divelab/Sys2Bench huggingface dataset:
Question: A data set with a mean of 60 has a standard deviation of 8.7. Which of the following is the smallest number that falls within one standard deviation of the mean?
Options:
A)51
B)56
C)59
D)63.5
E)65
Rationale: One standard deviation of the mean is from{mean}-{deviation}=60-8.7=51.3 to{mean}+{deviation}=60+8.7=68.7. The smallest number within this range from the options is 51.
Answer: A.
Hope this helps.
Answer: A
Question: Anne traveled from City A to City B in 4 hours, and her speed was between 20 miles per hour and 40 miles per hour. John traveled from City A to City B along the same route in 2 hours, and his speed was between 45 miles per hour and 60 miles per hour. Which of the following could be the distance, in miles, from City A to City B?
Options:
A)95
B)115
C)125
D)160
E)180
Rationale: In four hours Anne must travel 4 times her speed
so Anne's possible distances =
4(20 -40) or 80-160 miles
in two hours John travels 2 times his speed or
2(45-60) or 90-120 miles
the statement is only true if both distances are possible,
so you can tell its between or equal to
90-120
B is the answer.
Answer: B
Question: At the time of marriage, a man was 6 years elder to his wife. 14 years after their marriage, his age is 8/7 times the age of his wife. What was wife's age at the time of marriage ? Choose one answer.
Options:
A)36 years
B)30 years
C)28 years
D)14 years
E)26 years
Rationale: let wifes age= x
husband age = x+6
now after 14 years of mrg x+14 wifes age
x+6+14 husbands age
8/7(x+14)=x+6+14
after solving x=28
ANSWER:C
Answer: C
Question: g(a) is defined as the product of all even integers k such that 0 < k ≤ x. For example, g(14) = 2 × 4 × 6 × 8 × 10 × 12 × 14. If g(y) is divisible by 4^11, what is the smallest possible value for a?
Options:
A) 22
B) 24
C) 28
D) 32
E) 44
Rationale: g(a)=4^11=2^22. So we have to find a product with atleast 22 2's in it.
in option 1 22 the total no of 2's = [22/2] + [22/4] +[22/8] +[22/16] = 11+5+2+1 = 19
in option 2 24 the total no of 2's = [24/2] + [24/4] +[24/8] +[24/16] = 12+6+3+1 = 22 . Hence B
Answer: B
Question: A merchant has 1000 kg of sugar part of which he sells at 8% profit and the rest at 18% profit. He
gains 14% on the whole. The Quantity sold at 18% profit is
Options:
A)300
B)400
C)600
D)500
E)None of these
Rationale: Explanation :
By the rule of alligation,we have
Profit% by selling 1st part Profit% by selling 2nd part
8 18
Net % profit
14
18-14=4 14-8=6
=> Quantity of part1 : Quantity of part2 = 4 : 6 = 2 : 3
Total quantity is given as 1000Kg
So Quantity of part2 (Quantity sold at 18% profit) = 1000×35=600Kg
Answer : Option C
Answer: C
Question: A train 960 m long passed a pole in 24 sec. How long will it take to pass a platform 800 m long?
Options:
A)40
B)44
C)48
D)52
E)56
Rationale: Speed = 960/24
= 40 m/sec.
Required time
= (960 + 800)/40
= 44 sec.
Answer:B
Answer: B
Question: All the students of class are told to sit in circle shape. Here the boy at the 6 th position is exactly opposite to 16 th boy. Total number of boys in the class?
Options:
A)10
B)15
C)20
D)25
E)30
Rationale: As half the circle shape consist of 16-6=10 boys,
So total number of boys in full circle=2*10=20
ANSWER:C
Answer: C
Question: The speed of a boat in upstream is 75 kmph and the speed of the boat downstream is 115 kmph. Find the speed of the boat in still water and the speed of the stream?
