divelab/Sys2Bench huggingface dataset:
Question: For a finite sequence of non zero numbers, the number of variations in the sign is defined as the number of pairs of consecutive terms of the sequence for which the product of the two consecutive terms is positive. What is the number of variations in sign for the sequence 1, -3, 2, 5, -4, -6,7,-9,8?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: The questions basically asks: how many pairs of consecutive terms are there in the sequence such that the product of these consecutive terms is positive.
2*(5)=10=positive;
-4*(-6)=24=positive;
So there are 2 pairs of consecutive terms.
Answer: B
Answer: B
Question: A, B and C started a partnership business by investing Rs.12000, Rs.16000, Rs.20000 respectively. At the end of the year , the profit were distributed among them. If C's share of profit is 36000, What is the total profit?
Options:
A)70000
B)60000
C)86400
D)90000
E)50000
Rationale: A:B:C =12000:16000:20000
=3:4:5
Let total profit =p
Then pÃ—5/12=36000
p=(36000Ã—12)/5=86400
Answer is C.
Answer: C
Question: A man spends 18% of his income in house rent, 22% of the rest on his children’s education, 28% of the rest miscellaneous causes. If he now posses Rs. 9877 then his income is?
Options:
A)A)Rs.21472
B)B)Rs.31472
C)C)Rs.41472
D)D)Rs.61479
E)E)Rs.56979
Rationale: X * (82/100) * (78/100) * (72/100) = 9877
X * 0.82 * 0.78 * 0.72 = 9877
X = 9877/0.46
X = 21472
ANSWER:A
Answer: A
Question: A group of Students take a test:
Two people scored 45
Two people scored 50
Then every other persons scores were 40,60,70,75,95,100
Which score that is greater than the median but less than the mean?
Options:
A)40
B)50
C)60
D)70
E)75
Rationale: List in order: 40,45,45,50,50,60,70,75,95,100
The median = (the average of two middle terms) = (50 + 60)/2 = 55.
The mean = (the sum)/(# of terms) = 630/10 = 63.
The score of 60 is between 55 and 63.
Answer: C.
Answer: C
Question: Ram and Shakil run a race of 2000m. First Ram gives Shakil a start of 200m and beats him by 1 minute.Next Ram gives shakil a start of 6 min and is beaten by 1000 meters . Find the time in minutes in which Ram and Shakil can run the race seperately.
Options:
A)12.18
B)10.18
C)10.12
D)8.1
E)8.2
Rationale: LET r be velocity of ram and s be the velocity of Shakil then (2000/r)=(1800/s)-60......(1)
second case distance Shakil travel in 6 min=360s
again equating time for both 1000/r=(2000-360s)/s.......(2)
solving (1) &(2) we get
s=20/6
putting value in first we get time =480sec=8min
ANSWER:D
Answer: D
Question: What least number must be subtracted from 427398 so that remaining no.is divisible by 13
Options:
A)3
B)5
C)6
D)7
E)10
Rationale: Explanation:
On dividing 427398 by 13 we get the remainder 10, so 10 should be subtracted
Answer: Option E
Answer: E
Question: A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 20 sec. What is the length of the platform?
Options:
A)389 m
B)350 m
C)285 m
D)299 m
E)219 m
Rationale: Speed = 300/20 = 15 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/39 = 15
=> x = 285 m.
Answer:C
Answer: C
Question: Water is leaking out from a cylinder container at the rate of 0.31 m^3 per minute. After 10 minutes, the water level decreases 1/9 meters. What is value of the radius in meters?
Options:
A)2
B)3
C)4
D)6
E)9
Rationale: 10*0.31 = 3.1 = pi*R^2*h
R^2 = 3.1 / (pi*1/9) which is about 9
R = 3
The answer is B.
Answer: B
Question: What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 58?
Options:
A)3944
B)920
C)7290
D)6928
E)3729
Rationale: Explanation:
Let the side of the square plot be a ft.
a2 = 289 => a = 17
Length of the fence = Perimeter of the plot = 4a = 68 ft.
Cost of building the fence = 68 * 58 = Rs. 3944.
Answer: Option A
Answer: A
Question: A boat having a length 7 m and breadth 3 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of the man is:
Options:
A)100 kg
B)120 kg
C)89 Kg
D)80 Kg
E)210 Kg
Rationale: Volume of water displaced	= (7 x 3 x 0.01) m3
= 0.21 m3.
Mass of man = Volume of water displaced x Density of water
= (0.21 x 1000) kg
= 210 kg.
