divelab/Sys2Bench huggingface dataset:
Question: what is the value of (2)^-3?
Options:
A)1/6
B)1/5
C)1/8
D)1/9
E)1/7
Rationale: 2^-3= 1/(2)^3= 1/8
ANSWER:C
Answer: C
Question: A man can row upstream at 6km/hr and down stream at 11km/hr find mans rate in still water ?
Options:
A)2.9km/hr
B)8.5km/hr
C)7.8km/hr
D)85.4km/hr
E)6.6km/hr
Rationale: given upstream(u) =6km/hr
down stream (v)= 11km/hr rate in still water =1/2(u+v)=1/2(6+11)=8.5km/hr Answer is (B)
Answer: B
Question: If a card is drawn from a well shuffled deck of cards, what is the probability of drawing a black card or a face card?
Options:
A)7/13
B)15/26
C)9/12
D)8/13
E)29/52
Rationale: P(Bá´œF) = P(B) + P(F) - P(Bâˆ©F), where B denotes black cards and F denotes face cards.
P(Bá´œF) = 26/52 + 12/52 - 6/52
= 8/13
Answer: D
Answer: D
Question: The sum of 3 consecutive numbers is definitely
Options:
A)Positive.
B)Divisible by 3.
C)Divisible by 2.
D)Divisible by 4.
E)Divisible by 5.
Rationale: If 1st term is x:
x+(x+1)+(x+2)=3x+3--->Always divisible by 3
If 2nd term is x:
(x-1)+x+(x+1)=3x--->Always divisible by 3
If 3rd term is x:
(x-2)+(x-1)+x=3x-3--->Always divisible by 3
Answer: B
Answer: B
Question: If w, x, and y are consecutive even positive integers and w < x < y, which of the following could be equal to y - x - w ?
Options:
A)-4
B)-2
C)-1
D)0
E)3
Rationale: Since W, X and Y are CONSECUTIVE EVEN POSITIVE INTEGERS and W < X < Y, we can start with the easiest set of values that comes to mind:
W = 2
X = 4
Y = 6
The question asks for what COULD be the value of Y - X - W.
In this case, the value would be...
6 - 4 - 2 = 0
0 IS among the answer choices, so we're done.
D
Answer: D
Question: If C.P. of 24 books is equal to S.P of 30 books , then your gain or loss is ?
Options:
A)23 1/3 gain %
B)30 10/23 loss %
C)20% loss %
D)30 1/3 loss %
E)40 1/3 loss %
Rationale: Say the cost price of 24 books is $24 so $1 for a book.
The cost of 30 books would be $30, and the selling price of 30 books would be 24$, hence the loss = ($30 - $24)/$30 = 20%.
Answer: C.
Answer: C
Question: 75% of a number when added to 75 is equal to the number. The number is ?
Options:
A)150
B)200
C)225
D)300
E)None
Rationale: Answer
75 + 75% of N = N
⇒ N -3N/4 = 75
⇒ N/4 = 75
∴ N = (75 x 4) = 300
Correct Option: D
Answer: D
Question: Given two sets A = {1,1,6,6,7,7} and B = {0,1}, if one number is chosen from each set at random, what is the probability that the sum of both numbers is an even number
Options:
A)1/4
B)1/6
C)1/2
D)1/3
E)1/5
Rationale: One way to look at it:
The number from set A can be ANYTHING.
The number selected from set B will determine whether the sum is odd or even.
For example, if a 6 is selected from set A, we need a 0 from set B to get an even sum.
If a 7 is selected from set A, we need a 1 from set B to get an even sum.
And so on.
So, P(sum is even) = P(select ANY number from set AANDselect the number from set B that makes the sum even)
= P(select ANY number from set A)xP(select the number from set B that makes the sum even)
= 1x1/2
= 1/2
= C
Answer: C
Question: A, B and C invests Rs.2000, Rs.3000 and Rs.4000 in a business. After one year A removed his money; B and C continued the business for one more year. If the net profit after 2 years be Rs.3200, then A's share in the profit is?