Options:
A)20 kmph
B)76 kmph
C)12 kmph
D)97 kmph
E)15 kmph
Rationale: Speed of the boat in still water
= (75+115)/2
= 90 kmph. Speed of the stream
= (115-75)/2
= 20 kmph.
Answer:A
Answer: A
Question: Data sufficiency question:
There are six people. Each cast one vote in favor of other five. Who won the elections?
i) 4 older cast their vote in favor of the oldest candidate
ii) 2 younger cast their vote to the second oldest
Options:
A)287
B)27
C)199
D)17
E)191
Rationale: xplanation:
Total possible votes are 6. Of which 4 votes went to the oldest person. So he must have won the election. Statement 1 is sufficient.
Answer:D
Answer: D
Question: A committee has 5 men and 6 women. What are the number of ways of selecting 2 men and 3 women from the given committee?
Options:
A)187
B)200
C)827
D)289
E)270
Rationale: The number of ways to select two men and three women
= ⁵C₂ * ⁶C₃
= (5 *4 )/(2 * 1) * (6 * 5 * 4)/(3 * 2)
= 200
Answer:B
Answer: B
Question: What is the smallest positive integer x such that 864x is the cube of a positive integer
Options:
A)6
B)12
C)9
D)5
E)2
Rationale: Given 864x is a perfect cube
so we will take 1728= 12*12*12
864x = 1728
x =1728/864= 2
correct option is E
Answer: E
Question: The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 12 units?
Options:
A)140
B)99
C)88
D)72
E)168
Rationale: Given that the area of the square = 1225 sq.units
=> Side of square = √1225 = 35 units
The radius of the circle = side of the square = 35 units Length of the rectangle = 2/5 * 35 = 14 units
Given that breadth = 12 units
Area of the rectangle = lb = 14 * 12 = 168 sq.units
Answer: E
Answer: E
Question: A is twice as good a work man as B and together they finish a piece of work in 24 days.The number of days taken by A alone to finish the work is :
Options:
A)28 days.
B)16 days.
C)12 days.
D)24 days.
E)36 days.
Rationale: Solution
(A’s 1 day’s work): (B’s 1 day’s work)= 2 : 1.
(A + B)'s 1 day’s work = 1/24
Divide 1/14 in the ratio 2 : 1.
∴ A’s 1 day’s work = (1/24 x2/3)= 1/36
Hence,A alone can finish the work in 36 days.
Answer E
Answer: E
Question: For a particular American football game, the probability of a team's quarterback throwing a completed pass on each throw is 3/10. What is the least number of times that the quarterback should throw the ball that will increase the probability of getting a completed pass at least once to more than 50%.
Options:
A)10
B)5
C)2
D)3
E)1
Rationale: Rule of Subtraction: P(A) = 1 - P(A')
Rule of Multiplication: P(A ∩ B) = P(A) P(B)
The probability that the quarterback throws a completed pass at least once in 2 throws is 1- (7/10)^2 = 1 - 49/100 = 51/100 > 50%
Answer: C
Answer: C
Question: If x and y are multiples of 2 then which are all the multiples of 2
1) x*y
2) x^y
3) x+y
4) x-y
5) x/y
Options:
A)1,3
B)1,2,4,5
C)1,2,5
D)1,2,3,4
E)all of these
Rationale: x*y,x^y,x+y, x-Y are even numbers
ANSWER:D
Answer: D
Question: A father was as old as his son's present at the time of your birth. If the father's age is 38 years now, the son's age 5years back was?
Options:
A)10 years
B)12 years
C)14 years
D)16 years
E)18 years
Rationale: 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) = 14 years.
C
Answer: C
Question: what is the sum of the first 30 odd natural numbers
Options:
A)300
B)400
C)900
D)600
E)700
Rationale: sum of first n odd natural nuber is = n^2
so sum of the first 30 odd natural numbers=(30)^2=900
ans 900
ANSWER:C
Answer: C
Question: How many times digit 10 is used while writing numbers from 100 to 1000?
