 a + 5^3 b + 6 = 10
or, 5^5 a + 5^3 b = 4
g(-5) = -5^5 a - 5^3 b + 6 = - (5^5 a + 5^3 b) + 6 = - 4 + 6 = 2 = (E)
Answer: E
Question: If 5 men and 2 boys working together, can do three times as much work per hour as a man and a boy together. Find the ratio of the work done by a man and that of a boy for a given time?
Options:
A)9:2
B)5:2
C)1:2
D)1:4
E)1:8
Rationale: M + 2B = 3(1M + 1B)
5M + 2B = 3M + 3B
2M = 1B
The required ratio of work done by a man and a boy = 1:2
ANSWER:C
Answer: C
Question: P and Q invested in a shop. The profits were divided in the ratio of 5: 2 respectively. If P invested Rs. 5600, the amount invested by Q is:
Options:
A)3500
B)5600
C)2200
D)2400
E)None
Rationale: Suppose Q invested Rs. y. Then, 5600/y = 5/2 or y = [5600 x 2 / 5] = 2240
Answer E
Answer: E
Question: The average weight of 16 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg. Find the average weights of all the boys in the class.
Options:
A)47.55 kg
B)48 kg
C)48.55 kg
D)49.25 kg
E)59.25 kg
Rationale: 16*50.25+8*45.15/24=48.55
ANSWER:C
Answer: C
Question: What is the least integer that is a sum of four different prime numbers each greater than 30?
Options:
A)148
B)150
C)152
D)154
E)156
Rationale: The sum of the four smallest primes greater than 30 is 31+37+41+43=152.
The answer is C.
Answer: C
Question: Here are 5 Rock songs, 6 Carnatic songs and 3 Indi pop songs. How many different albums can be formed using the above repertoire if the albums should contain at least 1 Rock song and 1 Carnatic song?
Options:
A)15624
B)1634
C)16144
D)240
E)3214
Rationale: There are 2n ways of choosing ‘n’ objects. For e.g. if n = 3, then the three objects can be chosen in the following 23 ways - 3C0 ways of choosing none of the three, 3C1 ways of choosing one out of the three, 3C2 ways of choosing two out of the three and 3C3 ways of choosing all three.
In the given problem, there are 5 Rock songs. We can choose them in 25 ways. However, as the problem states that the case where you do not choose a Rock song does not exist (at least one rock song has to be selected), it can be done in 25 - 1 = 32 - 1 = 31 ways.
Similarly, the 6 Carnatic songs, choosing at least one, can be selected in 26 - 1 = 64 - 1 = 63 ways.
And the 3 Indi pop can be selected in 23 = 8 ways. Here the option of not selecting even one Indi Pop is allowed.
Therefore, the total number of combinations = 31 * 63 * 8 = 15624
Option A
Answer: A
Question: A football coach must choose 5 freshers from a team of 12players. How many different ways can the coach choose the freshers?
Options:
A)500
B)650
C)729
D)800
E)890
Rationale: Choose 5 starters from a team of 12 players. Order is not important.
\inline {\color{Black} 12C_{5}}= 729
C
Answer: C
Question: The number of ways in which six boys and six girls can be seated in a row for a photograph so that no two girls sit together is?
Options:
A)9! * ⁷P₆
B)6! * ⁷P₆
C)7! * ⁷P₆
D)6! * ⁷7₆
E)2! * ⁷P₆
Rationale: We can initially arrange the six boys in 6! ways.
Having done this, now three are seven places and six girls to be arranged. This can be done in ⁷P₆ ways.
Hence required number of ways = 6! * ⁷P₆
Answer:B
Answer: B
Question: What is the smallest integer k for which 64^k > 4^17?
Options:
A)4
B)5
C)6
D)7
E)8
Rationale: 64^k > 4^17
4^(3k) > 4^17
3k > 17
k = 6
The answer is C.
Answer: C
Question: Three interviewers, X, Y, and Z are interviewing 40 applicants. Only with three interviewers' admission can an applicant be admitted. If interviewer X admitted 15 applicants, Y admitted 17 applicants, and Z admitted 20 applicants, at least how many applicants get the admission?
Options:
A) 0
B) 2
C) 6
D) 8
E) 12
Rationale: If X admitted 15 are overlapping with Y admission of 17 But Z does not overlap with anybody.
Then no student will get nod from all the 3.
Hence 0 student will get admission.
Answer : A
Answer: A
Question: Rahul went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
Options:
A)19.7
B)20
C)23
D)25
E)27
Rationale: Total cost of the items he purchased = Rs.25
Given that out of this Rs.25, 30 Paise is given as tax
=> Total tax incurred = 30 Paise = Rs.30/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (25−30/100−x)6/100 = 30/100
⇒ 6(25 −0.3 −x) = 30
⇒ (25 − 0.3 − x) = 5
⇒ x = 25 − 0.3 − 5 = 19.7
A)
Answer: A
Question: A and B can do a piece of work in 7 days. With the help of C they finish the work in 5 days. C alone can do that piece of work in?