Answer: E
Answer: E
Question: If $910 are divided between worker A and worker B in the ratio 5:9,what is the share that worker B will get?
Options:
A)62.27%
B)63.28%
C)64.29%
D)65.31%
E)66.32%
Rationale: Worker B will get 9/14 = 64.29%
The answer is C.
Answer: C
Question: The parameter of a square is double the perimeter of a rectangle. The area of the rectangle is 480 sq cm. Find the area of the square?
Options:
A)287
B)278
C)629
D)480
E)283
Rationale: Let the side of the square be a cm. Let the length and the breadth of the rectangle be l cm and b cm respectively.
4a = 2(l + b)
2a = l + b
l . b = 480
Answer:D
Answer: D
Question: If a fair coin lands on heads 3 times out of 4 tosses, what is the probability that it will land on heads on the 5th toss?
Options:
A)2/4
B)1/4
C)1/8
D)2/8
E)3/4
Rationale: As the given coin is a fair coin,t the probability of getting ail on the fifth toss is independent of the out comes in the previous 4 tosses. So probability = 2/4 => 1/2
Answer:A
Answer: A
Question: At a certain restaurant, the ratio of the number of cooks to the number of waiters is 3 to 8. When 12 more waiters are hired, the ratio of the number of cooks to the number of waiters changes to 1 to 4. How many cooks does the restaurant have?
Options:
A)4
B)6
C)9
D)12
E)15
Rationale: Originally there were 3k cooks and 8k waiters.
The new ratio is 1:4 which equals 3:12.
12k = 8k+12
k=3
There are 9 cooks.
The answer is C.
Answer: C
Question: If 5 workers collect 48 kg of cotton in 4 days, how many kg of cotton will 9 workers collect in 2 days?
Options:
A)47.6 kg
B)52.6 kg
C)59.6 kg
D)56.6 kg
E)57.6 kg
Rationale: (3 * 5)/48 = (9 * 2)/ x
x = 57.6 kg
ANSWER:E
Answer: E
Question: A number when divided by a divisor leaves a remainder of 24.
When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?
Options:
A)37
B)39
C)41
D)42
E)43
Rationale: Let the original number be 'a'
Let the divisor be 'd'
Let the quotient of the division of aa by dd be 'x'
Therefore, we can write the relation as a/d = x and the remainder is 24.
i.e., a=dx+24 When twice the original number is divided by d, 2a is divided by d.
We know that a=dx+24. Therefore, 2a = 2dx + 48
The problem states that (2dx+48)/d leaves a remainder of 11.
2dx2dx is perfectly divisible by d and will therefore, not leave a remainder.
The remainder of 11 was obtained by dividing 48 by d.
When 48 is divided by 37, the remainder that one will obtain is 11.
Hence, the divisor is 37.
A)
Answer: A
Question: Sonika deposited Rs.13000 which amounted to Rs.10200 after 4 years at simple interest. Had the interest been 5% more. She would get how much?
Options:
A)18990
B)13002
C)12800
D)12300
E)14500
Rationale: (13000*4*5)/100 = 2600
10200
--------
12800
Answer: C
Answer: C
Question: A train passes a station platform in 40 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
Options:
A)300
B)220
C)240
D)250
E)260
Rationale: Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, x + 300 / 40 = 15
x + 300 = 600
x = 300 m.
Answer: Option A
Answer: A
Question: What is the sum of the multiples of 4 between 13 and 125 inclusive?
Options:
A)1,890
B)1,960
C)2,200
D)3,780
E)4,400
Rationale: The first multiple of 12 between 13 and 125 is 16 while the last is 124
total number of terms is given by 124=16+(n-1)4
4n-4=108
n=112/4=28
or,
(124-16)/4 + 1 =28
so , we have 28 multiples of 12 between 13 and 125
sum =14(2*16+(27)4)
=14(140)
=1960
ANSWER:B
Answer: B
Question: The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is?
Options:
A)6.05
B)6.79
C)6.02
D)6.09
E)6.01
Rationale: Amount of Rs. 100 for 1 year when compounded half-yearly = [100 * (1 + 3/100)2] = Rs. 106.09 Effective rate = (106.09 - 100) = 6.09%.Answer: D
Answer: D
Question: The average age of students of a class is 15.8 years. The average age of boys in the class is 16.4 years and that of the girls is 15.4 years. The ration of the number of boys to the number of girls in the class is:
Options:
A)1:2
B)2:3
C)3:4
D)3:5
E)3:6
Rationale: Let the ratio be k : 1. Then,
k * 16.4 + 1 * 15.4 = (k + 1) * 15.8
= (16.4 - 15.8)k = (15.8 - 15.4)
= k = 0.4/0.6 = 2/3
Required ratio = 2/3 : 1 = 2:3.