Options:
A)100
B)90
C)85
D)110
E)120
Rationale: in 100 to 300 there are 20 ten's
in 300 to 500 there are 20 ten's
in 500 to 700 there are 20 ten's
in 700 t0 900 there are 20 ten's
in 900 to 1000 there are 10 ten's
so total is 90 ten's
CORRECT OPTION :B
Answer: B
Question: Workers at a campaign office have 3000 fliers to send out. If they send out 1/5 of them in the morning and 1/4 of the remaining ones out during the afternoon, how many are left for the next day?
Options:
A)1800
B)800
C)1100
D)1200
E)1900
Rationale: (1/5)*3000 = 600
Remaining = 3000-600 = 2400
(1/4) of remaining = (1/4)*2400 = 600
Remaining now = 2400-600 = 1800
Answer: Option A
Answer: A
Question: Arun went for a movie nine days ago. He goes to watch movies only on Thursdays. What day of the week is today?
Options:
A)Wednesday
B)Saturday
C)Friday
D)Sunday
E)Monday
Rationale: Explanation:
Clearly it can be understood from the question that 9 days ago was a Thursday
Number of odd days in 9 days = 2 (As 9-7 = 2, reduced perfect multiple of 7 from total days)
Hence today = (Thursday + 2 odd days) = Saturday
Answer: Option B
Answer: B
Question: By selling 12 toffees for a rupee, a man loses 20%. How many for a rupee should be sell to get a gain of 20%?
Options:
A)7
B)8
C)9
D)6
E)4
Rationale: Let S.P. of 12 toffees be Rs. x.
Then, 80:1 = 120:x or x = 120/180 = 3/2
For Rs. 3/2, toffees sold = 12.
For Re. 1, toffees sold = 12 * 2/3 = 8
Answer: B
Answer: B
Question: When working alone, painter W can paint a room in 2 hours, and working alone, painter X can paint the same room in f hours. When the two painters work together and independently, they can paint the room in 3/4 of an hour. What is the value of f?
Options:
A)3/4
B)1[1/5]
C)1[2/5]
D)1[3/4]
E)2
Rationale: Rate*Time=Work
Let Painter W's rate be W and Painter X's rate be X
R*T = Work
W * 2 = 1 (If the work done is same throughout the question then the work done can be taken as 1) => W = 1/2
X * f = 1 => X = 1/f
When they both work together then their rates get added up
Combined Rate = (W+X)
R*T = Work
(W+X) * 3/4 = 1
=> W+X = 4/3
=> 1/2 + 1/f = 4/3
=> 1/f = (8-3)/6 = 5/6
=> f = 6/5 = 1[1/5]
Answer B
Answer: B
Question: If 2 tables and 3 chairs cost Rs, 3500 and 3 tables and 2 chairs cost Rs. 4000, then how much does a table cost ?
Options:
A)2377
B)1000
C)2778
D)766
E)18811
Rationale: Let the cost of a table and that of a chair be Rs. x and Rs, y respectively.
Then, 2x + 3y = 3500 ...(i)
and 3x + 2y = 4000 .....(ii)
solving (i) and (ii) we get x = 1000, y = 500
Answer: B) 1000
Answer: B
Question: A type A machine can complete a job in 5 hours and a type B machine can complete the job in 7 hours. How many hours will it take 2 type A machines and 3 type B machines working together and independently to complete the job?
Options:
A)1/5
B)29/35
C)5/6
D)35/29
E)35/12
Rationale: A needs 5 hours to complete the job
2A need 5/2 hours to complete the job,
similarly 3B need 7/3 hours to complete the job
Lets consider 2A and 3B as single entity (X, Y)
so
1/X + 1/Y = 1/Z Z is the time to complete the job if working together.
1/(2/5) + 1/(7/3) =1/Z
2/5 + 3/7 =1/Z
29/35 = 1/Z
Z = 35/29
so if 2A and 3 B working together, they would need 35/29 hours to complete the job.