Options:
A)238
B)288
C)237
D)400
E)281
Rationale: Explanation:
2*12 : 3*12 : 4*24
1: 3: 4
1/8 * 3200 = 400
Answer: D
Answer: D
Question: An outlet pipe empties a tank which is full in 5 hours. If the inlet pipe is kept open, which lets water in at the rate of 4 litres/min then outlet pipe would take 3 hours longer. Find the capacity of the tank.
Options:
A)8600 litres
B)3200 litres
C)12800 litres
D)11200 litres
E)13200 litres
Rationale: Let the rate of outlet pipe be x liters/hour;
Rate of inlet pipe is 8 litres/min, or 4*60 = 240 liters/hour;
Net outflow rate when both pipes operate would be x-240 liters/hour.
Capacity of the tank = x*5 hours = (x-240)*(5+3) hours
5x=(x-240)*8 --> x=640 --> capacity = 5x = 3200 liters.
Answer: B.
Answer: B
Question: Some persons can do a piece of work in 20 days. Two times the number of these people will do half of that work in?
Options:
A)3
B)4
C)5
D)6
E)8
Rationale: 20/ (2 * 2) = 5 days
Answer:C
Answer: C
Question: If log	(a/b)+log(b/a)	= log (a + b), then:
Options:
A)a=b
B)a+b=0
C)a-b=1
D)a+b=1
E)a-b = 0
Rationale: log(a/b)+ log(b/a)	= log (a + b)
log (a + b) = log{(a/b)x(b/a)}	= log 1.
So, a + b = 1.
Answer is D
Answer: D
Question: 1. Internet: $90, with no sales tax, plus $10 shipping fee
2. Store X: $90, a 10% discount, plus 30% tax on discounted price
3. Store Y: $100, no tax
4. Store Z: $90, a 20% sales tax, and $10 rebate after tax
Isaac can purchase a certain item in four different ways, as shown in the table. What is the lowest price for which he can purchase this item?
Options:
A)88.1
B)89.0
C)89.1
D)89.5
E)98.0
Rationale: Option 2 = (90 - 9) + 0.3 * 81
=105.3
Option 4 = 90 + 0.2 * 90 - 10
= 98
So the OA is correct - E
Answer: E
Question: A man can row with a speed of 15 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?
Options:
A)27
B)27
C)20
D)99
E)2
Rationale: M = 15
S = 5
DS = 15 + 5 = 20'
Answer:C
Answer: C
Question: Aishwarya was first to board to her flight to delhi.
She forgot her seat number and picks a random seat for herself.
After this, every single person who get to the flight sits on his seat if its available else chooses any available seat at random.
Abhishek is last to enter the flight and at that moment 99/100 seats were occupied.
Whats the probability what Abhishek gets to sit in his own seat ?
Options:
A)1/2
B)1/5
C)2/9
D)4/7
E)3/6
Rationale: A
1/2
one of two is the possibility
1. If any of the first 99 people sit in Abhishek seat, Abhishek will not get to sit in his own seat.
2. If any of the first 99 people sit in Aishwarya's seat, Abhishek will get to sit in his seat.
Answer: A
Question: A diagonal of a polygon is an segment between two non-adjacent vertices of the polygon. How many diagonals does a regular 10-sided polygon have?
Options:
A) 875
B) 35
C) 1425
D) 2025
E) 2500
Rationale: There's a direct formula for this.
Number of diagonals in a regular polygon = [n*(n-3)] / 2, n = number of sides of the regular polygon.
Here, n = 10.
Plugging it in, we get 35 diagonals!
Answer (B).
Answer: B
Question: The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ Rs. 26.50 per metre is Rs. 9540, what is the length of the plot in metres?
Options:
A)20
B)200
C)300
D)400
E)100
Rationale: Let length of plot = L meters, then breadth = L - 20 meters
and perimeter = 2[L + L - 20] = [4L - 40] meters
[4L - 40] * 26.50 = 9540
[4L - 40] = 9540 / 26.50 = 360
4L = 400
L = 400/4= 100 meters. Answer: E
Answer: E
Question: To mail a package, the rate is 20 cents for the first pound and 5 cents for each additional pound. Two packages weighing 3 pounds and 5 pounds, respectively can be mailed seperately or combined as one package. Which method is cheaper and how much money is saved?