Options:
A)33 days
B)77 days
C)30 days
D)17 days
E)18 days
Rationale: C = 1/5 – 1/6 = 1/30 => 30 days
Answer:C
Answer: C
Question: How many prime numbers are between 29/4 and 87/5?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: 29/4 = 7.xxx
87/5 = 17.xxx
So we need to find Prime numbers between 7 (Exclusive) - 16 (Inclusive)
There are 2 Prime numbers 1113
Hence answer will be (B) 2
B
Answer: B
Question: If there are only 2 wheelers and 4 wheelers parked in a school located at the heart of the city, find the number of 4 wheelers parked there if the total number of wheels is 82?
Options:
A)11
B)12
C)13
D)20
E)25
Rationale: four wheeler=20*4=80(max)
2 wheel=1
so no of 4 wheeler=20
ANSWER:D
Answer: D
Question: If m is a positive integer and (n+1)(n+3)(n+1)(n+3) is odd, then (n+2)(n+4)(n+2) must be a multiple of which one of the following is correct?
Options:
A)2
B)4
C)6
D)7
E)8
Rationale: (n+1)(n+3)(n+1)(n+3) is odd only when both (n+1)(n+1) and (n+3)(n+3) are odd. This is possible only when nn is even.
Hence, n=2mn=2m, where mm is a positive integer. Then,
(n+2)(n+4)=(2m+2)(2m+4)=2(m+1)2(m+2)=4(m+1)(m+2)(n+2)(n+4)=(2m+2)(2m+4)=2(m+1)2(m+2)=4(m+1)(m+2)
=4 * (product of two consecutive positive integers, one which must be even)=4 * (product of two consecutive positive integers, one which must be even) =4 * (an even number), and this equals a number that is at least a multiple of 8=4 * (an even number), and this equals a number that is at least a multiple of 8
Hence, the answer is (D).
Answer: D
Question: A train running at the speed of 48 km/hr crosses a pole in 9 seconds. What is the length of the train?
Options:
A)140
B)130
C)120
D)170
E)160
Rationale: Speed=(48x5/18)m/sec = (40/3) m/sec.
Length of the train = (Speed x Time).
Length of the train = (40/3 x 9)m = 120 m.
Answer is C.
Answer: C
Question: A technician makes a round-trip to and from a certain service center by the same route. If the technician completes the drive to the center and then completes 20 percent of the drive from the center, what percent of the round-trip has the technician completed?
Options:
A)60
B)50
C)40
D)70
E)45
Rationale: round trip means 2 trips i.e.to and fro. He has completed one i.e 50% completed. then he traveled another 20% of 50% i.e 10%. so he completed 50 +10 =60 % of total trip
A
Answer: A
Question: A line that passes through (–3, –4) and (3, k) has a slope = k. What is the value of k?
Options:
A) 3/4
B) 1
C) 4/5
D) 2
E) 7/2
Rationale: Slope = (y2-y1)/(x2-x1)
=> k = (k+4)/(3+3)
=> 6k = k+4
=> k =4/5
Ans C it is!
Answer: C
Question: The monthly rent of a shop of dimension 18feet × 20feet is Rs.3600. What is the annual rent per square foot of the shop?
Options:
A)120
B)56
C)68
D)87
E)92
Rationale: Sol. Monthly rent per square feet = 3600/(18*20) = 10
& Annual rent per square feet
=12*10=120
Answer : A
Answer: A
Question: If A = {10, 15, 18, 22, 36, 44}, what is the product of mean and median of the numbers in A?
Options:
A)105
B)245
C)360
D)480
E)542
Rationale: Mean = (10 + 15 +18 + 22 + 36 + 43)/6 = 24
Median = (18+22)/2 = 20
product = 24*20 = 480
Option D
Answer: D
Question: What is the sum of the different positive prime factors of 650?
Options:
A)9
B)10
C)15
D)17
E)20
Rationale: The prime factorization of 650
= 65 * 10
= 5*13 * 2*5
The sum of the different positive prime factors = 2+5+13 = 20
The answer is E.
Answer: E
Question: In Orange County, one eighth of the people are gathering mushrooms and one seventh of the people are collecting apples. What can be the number of people in Orange County?
Options:
A)200
B)210
C)216
D)224
E)235
Rationale: The number must be a multiple of both 8 and 7 so the answer is 224.
The answer is D.
Answer: D
Question: By selling a house for Rs.45000, it was found that 1/8 of the outlay was gained, what ought the selling to price to have been in order to have lost 8 p.c?
Options:
A)36800
B)38000
C)32977
D)38128
E)38982
Rationale: CP + CP/8 = 45000
CP = 40000
SP = 40000*(92/100)
= 36800
Answer:A
Answer: A
Question: A board of length L feet is cut into two pieces such that the length of piece A is 2 feet less than twice the length of piece B. Which of the following is the length, in feet, of piece A ?
Options:
A)(L - 1)/2
B)(2L + 1)/3
C)(L + 1)/3
D)(2L + 2)/3
E)(2L - 2)/3
Rationale: A+B = L so we know that B = L - A.
A = 2B-2
A = 2(L-A) - 2
3A = 2L - 2
A = (2L-2) / 3
The answer is E.
Answer: E