ANSWER:D
Answer: D
Question: A boat ma goes 2km against the current of the stream in 1 hr and goes 1 km along the current in 10 min. how long will it take to go 5 km in stationary water
Options:
A)40 min
B)1hr
C)1hr 15 min
D)1hr 30 min
E)4 hr
Rationale: rate down stream=(1/10*60)km/hr=6km/hr
rate up stream=2km/hr
speed still water =1/2(6+2)=4km/hr
required time =(5/4)=1 1/4=1hr 15 min
Answer(C)
Answer: C
Question: A bowl was filled with 10 ounces of water, and 0.012 ounce of the water evaporated each day during a 50-day period. What percent of the original amount of water evaporated during this period?
Options:
A)0.004%
B)0.04%
C)0.40%
D)6%
E)40%
Rationale: Total amount of water evaporated each day during a 50-day period = .012 * 50
=.012 * 100/2
= 1.2/2
= .6
percent of the original amount of water evaporated during this period = (.6/10) * 100%
= 6 %
Answer D
Answer: D
Question: By selling 12 toffees for a rupee, a man loses 20%. How many for a rupee should be sell to get a gain of 20%?
Options:
A)5
B)8
C)10
D)15
E)20
Rationale: Explanation:
Let S.P. of 12 toffees be Rs. x.
Then, 80:1 = 120:x or x = 120/180 = 3/2
For Rs. 3/2, toffees sold = 12.
For Re. 1, toffees sold = 12 * 2/3 = 8
ANSWER IS B
Answer: B
Question: If John invested $ 1 at 6 percent interest compounded annually, the total value of the investment, in dollars, at the end of 4 years would be
Options:
A)(1.5)^4
B)4(1.5)
C)(1.05)^4
D)1 + (0.05)^4
E)(1.06)^4
Rationale: In this prompt, the answer choices show that we don't actually have to calculate anything - we just need to 'format' the calculation correctly. We're told that the interest is COMPOUNDED ANNUALLY, so we need the Compound Interest Formula, with a Principal of $1, an R of 5% (which would 'translate' as .05) and a T of 4. We'd have....
E
Answer: E
Question: 2, -6, 18, -54, 162, (...)
Options:
A)486
B)422
C)-422
D)-468
E)-486
Rationale: 2 × -3 = -6
-6 × -3 = 18
18 × -3 = -54
-54 × -3 = 162
162 × -3 = -486
Answer is E.
Answer: E
Question: A trader bought a car at 20% discount on its original price. He sold it at a 40% increase on the price he bought it. What percent of profit did he make on the original price?
Options:
A)12%
B)19%
C)15%
D)14%
E)22%
Rationale: Original price = 100
CP = 80
S = 80*(140/100) = 112
100 - 112 = 12%
Answer:A
Answer: A
Question: A man can row his boat with the stream at 22 km/h and against the stream in 10 km/h. The man's rate is?
Options:
A)1 kmph
B)6 kmph
C)7 kmph
D)4 kmph
E)9 kmph
Rationale: Explanation:
DS = 22
US = 10
S = ?
S = (22 - 10)/2 =6 kmph
Answer: B
Answer: B
Question: Every year an amount increases by 1/8th of itself. How much will it be after two years if its present value is Rs.2880?
Options:
A)8100
B)3388
C)7767
D)2009
E)3645
Rationale: 2880* 9/8 * 9/8
= 3645
Answer: E
Answer: E
Question: Rahim travels 4 Kms in 15 minutes and another 4 Kms in 5 mins. Deepak travels at the average speed of Rahim. Then what could be the distance covered by him in 50 minutes:
Options:
A)10.m.
B)12 km.
C)20 km.
D)13.5km.
E)15.5km.
Rationale: Distence=8kms,time=20mins;
the ditence covered by him in 50mins=50*8/20=20km
ANSWER:C
Answer: C
Question: If the positive integer x is a multiple of 3 and the positive integer y is a multiple of 3, then xy must be a multiple of which of the following?