Options:
A)Combined, with a saving of 5 cents
B)Separately, with a saving of 5 cents
C)Combined, with a saving of 15 cents
D)Separately, with a saving of 10 cents
E)Combined, with a saving of 10 cents
Rationale: 3 pounds = 1*20+2*5 = 30
5 pounds = 1*20+4*5 =40
total = 70
8 pound = 1*20+7*5 = 55
dif. 15
Answer : C
Answer: C
Question: Every day Daniel drives 64 miles back from work. On Sunday, Daniel drove all the way back from work at a constant speed of x miles per hour. On Monday, Daniel drove the first 32 miles back from work at (2x) miles per hour, and the rest of the way at (x/2) miles per hour. The time it took Daniel to drive back from work on Monday is longer than the time it took him to drive back from work on Sunday by what percent?
Options:
A)15%
B)25%
C)35%
D)45%
E)55%
Rationale: Let's TEST X = 4....
On Sunday, Daniel drove 64 miles at 4 miles/hour.
D = (R)(T)
64 = (4)(T)
64/4 = 16 = T
It takes 16 hours to drive home
On Monday, Daniel drove the first 32 miles at (2)(4) = 8 miles/hour and the rest of the way (32 miles) at 4/2 = 2 miles/hour
D = (R)(T)
32 = (8)(T)
32/8 = 4 = T
It takes 4 hours for the first part
D = (R)(T)
32 = (2)(T)
32/2 = 16 = T
It takes 16 hours for the second part
Total time to drive home on Monday = 4+16 = 20 hours
We're asked by what percent 20 hours is greater than 16 hours.
20/16 = 1.25, so it is 25% greater.
B
Answer: B
Question: Three fifth of the square of a certain number is 126.15. What is the number?
Options:
A)210.25
B)75.69
C)14.5
D)145
E)150
Rationale: Let the number be X
Given, 3/5 X^2 = 126.5
X^2 = 126.15 * 5/3
X^2 = 42.05 * 5 = 210.25
X = 14.5
Answer C.
Answer: C
Question: For any integer k > 1, the term “length of an integer” refers to the number of positive prime factors, not necessarily distinct, whose product is equal to k. For example, if k = 24, the length of k is equal to 4, since 24 = 2 × 2 × 2 × 3. If x and y are positive integers such that x > 1, y > 1, and x + 3y < 980, what is the maximum possible sum of the length of x and the length of y?
Options:
A)16
B)14
C)18
D)10
E)20
Rationale: we know that : x > 1, y > 1, and x + 3y < 980,
and it is given that length means no of factors.
for any value of x and y, the max no of factors can be obtained only if factor is smallest no all factors are equal.
hence, lets start with smallest no 2.
2^1 =2
2^2 =4
2^3=8
2^4=16
2^5=32
2^6=64
2^7=128
2^8=256
2^9=512
2^10 =1024 (it exceeds 1000, so, x can't be 2^10)
so, max value that X can take is 2^9 , for which has length of integer is 9.
now, since x =512 ,x+3y<980
so, 3y<468
==> y<156
so, y can take any value which is less than 162. and to get the maximum no of factors of smallest integer, we can say y=2^7
for 2^7 has length of integer is 7.
SO, combined together : 9+7 = 16.
A
Answer: A
Question: If |z|/w = 5,which of the following must be true?
Options:
A)z = -5w
B)z = 5w
C)z^2 = 25w^2
D)z^2 = 25w^3
E)z^3 = 125w^3
Rationale: |z|/w = 5.
|z| = 5w.
Then z = 5w or -5w and so z^2 = 25w^2.
The answer is C.
Answer: C
Question: .3+33+333+33.3=?
Options:
A)362.33
B)399.6
C)702.33
D)702
E)None of them
Rationale: .3
33
333
33.3
----------
399.6
----------
Answer is B
Answer: B
Question: Which of the following will divide evenly into 347,406,520?
Options:
A)4
B)11
C)9
D)3
E)13
Rationale: Rule:
4: Last two digits should be divisible by 4
the last two digits are 00, which are divisible by 4
Answer: A
Answer: A
Question: Integers a, b, c and d, not necessarily distinct, are chosen independently and at random from 0 to 2007, inclusive. What is the probability that ad - bc is even?