ANSWER:B
Answer: B
Question: According to the formula F=9/5 (C) +32, if the temperature in degrees Farenheit (F) increases by 30, by how much does the temperature in degrees Celsius (C) increase?
Options:
A)9
B)16.66
C)47
D)48 3/5
E)59
Rationale: You can plug in values.
C = 5/9*(F-32)
F=32 --> C=0;
F=32+30=62 --> C=5/9*30=16.66.
Increase = 16.66 degrees.
Answer: B.
Answer: B
Question: In 2005, 25 percent of the math department’s 50 students were female, and in 2007, 40 percent of the math department’s 65 students were female. What was the percent increase from 2005 to 2007 in the number of female students in the department?
Options:
A)15%
B)50%
C)62.5%
D)108%
E)160%
Rationale: Female students in 2005 = 25% of 50 = 12.5
Female students in 2007 = 40% of 65 = 26
Percentage increase = [(26 - 12.5)/12.5] *100 % = 108%
Correct Option: D
Answer: D
Question: Find the odd man out. 4, 6, 8 , 10, 17, 18
Options:
A)4
B)6
C)17
D)10
E)18
Rationale: All numbers except 17 are multiples of 2
Answer is C
Answer: C
Question: A question paper consists of five problems, each problem having three internal choices. In how many ways can a candidate attempt one or more problems?
Options:
A)1029
B)1020
C)1023
D)1098
E)1012
Rationale: Given that, the question paper consists of five problems. For each problem, one or two or three or none of the choices can be attempted.
Hence, the required number of ways = 45 - 1.
= 210 - 1 = 1024 - 1
= 1023
Answer:C
Answer: C
Question: While playing a certain dice game, Chris wins if the sum of the two dice is 11, at which point the game is over. If the game allows Chris three rolls in an attempt to win, what is the probability that Chris will win?
Options:
A)1/2
B)17/36
C)26/165
D)11/36
E)25/216
Rationale: Probability of winning game = 1- Probability of losing game
Probability of losing game = (Probability of not getting sum 7 in any of the three attempts)
Ways of getting sum 11 = (5,6)(6,5)= 2 ways
Total ways of getting outcome on two dice =6*6=36
Probability of getting sum as 11 in any attempt =2/36=1/18
Probability of NOT getting sum as 11 in any attempt = 1-(1/18)= 17/18
Probability of losing game =(17/18)*(17/18)*(17/18)=139/165
I.e. Probability of wining game = 1-(139/165) =26/165
Answer : Option C
Answer: C
Question: Michele invests 100 of her money in a mutual fund that quickly goes sour, losing 25% of its value each day for a week. Which of the following COULD BE be the value of Michele’s investment at the close-of-business any day that week?
Options:
A)$0.00
B)$13.300
C)$250.05
D)$1575.00
E)$10000.00
Rationale: Suppose she invests n$ in the starting then in the subesequent days the money left after the day will be
n/2, n/4, n/8, n/16, n/32
So, answer will be B
Answer: B
Question: A, B and C started a business with capitals of Rs. 8000, Rs. 10000 and Rs. 12000 respectively. At the end of the year, the profit share of B is Rs. 1500. The difference between the profit shares of A and C is?
Options:
A)Rs. 300
B)Rs. 400
C)Rs. 500
D)Rs. 600
E)None of these
Rationale: Ratio of investments of A, B and C is 8000 : 10000 : 12000 = 4 : 5 : 6
And also given that, profit share of B is Rs. 1500
=> 5 parts out of 15 parts is Rs. 1500
Now, required difference is 6 - 4 = 2 parts
Required difference = 2/5 (1500) = Rs. 600
ANSWER:D
Answer: D
Question: You collect coins. Suppose you start out with 11. Since you're nice, you give Sharon 3 coins. Since you're nice, you give Steven 6 coins. How many coins do you have at the end?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: Solution
Start with 11 coins.
Sharon takes 3 coins from you: 11 - 3 = 8 coins.
Steven takes 6 coins from you: 8 - 6 = 2 coins.
So you have 2 at the end.
Correct answer : A
Answer: A
Question: To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to two-fifth of its present ?
Options:
A)10
B)35
C)62.5
D)Cannot be determined
E)None of these
Rationale: EXPLANATION
Let the capacity of 1 bucket = x.