I. 3
II. 12
III. 9
Options:
A)II only
B)I and III only
C)I and II only
D)II and III only
E)I, II, and III
Rationale: x=3a
y=3b
xy=9ab
where a,b are integers
Hence , xy will always be divisible by 3,9 .
B is the answer.
Answer: B
Question: A man buys a cycle for Rs. 800 and sells it at a loss of 15%. What is the selling price of the cycle?
Options:
A)s. 1090
B)s. 1160
C)s. 680
D)s. 520
E)s. 700
Rationale: S.P. = 85% of Rs. 800 = Rs.85/100x 800 = Rs. 680
ANSWER :C
Answer: C
Question: If n divided by 7 has a remainder of 2, what is the remainder when 5 times n is divided by 7?
Options:
A)1
B)2
C)3
D)5
E)6
Rationale: As per question => N=7P+2 for some integer p
hence 5N => 35Q + 10 => remainder =>10 for some integer Q
Alternatively => N=2 > 5N=> 10 => 10 divided by 7 will leave a remainder 3
hence C
Answer: C
Question: If the simple interest on a sum of money for 2 years at 5% per annum is Rs.50, what is the compound interest on the same at the same rate and for the same time?
Options:
A)Rs.51.25
B)Rs.52
C)Rs.54.25
D)Rs.60
E)None
Rationale: Solution
Sum	=Rs.(50 x 100/2x5)
= Rs. 500.
Amount	=[Rs.(500 x(1+5/100)²]
= Rs(500x21/20x21/20).
=Rs. 551.25
C.I	= Rs. (551.25 - 500)
= Rs. 51.25
Answer A
Answer: A
Question: Find the product of the local value and absolute value of 6 in 564823
Options:
A)8000
B)16000
C)12000
D)18000
E)360000
Rationale: Explanation:
Place value = Local value
Face value = Absolute value
The place value of 6 in 564823 is 6 x 10000 = 60000
The face value of 6 in 564823 is nothing but 6.
=> 60000 x 6 = 360,000
Answer: Option E
Answer: E
Question: In how much time will a train of length 130 m, moving at 36 kmph cross an electric pole?
Options:
A)sec
B)sec
C)sec
D)sec
E)sec
Rationale: Convert kmph to mps. 36 kmph = 36 * 5/18 = 10 mps.
The distance to be covered is equal to the length of the train.
Required time t = d/s = 130/10 = 13 sec.
Answer:D
Answer: D
Question: The original price of a certain TV set is discounted by s percent, and the reduced price is then discounted by 2s percent. If P is the original price of the TV Set, which of the following represents the price of the television set after the two successive discounts?
Options:
A)P(1 - 0.03x + 0.02x^2)
B)P(1 - 0.03s + 0.0002s^2)
C)P(1 - 0.03x + 0.002x^2)
D)P(1 - 2x^2)
E)P(1 - 3x + 2x^2)
Rationale: Youcansolve this problem with number plugging.
Say the original price was $10 and s=50. Then after the first reduction the price would become $5 and after the second reduction of 2*50=100% the rprice would become $0.
Now, since P is not zero, then the expression in the brackets must be zero for s=50. Only answer choice B works.
Answer: B.
On this problem - number pluggin is not giving me the answer.. I initially used s = 10, then 2s = 20 and P = 100. Answer should after both consecutive discounts = 72. I plug in the respective values and I keep getting 68. Can you double check my math.
100 (1-0.03(10) + 0.0002 (10)^2)
100 (1-0.3 + 0.0002 (100))
100 (0.7 + 0.02)
100 (0.68) = 68????
double check my math. Am I missing something? I also plugged in your numbers and still did not get zero as final answer with choice B..
Answer: B
Question: A, B and C play a cricket match. The ratio of the runs scored by them in the match is A:B = 1:3 and B:C = 1:5. If the total runs scored by all of them are 95, the runs scored by C are?