Options:
A)3/8
B)7/16
C)1/2
D)9/16
E)5/8
Rationale: First of all notice that half of the numbers from from 0 to 2007, inclusive are odd and half even.
Next, let's find the probability of ad - bc being odd and subtract it from 1.
The difference of two integers to be odd we should have either ODD-EVENOREVEN-ODD:
ODD-EVEN = ad - bc = odd*odd-even*evenorodd*odd-odd*evenorodd*odd-even*odd. Three cases. The probability of each is 1/2^4, so the probability of 3 cases is 3/2^4.
The same for EVEN-ODD: p=3/2^4.
P(even) = 1 - P(odd) = 1 - (3/2^4 + 3/2^4) = 10/16 = 5/8.
Answer: E.
Answer: E
Question: The greatest common factor of positive integers m and n is 12. What is the greatest common factor of (2m^2, 2n^2)?
Options:
A)2
B)12
C)24
D)144
E)288
Rationale: Given : GCD of (m and n) = 12 = 2^2*3
i.e. m and n are both multiples of 2^2*3
i.e. m^2 and n^2 will both be multiples of (2^2*3)^2 = 2^4*3^2
i.e. 2m^2 and 2n^2 will both be multiples of 2(2^2*3)^2 = 2^5*3^2 = 288
Answer: Option E
Answer: E
Question: (1.1 + 1.1 + 1.1 + 1.1) x 1.1 x 1.1 = ? = ? x 0.121
Options:
A)54
B)33
C)44
D)22
E)26
Rationale: Explanation:
? = (1.1 + 1.1 + 1.1 + 1.1) x 1.1 x 1.1/0.121
= (4.4 x 1.1 x 1.1)/0.121 = 44
Answer: Option C
Answer: C
Question: Age of Raghav who is 30 years old is 3/5 times of Ram and Ram is older than Mohan by 35 years.If vijay's age is just between the age of Ramesh and and Mohan and Ramesh is 21 years old.What is age of vijay?
Options:
A)20
B)25
C)18
D)17
E)16
Rationale: Solution:
Raghav's age=3/5 Ram's age
=>30=3/5 Ram's age
=>Ram's age=30/3 * 5=50
Ram's age=Mohan's age +35
=>Mohan's age=Ram's age -35
=>Mohan's age=50-35
=>Mohan's age =15
Vijay's age=(Ramesh's age +Mohan's age)/2
=>Vijay's age=(21+15)/2
=>Vijay's age=18 years.
Answer C
Answer: C
Question: A man walking at the rate of 6km per hour crosses a square field diagonally in 9 seconds the area of the field is
Options:
A)110sq.m
B)111.5aq.m
C)112.5sq.m
D)114sq.m
E)None of these
Rationale: Explanation:
Distance covered in 9 seconds = (6×1000/3600)×9 = 15m
Diagonal of square field = 15m
Side of square =a then diagonal of that square= √2 a
Hence area of the square = a2= (152)/2 =112.5 sq.m
Answer: Option C
Answer: C
Question: A is half good a work man as B and together they finish a job in 26 days. In how many days working alone B finish the job?
Options:
A)98 days
B)21 days
C)17 days
D)39 days
E)19 days
Rationale: WC = 1:2
2x + x = 1/26 => x = 1/78
2x = 1/78 => 39 days
Answer:D
Answer: D
Question: What approximate value should come in place of (x) in the following question?
139.25 + 223.94 / 4.002 = x
Options:
A)195
B)276
C)188
D)166
E)161
Rationale: Explanation:
Given: 139.25 + 223.94 / 4.002 = x
Approximate 139.25 as 140, 223.94 as 224, 4.002 as 4,
we get, x = 140 + 224 / 4 = 140 + 56 = 196 =>195
ANSWER: A
Answer: A
Question: A and B can do a piece of work in 6 days, B and C in 7 days, C and A in 8 days. How long will C take to do it?
Options:
A)12.6 days
B)14.4 days
C)15.2 days
D)16.8 days
E)18.2 days
Rationale: 2c = 1/7 + 1/8 – 1/6 = 20/168 = 10/84
c = 5/84 => 84/5 = 16.8 days
The answer is D.