Then, the capacity of tank = 25x.
New capacity of bucket = 2/5x
Required number of buckets = 25x /(2x/5)
=( 25x x 5/2x)
=125/2
= 62.5
Answer C
Answer: C
Question: 11 + 12 + 13 + ... 51 + 52 = ?
Options:
A)1361
B)1362
C)1323
D)1364
E)1365
Rationale: Sum = 11 + 12 + 13 + ... 50 + 51 + 52
Sum of n consecutive positive integers starting from 1 is given as n(n+1)/2
Sum of first 52 positive integers = 52*53/2
Sum of first 10 positive integers = 10*11/2
Sum = 11 + 12 + 13 + 14 + ... 51 + 52 = 52*53/2 - 10*11/2 = 1323
Answer : C
Answer: C
Question: A man rows down stream 22km and 7 km upstream. if he takes 6 hrs to covereach distance, then the velocity of the current is
Options:
A)0.5kmph
B)1.25kmph
C)8.5kmph
D)6.3kmph
E)4.9kmph
Rationale: Rate down stream=(22/6)kmph;
Rate up stream=(7/6)kmph;
velocity of the current =1/2(22/6-7/6)kmph
=1.25kmph
Answer(B)
Answer: B
Question: A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 130 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
Options:
A)19 sec
B)37 sec
C)36 sec
D)16 sec
E)11 sec
Rationale: Speed of train relative to jogger = 45 - 9 = 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Distance to be covered = 240 + 130 = 370 m.
Time taken = 370/10 = 37 sec.
Answer: B
Answer: B
Question: There are two tanks A & B with same capacity of 20 litres. If the water inflow rate (speed) in Tank A is 2 litres per hour & in Tank B is 4 litres per hour. How much longer tank A takes to fill than Tank B?
Options:
A)4 hours
B)5 hours
C)3 hours
D)2 hours
E)1 hour
Rationale: Time taken for Tank A to fill = 20/2 = 10 hours
Time taken for Tank B to fill = 20/4 = 5 hours
So tank A takes 5 more hours to fill
Answer : B
Answer: B
Question: Three candidates contested an election and received 5136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate got
Options:
A)55%
B)56%
C)47.6%
D)58%
E)59%
Rationale: Explanation:
Total number of votes polled = (5136 + 7636 + 11628) = 24400
So, Required percentage = 11628/24400 * 100 = 47.6%
Answer: Option C
Answer: C
Question: Max scored 6 marks more than what he did in the previous examination in which he scored 30. Maria scored 30 marks more than she did in the previous examination in which she scored 60. Who showed less improvement?
Options:
A)58%
B)50%
C)80%
D)20%
E)55%
Rationale: Max percentage improvement in the first exam = (6/30 × 100) %
= (600/30) %
= 20 %
Maria percentage improvement in the first exam = (30/60 × 100) %
= (3000/60) %
= 50 %
Hence, 20 % < 50 %
Therefore, Max showed less improvement.
Answer:B
Answer: B
Question: Town A	Town B	Town C	Town D	Town E	Town F ; Town A Town B Town C Town D Town E Town F In the table above, what is the least number of table entries that are needed to show the mileage between each Town and each of the other five Towns?
Options:
A)20
B)22
C)15
D)18
E)25
Rationale: Easy way to go about this problem is we have 6*6 = 36 enteries in table the least number of enteries would be (36 - 6) /2 since 6 enteries represent the distances between same points .
Alternatively this can be solved as combination problem.
Correct Answer C
Answer: C
Question: Find the least number of complete years in which a sum of money put out at 33.3% compound interest will be more than double of itself?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: 3 years
Answer: A
Answer: A
Question: In a group of cows and hens, the number of legs are 16 more than twice the number of heads. The number of cows is :
Options:
A)5
B)6
C)7
D)8
E)12
Rationale: Let no of cows be x, no of hens be y.
So heads=x+y
Legs=4x+2y
Now, 4x+2y = 2(x+y)+ 16
2x = 16
x = 8.
ANSWER:D
Answer: D
Question: The average weight of a class of 20 boys was calculated to be 58.4 kgs and it was later found that one weight was misread as 56 kg instead of 65 kg. What is the correct weight?