Options:
A)20.23
B)20.13
C)75
D)20.93
E)10.93
Rationale: A:B = 1:3
B:C = 1:5
A:B:C = 1:3:15
15/19 * 95 = 75
ANSWER:C
Answer: C
Question: There are 15 stamps from which two stamps will be selected. Tom has five stamps which are same as five of the ten stamps to be selected. What is the probability that two stamps selected will not be one of the stamps that Tom has?
Options:
A)3/7
B)8/15
C)6/17
D)5/18
E)7/15
Rationale: the highlighted portion is NOT clear and poorly written, But I believe you mean that Tom has five stamps of the 15 from which two are being selected..
so we have ONLY 10 which can be selected..
P=10/15∗9/14=3/7
ANSWER:A
Answer: A
Question: During the first two weeks of June, the total rainfall in Springdale was 40 inches. If the rainfall during the second week was 1.5 times the rainfall during the first week, what was the rainfall in inches during the second week of June?
Options:
A)15
B)18
C)21
D)24
E)27
Rationale: Let x be the rainfall in the first week. Then 1.5x was the rainfall in the second week.
2.5x = 40
x = 16
The rainfall during the second week was 1.5 * 16 = 24 inches
The answer is D.
Answer: D
Question: On selling 17 balls at Rs. 720, there is a loss equal to the cost price of 5 balls. The cost price of a ball is:
Options:
A)Rs. 45
B)Rs. 50
C)Rs. 55
D)Rs. 60
E)Rs. 60
Rationale: (C.P. of 17 balls) - (S.P. of 17 balls) = (C.P. of 5 balls)
C.P. of 12 balls = S.P. of 17 balls = Rs.720.
C.P. of 1 ball = Rs.720/12	= Rs. 60.
Answer: Option D
Answer: D
Question: A sock drawer contains 3 socks, each one a different solid color. The colors of the socks are red, orange and violet. If a person reaches into the drawer and pulls out two socks, how many different color combinations are possible in the selected pair of socks?
Options:
A)12
B)15
C)21
D)3
E)42
Rationale: Since the order in which we select the socks does not matter , we can use combinations.
We can select 2 socks from 3 socks in 3C2 ways.
3C2 = 3
Answer : D
Answer: D
Question: A shopkeeper buys two articles for Rs.1000 each and then sells them, making 60% profit on the first article and 60% loss on second article. Find the net profit or loss percent?
Options:
A)200
B)278
C)282
D)202
E)600
Rationale: Profit on first article = 60% of 1000 = 600.
This is equal to the loss he makes on the second article. That, is he makes neither profit nor loss.
Answer: E
Answer: E
Question: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 265 m long?
Options:
A)50
B)99
C)88
D)77
E)21
Rationale: :
Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 360 + 265 = 625 m
Required time = 625 * 2/25 = 50 sec
Answer:A
Answer: A
Question: -20 , -16 , -12 , -8 ....
In the sequence above, each term after the first is 3 greater than the preceding term. Which of the following could not be a term in the sequence?
Options:
A)0
B)200
C)441
D)663
E)762
Rationale: Ans : B
Since 762 is not divisible by 3 , all the other options are divisible by 3
Answer: B
Question: If x and y are integers such that |y + 3| ≤ 3 and 2y – 3x + 6 = 0, what is the least possible value T of the product xy?
Options:
A)	-12
B)	-3
C)	0
D)	2
E)	None of the above
Rationale: How to deal with inequalities involving absolute values? First example shows us the so callednumber case
In this case we have |y + 3| ≤ 3 which is generalized |something| ≤ some number. First we solve as if there were no absolute value brackets:
y + 3 ≤ 3
y ≤ 0
So y is 0 or negative
Second scenario - remove the absolute value brackets. Put a negative sign around the other side of the inequality,ANDflip the sign:
y + 3 >= -3
y >= -6
Therefore we have a possible range for y: -6=<y<=0
Ok, so far so good, we're half way through. What about x?
Here's the formula: 2y – 3x + 6 = 0, rewrite it as 2y + 6 = 3x.