Answer: D
Question: Two brothers Ram and Ravi appeared for an exam. The probability of selection of Ram is 5/7 and that of Ravi is 1/5. Find the probability that both of them are selected.
Options:
A)2/35
B)2/3
C)7/35
D)1/7
E)7/5
Rationale: Let A be the event that Ram is selected and B is the event that Ravi is selected.
P(A) = 5/7
P(B) = 1/5
Let C be the event that both are selected.
P(C) = P(A) x P(B) as A and B are independent events:
= 5/7 x 1/5 = 1/7
ANSWER:D
Answer: D
Question: Find the wrong number below mentioned series
11,150,280,560,800
Options:
A)800
B)560
C)280
D)150
E)11
Rationale: 11 is the only prime number or odd number in the series.
ANSWER:E
Answer: E
Question: If XY denotes X is raised to the power Y, Find the last two digits of 19413844+ 19714181
Options:
A)154
B)677
C)784
D)148
E)132
Rationale: 1941^3844
unit digit= 1^4=1
10th digit=4*4=16=2 means last two digit =61
and 1971^4181
unit digit=1
10th digit=7*1=7 mean last two digit= 71
hence,
71+61= 132
Answer: E
Question: Three business people who wish to invest in a new company. Each person is willing to pay one third of the total investment. . After careful calculation, they realize that each of them would pay $ 7000 less if they could find two more equal investors. How much is the total investment in the new business.
Options:
A)a)	$ 64,000
B)b)	$ 54,000
C)c)	$ 21,000
D)d)	$ 52,500
E)e)	$3,600
Rationale: Initially each invest in x. Hence total investment is 3x.
Total investment is also 5(x-7000).
3x = 5(x-7000)
x= 5*7000/2 = 17500
3x = 52500 and the answer is D.
Answer: D
Question: Ron walks to a viewpoint and returns to the starting point by his car and thus takes a total time of 6 hours 45 minutes. He would have gained 2 hours by driving both ways. How long W would it have taken for him to walk both ways.
Options:
A)8 h 45 min
B)7 h 45 min
C)6 h 45 min
D)5 h 30 min
E)None of these
Rationale: 1.Walking to to a viewpoint+Driving back=6 hours 45 minutes
2.Driving to a viewpoint+Driving back=6 hours 45 minutes - 2 hours=4 hours 45 minutes, thereforeone way driving=4 hours 45 minutes/2 =2 hours 22.5 minutes.
3. From 1.one way driving=6 hours 45 minutes-2 hours 22.5 minutes=4 hours 22.5 minutes.
4.Walking to to a viewpoint+Walking back W=4 hours 22.5 minutes+4 hours 22.5 minutes=8 hours 45 minutes.
Answer: A.
Answer: A
Question: A and B can do a work in 12 days and 36 days respectively. If they work on alternate days beginning with B, in how many days will the work be completed?
Options:
A)11
B)17
C)10
D)17
E)18
Rationale: The work done in the first two days = 1/12 + 1/36 = 1/9
so, 9 such two days are required to finish the work.
i.e., 18 days are required to finish the work.
Answer: E
Answer: E
Question: Can anyhow help me with an easy solution for this
3, 4, 81, 4, 5, 121, 6, 7, ?
Options:
A)144
B)121
C)256
D)225
E)376
Rationale: 3, 4, 81, 4, 5, 121, 6, 7, ?
3+4=7 and 7+2=9 and 9^2=81
4+5=9 and 9+2=11 and 11^2=121
6+7=13 and 13+2=15 and 15^2=225
ANSWER:D
Answer: D
Question: If the range E of the six numbers 4,3,14,7,10 and x is 12, what is the difference between the greatest possible value of x and least possible value of x?
Options:
A)	0
B)	2
C)	12
D)	13
E)	15
Rationale: The range E of a set is the difference between the largest and smallest elements of a set.
Without x, the difference between the largest and smallest elements of a set is 14-3=11<12, which means that in order 12 to be the range of the set x must be either the smallest element so that 14-x=12 ---> x=2 OR x must the largest element so that x-3=12 --> x=15.