Options:
A)57 kgs
B)58 kgs
C)58.85 kgs
D)60 kgs
E)61 kgs
Rationale: Actual total weight is (20X 58.4 - 56 + 65) = 1177 Kgs
Actual average weight is 1177/20 = 58.85 kgs
C)
Answer: C
Question: What is the sum between the place values of three 7's in the numeral 87953.0727
Options:
A)21
B)7000.0707
C)7777
D)7014
E)7000.0077
Rationale: Required sum = 7000 + 0.0700 + 0.0007 = 7000.0707
Answer is B
Answer: B
Question: Vijay sells a cupboard at 16% below cost price. Had he got Rs.1800 more, he would have made a profit of 16%. What is the cost price of the cupboard?
Options:
A)7450
B)14900
C)5625
D)7500
E)None of these
Rationale: Explanation:
Cost price = 1800/(0.16 + 0.16) = 1800/0.32
= Rs.5625
ANSWER C
Answer: C
Question: Howmany words (with or without meaning) of three distinct letters of the English alphabets are there?
Options:
A)15500
B)15800
C)15700
D)15400
E)15600
Rationale: Here we have to fill up three places by distinct letters of the English alphabets. This can be done in 26 ways. The second place can be filled in by 25 ways. The third place can be filled in 24 ways. Hence the required number of words is 26x25x24=15600. Ans : E
Answer: E
Question: A straight fence is to be constructed from posts 6 inches wide and separated by lengths of chain 6 feet long. If a certain fence begins and ends with a post, which of the following could not be the length of the fence in feet? (12 inches = 1 foot)
Options:
A)20
B)33
C)46
D)52
E)59
Rationale: There is one post for each length of chain, plus one final post at the end.
The length of the fence in feet is 6.5x + 0.5, where each is the number of chain lengths.
The length of the fence is an integer when x = 1,3,5,7,...
The length of the fence could be 7, 20, 33, 46, 59,...
The answer is D.
Answer: D
Question: Last year Elaine spent 20% of her annual earnings on rent. This year she earned 35% more than last year and she spent 30% of her annual earnings on rent. The amount she spent on rent this year is what percent of the amount spent on rent last year?
Options:
A) 202.5
B) 194.5
C) 197.5
D) 182.5
E) 177.5
Rationale: For this it is easiest to use simple numbers. Let's assume that Elaine's annual earnings last year were $100.
She would've spent $20 of this on rent.
This year she earned 15% more, or $135.
She would've spent 30% of this on rent, or $40.5
Do $40.5/$20
This will give you 202.5%
A is the correct answer.
Answer: A
Question: Find the C.I. on a sum of Rs.1600 for 9 months at 20% per annum, interest being compounded quarterly?
Options:
A)Rs.1652
B)Rs.2569
C)Rs.4587
D)Rs.479
E)Rs.2522
Rationale: Explanation:
A = 1600(21/20)3 = Rs.2522
Answer:E
Answer: E
Question: If f(x)=x^2 and x is an integer, which of the following CANNOT be the value of f(f(x))?
Options:
A)144
B)16
C)81
D)1
E)256
Rationale: f(x)=x^2
f(f(x)) = (x^2)^2
=x^4
D. 1 , x=1
B. 16 , x=2
C. 81 , x=3
A. 144
f(x)=12
Square root of 12 is not a positive integer . Hence 144 can not be the value of f(f(x)) .
E. 256 , x=4
Answer A
Answer: A
Question: What is the difference between the largest number and the least number written with the figures 3, 4, 7, 0, 3?
Options:
A)70983
B)43893
C)43983
D)43883
E)43823
Rationale: 74330 Largest
30347 Smallest
-------------
43983
ANSWER:C
Answer: C
Question: A worker makes a toy in every 2h. If he works for 100h, then how many toys will he make ?
Options:
A)50
B)54
C)45
D)39
E)None
Rationale: No. of toys = 100/2 = 50
Answer : A
Answer: A
Question: HCF of two numbers is 15 and their LCM is 180. If their sum is 105, then the numbers are:
Options:
A)30 and 75
B)35 and 70
C)40 and 65
D)45 and 60
E)55 and 70
Rationale: Explanation:
Let the numbers be 15a and 15b. Then,
15a + 15b = 105 or a+ b = 7 .. (i)
LCM = 15ab = 180
ab = 12..(ii)
Solving equations (i) and (ii), we get a=4, b=3
So, the numbers are 15 ×4 and 15 ×3, i.e., 60 and 45
Answer: D
Answer: D
Question: By selling 100 oranges, a fruit-seller gains the selling price of 30 oranges. Find the gain percent?