You can say that 2y + 6 is a multiple of 3 (=3x). So all values which must be integer must also satisfy this constraint. I'm just saying that, so it's easier to evaluate all the possible numbers (-6, -3, 0). If you plug in y = 0, x will be 2 and xy = 0 as the lowest possible value T.
Hence, Answer Choice C is the one to go.
Answer: C
Question: In a certain alphabet, 8 letters contain a dot and a straight line. 24 letters contain a straight line but do not contain a dot. If that alphabet has 40 letters, all of which contain either a dot or a straight line or both, how many letters contain a dot but do not contain a straight line?
Options:
A)4
B)8
C)14
D)20
E)28
Rationale: We are told that all of the letters contain either a dot or a straight line or both, which implies that there are no letters without a dot and a line (no line/no dot box = 0).
First we find the total # of letters with lines: 8 +24 = 32;
Next, we find the total # of letters without line: 40 - 32= 8;
Finally, we find the # of letters that contain a dot but do not contain a straight line:8- 0 = 8.
B
Answer: B
Question: A man invests Rs. 6,000 at the rate of 5% per annum. How much more should he invest at the rate of 8%, so that he can earn a total of 6% per annum?
Options:
A)Rs. 1200
B)Rs. 1300
C)Rs. 1500
D)Rs. 3000
E)None of these
Rationale: Explanation :
Interest on Rs.6000 at 5% per annum = ( 6000 × 5 × 1) / 100 = Rs. 300
Let his additional investment at 8% = x
Interest on Rs.x at 8% per annum = ( x × 8 × 1 ) / 100 = 2x/25.
To earn 6% per annum for the total, interest = (6000 + x) × 6 × 1/100.
=> 300 + 2x/25 = (6000 + x) × 6 × 1/100.
=> 30000 + 8x = (6000 + x) × 6.
=> 30000 + 8x = 36000 + 6x.
=> 2x=6000.
=> x=3000.
Answer : D
Answer: D
Question: When a certain number X is divided by 63, the remainder is 11. What is the remainder when X is divided by 9?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: When a certain number X is divided by 63, the remainder is 11. What is the remainder when X is divided by 9?
Putting a value say x = 11 we get remainder as 11 when divided by 63.
When 11 divided by 9 we get 2 as remainder.
A is the answer.
Answer: A
Question: Three pipes of same capacity can fill a tank in 8 hours. If there are only two pipes of same capacity, the tank can be filled in.
Options:
A)17 hours
B)12 hours
C)16 hours
D)24 hours
E)None of these
Rationale: Explanation:
The part of the tank filled by three pipes in one hour = 1/8
=> The part of the tank filled by two pipes in 1 hour = 2/3 * 1/8 = 1/12.
The tank can be filled in 12 hours.
ANSWER IS B
Answer: B
Question: The ratio between the present ages of P and Q is 6:7. If Q is 4 years old than P, what will be the ratio of the ages of P and Q after 4 years?
Options:
A)7:5
B)7:0
C)7:3
D)7:2
E)7:8
Rationale: Let P's age and Q's age be 6x and 7x years respectively.
Then, 7x - 6x = 4 => x = 4
Required ratio = (6x + 4) : (7x + 4)
28 : 32 = 7:8.Answer: E
Answer: E
Question: Three unbiased coins are tossed. What is the probability of getting at most two heads?
Options:
A)3/4
B)1/4
C)3/8
D)7/8
E)5/8
Rationale: Explanation:
Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}
Let E = event of getting at most two heads.
Then E = {TTT, TTH, THT, HTT, THH, HTH, HHT}.
P(E) =n(E)/n(S)= 7/8	.
ANSWER : D
Answer: D
Question: Two numbers are in the ratio 3:5. If 9 be subtracted from each, they are in the ratio of 9:17. The first number is:
Options:
A)36
B)77
C)88
D)55
E)221
Rationale: (3x-9):(5x-9) = 9:17
x = 12 => 3x = 36
Answer: A
Answer: A