The the difference between the greatest possible value of x and least possible value of x is 15-2=13.
Answer: D.
Answer: D
Question: 8 identical machines, working alone and at their constant rates, take 6 hours to complete a job lot. How long would it take for 5 such machines to perform the same job?
Options:
A)2.25 hours
B)8.75 hours
C)12 hours
D)14.25 hours
E)9.6 hours
Rationale: Let each machine do 1 unit of work for 1 hour
8 machines --> 8 units of work in 1 hour
For 6 hours = 8*6 = 48 Units of total work is done.
Now this 48 Units of total work must be done by 5 machines
5 units of work(5 machines) ---> 1 hour
for 48 Units of work
5*9.6 ---> 1*9.6 hours
E 9.6 hours
Answer: E
Question: The mean of 50 observations is 200. But later he found that there is decrements of 47 from each observations. what is the the updated mean is ?
Options:
A)165
B)185
C)153
D)198
E)199
Rationale: 153
Answer is C
Answer: C
Question: Car R and Car Y traveled the same 80-mile route. If Car R took 2 hours and Car Y traveled at an average speed that was 50 percent faster than the average speed of Car R, how many hours did it take Car Y to travel the route?
Options:
A) 2/3
B) 1
C) 4/3
D) 8/5
E) 3
Rationale: The speed of car R is (distance)/(time) = 80/2 = 40 miles per hour.
The speed of car Y = 3/2*40 = 60 miles per hour --> (time) = (distance)/(speed) = 80/60 = 4/3 hours.
Answer: C.
Or: to cover the same distance at 3/2 as fast rate 2/3 as much time is needed --> (time)*2/3 = 2*2/3 = 4/3 hours.
Answer: C.
Answer: C
Question: A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:
Options:
A)10
B)6
C)5
D)4
E)None of these
Rationale: Explanation:
Speed of the motor boat =15 km/hr
Let speed of the stream =v
Speed downstream =15+v km/hr
Speed upstream =15-v km/hr
Time taken downstream =30/15+v
Time taken upstream =30/15-v
Total time =30/15+v + 30/15-v
Given that total time is 4 hours 30 minutes
=4 1/2hour =9/2hour
ANSWER IS C
Answer: C
Question: Find the missing number in the series.
2 , 3 , 6 , 0 , 10, -3 , 14...
Options:
A)-6
B)8
C)7
D)67
E)65
Rationale: Explanation:
There are two series in the question
1.	Add 4 : 2+3 = 6, 6+4 = 10
2.	Subtract 3 : 3-3 = 0, 0-3 - -3
Thus, following the series:
-3-3 = -6
ANSWER: A
Answer: A
Question: Solve the given two equations and find the inequality of X and Y.(a) x^2-7x+12=0 and (b) y^2+y-12=0
Options:
A)If x>y
B)If x>=y
C)If x < y
D)If x<=y
E)x=y or relationship cannot be established
Rationale: Solution:-
X=4,3
Y=-4,3
So, X>=Y
B
Answer: B
Question: A car travels at a speed of 65 miles per hour. How far will it travel in 7 hours?
Options:
A)125 miles
B)225 miles
C)455 miles
D)425 miles
E)525 miles
Rationale: During each hour, the car travels 65 miles. For 7 hours it will travel
65 + 65 + 65 + 65 + 65+ 65 + 65 = 7 × 65 = 455 miles
correct answer is C) 455 miles
Answer: C
Question: Triangle ATriangle B are similar triangles with areas 1536 units square and 1734 units square respectively. The ratio of there corresponding height would be
Options:
A)9:10
B)17:19
C)23:27
D)16:17
E)15:23
Rationale: Let x be the height of triangle A and y be the height of triangle of B.
since triangles are similar, ratio of area of A and B is in the ratio of x^2/y^2
Therefore, (x^2/y^2)=1536/1734
(x^2/y^2)=(16*16*6)/(17*17*7)
(x^2/y^2)=16^2/17^2
x/y=16/17
Ans=D
Answer: D
Question: Kyle, David, and Catherine each try independently to solve a problem. If their individual probabilities for success are 1/3, 2/7 and 5/9, respectively, what is the probability that Kyle and Catherine, but not David will solve the problem?