Options:
A)49.89%
B)45.36%
C)42.85%
D)48.26%
E)47.23%
Rationale: SP = CP + g
100 SP = 100 CP + 30 SP
70 SP = 100 CP
70 --- 30 CP
100 --- ? => 42.85%
Answer: C
Answer: C
Question: A certain number of horses and an equal number of men are going somewhere. Half of the owners are on their horses' back while the remaining ones are walking along leading their horses. If the number of legs walking on the ground is 60, how many horses are there ?
Options:
A)10
B)12
C)14
D)16
E)18
Rationale: legs 12*4 = 48
now half on their horses so remaining on the walk so 6 men
6 men has 12 legs
so, 12+ 48 = 60 legs walking
ANSWER:B
Answer: B
Question: In how many ways can 6 apples (identical) be distributed among 4 children? (Some children may get no apples.)
Options:
A)84
B)54
C)94
D)104
E)74
Rationale: Generalised form for n = number of identical objects, and r = number of children is n+r-1Cr-1.
n=6 r= 4
9C3 =84
Answer : A
Answer: A
Question: A clock is started at noon. By 10 minutes past 8, the hour hand has turned through how many degrees?
Options:
A)235Â°
B)240Â°
C)245Â°
D)250Â°
E)255Â°
Rationale: The angle traced by the hour hand in 12 hrs is 360Â°
The angle traced by the hour hand in 1 hour is 30Â°
The angle traced by the hour hand in 10 minutes is 5Â°
The angle traced by the hour hand in 8 hours and 10 minutes is 8*30Â° + 5Â° = 245Â°
The answer is C.
Answer: C
Question: A circular well with a diameter of 2 metres , is dug to a depth of 10 metres. What is the volume of the earth dug out?
Options:
A)32 m3
B)31.4 m3
C)40 m3
D)44 m3
E)None
Rationale: Solution
Volume	= πr2h
‹=› (22 /7 ×1×1×10)m3
‹=›31.4 m3.
Answer B
Answer: B
Question: Two cars are traveling towards each other. If car A is traveling at a speed of 60 mph and car B is traveling 12% slower, how much time will it take the cars to meet if the initial distance between the two is 705 miles?
Options:
A)Six hours and 30 minutes.
B)Seven hours and 30 minutes.
C)Eight hours and 20 minutes.
D)Nine hours and 15 minutes.
E)Ten hours and 20 minutes.
Rationale: Speed of second train= 60*88/100= 52.8
Time= toral distance /total speed
705/ (50+52.8)= 705/102.8= 6.___
A is the answer
Answer: A
Question: If P represents the product of the first 13 positive integers, which of the following must be true?
I. P is an odd number
II. P is a multiple of 18
III. P is a multiple of 29
Options:
A)I only
B)II only
C)III only
D)None of the above
E)All of the above
Rationale: Answer = B) II only
Answer: B
Question: If the sum of 10 consecutive integers is x, which of the must be true?
I. x is even
II. x is odd
III. x is a multiple of 3
Options:
A)I only
B)II only
C)III only
D)I and III
E)II and III
Rationale: sum of 3 consecutive integers
= (n) + (n+1) + (n+2) ++ (n+3) + (n+4) + (n+5)+(n+6)+(n+7)+(n+8)+(n+9)
=10n+45
= even + odd = odd
= 5(2n+9) = divisible by 5
Hence, x is even and divisible by 5.
Answer: D
Answer: D
Question: which of the following could be the greatest common factor of positive integers 4 and 5 ? I) 8 II) 4 III) None of these
Options:
A)III only
B)II only
C)I,II only
D)I only
E)I,III only
Rationale: 4=1*4
5=1*5
GCF =1
Answer : A
Answer: A
Question: What profit/loss percent did Ravi earn if he purchased an item of Rs.5,600 and sold it at three-fourth of its cost price?
Options:
A)Loss of 20 percent
B)Gain of 25 percent
C)Neither gain or loss
D)Loss of 15 percent
E)None of these
Rationale: Explanation:
C.P. = Rs.5600
S.P. = Rs.5600x ¾ = Rs.4200
Loss = Rs.5600-4200 = Rs.1400
Loss percentage = 1400x100/5600 = 25%
Answer: Option B
Answer: B
Question: Given 2 numbers; 16 and x, the LCM and HCF of both numbers is 144 and 2 respectively. Find x?
Options:
A)16
B)28
C)15
D)13
E)18
Rationale: HCF x LCM = Product of Numbers
2 x 144 = 16 x x
x = (2 x 144) / 16
x = 18
ANSWER : E
Answer: E