Options:
A)35/189
B)33/129
C)25/189
D)24/113
E)20/189
Rationale: P(Kyle will solve)=1/3
P(David will not solve)= 1 - 2/7 = 5/7
P(Catherine will solve) = 5/9
P= (1/3)*(5/7)*(5/9) = 25/189
Answer:C
Answer: C
Question: A and B invests Rs.5000 and Rs.6000 in a business. After 4 months, A withdraws half of his capital and 2 months later, B withdraws one-third of his capital. In what ratio should they share the profits at the end of the year?
Options:
A)2:3
B)82:31
C)32:45
D)34:89
E)35:21
Rationale: A : B
(5000*4)+(2500*8) : (6000*6)+(4000*6)
40000 : 60000
2 : 3
Answer:A
Answer: A
Question: A car traveled from San Diego to San Francisco at an average speed of 63 miles per hour. If the journey back took twice as long, what was the average speed of the trip?
Options:
A)24.
B)32.
C)36.
D)42.
E)44.
Rationale: Let the time taken be = x
One way distance = 63x
Total distance traveled = 2 * 63x = 126x
Total time taken = x + 2x = 3x
Average speed = 126x/3x = 42
Answer: D
Answer: D
Question: If the cost of x metres of wire is d rupees, then what is the cost of y metres of wire at the same rate?
Options:
A)Rs. (xd/y)
B)Rs. xd
C)Rs. (yd/x)
D)Rs. yd
E)None of these
Rationale: Explanation :
cost of x metres of wire = Rs. d
cost of 1 metre of wire = Rs.(d/x)
cost of y metre of wire = Rs.(y × (d/x)) = Rs. (yd/x).. Answer : Option C
Answer: C
Question: Mike took a taxi to the airport and paid $2.50 to start plus $0.25 per mile. Annie took a different route to the airport and paid $2.50 plus $5.00 in bridge toll fees plus $0.25 per mile. If each was charged exactly the same amount, and Annie's ride was 14 miles, how many miles was Mike's ride?
Options:
A)28
B)30
C)32
D)34
E)36
Rationale: The cost of Annie's ride was 2.5+5+(0.25*14) = $11
Let x be the distance of Mike's ride.
The cost of Mike's ride is 2.5+(0.25*x) = 11
0.25*x = 8.5
x = 34 miles
The answer is D.
Answer: D
Question: The rowing athletes in a rowing conference voted for coach of the year. Each rower who voted chose exactly 3 coaches to vote for among the 36 coaches in the conference. If each of the 36 coaches received exactly 5 votes (a 36 way tie), how many rowers voted for coach of the year?
Options:
A)60
B)70
C)75
D)84
E)90
Rationale: There were 36*5 = 180 total votes made. If each voter picked 3 coaches, there were 180/3 = 60 voters. A
Answer: A
Question: A seller uses 900 gm in place of one kg to sell his goods. Find
his actual % profit or loss When he sells his articles at 5 % profit
on cost price ?
Options:
A)15.5 %
B)16.5 %
C)16.67 %
D)17 %
E)None of these
Rationale: Explanation :
=[100-x]*z/y-100
=[100+5]1000/900-100=16.67 %
Answer : C
Answer: C
Question: Due to 10% decrease in the price of sugar and John can buy 5kg more sugar in Rs100 , then find the CP of sugar?
Options:
A)Rs. 1(2/7)
B)Rs. 2(1/9)
C)Rs. 3(2/11)
D)Rs. 2(2/13)
E)Rs. 2(2/7)
Rationale: Here r = 10 % ,x = 100 and A = 5 kg
Actual price of sugar = 10*100/((100-10 )*5) = Rs. 2(2/9)
B
Answer: B
Question: By selling an shirt for $300, a shop keeper gains 20% . During a clearance sale, the shopkeeper allows a discount of 10% on the marked price. His gain percent during the sale is:
Options:
A)2
B)14
C)8%
D)12
E)10
Rationale: C
8%
Marked price = $300
C.P. = 100/120 * 300 = $250
Sale price = 90% of $300 = $270
Required gain % = 20/250 * 100 = 8%.
Answer: C