divelab/Sys2Bench huggingface dataset:
Question: Two pipes A and B can fill a cistern in 10 and 30 minutes respectively, and a third pipe C can empty it in 50 minutes. How long will it take to fill the cistern if all the three are opened at the same time?
Options:
A)19 1/7 min
B)15 1/7 min
C)17 1/7 min
D)8.8 min
E)7 2/7 min
Rationale: 1/10 + 1/30 - 1/50 = 17/150
150/17 = 8.8
ANSWER:D
Answer: D
Question: What is the twenty-fourth decimal to the right in the fraction 47/48?
Options:
A)1
B)2
C)4
D)6
E)8
Rationale: 47/48 = 0.979166666666666....
The answer is D.
Answer: D
Question: In the equation a = 36.12b, b and a are integers. If a/b leaves a remainder of r, which of the following must divide into r?
Options:
A)2
B)3
C)4
D)6
E)12
Rationale: 1) It says it is a equation, so a=36.12b should be 36.12 * b..
2) It says b is an integer, again it means 36.12 * b..
Otherwise b would be just a digit and it would be mentioned..
Although not clearly mentioned that 36.12b is actually 36.12 * b, BUT entire info points towards that..
and that is why I have taken a/b = 36.12
Answer: B
Question: A flagpole 18 meters high casts a shadow of length 45 meters. If a building under similar conditions casts a shadow of length 55 meters, what is the height of the building (in meters)?
Options:
A)20
B)22
C)24
D)26
E)28
Rationale: The height:length ratio will be equal in both cases.
18 / 45 = x / 55
x = 22
The answer is B.
Answer: B
Question: Five friends go to a city where they can stay in 10 different hotels. In how many ways can they stay in these hotels if at least two of them stay together?
Options:
A)5^10−10C5∗5!
B)5^10−10C5
C)5^10−5!
D)10^5−10C5∗5!
E)10^5−10C5
Rationale: There are 10 hotels and each person can stay in 10 hotels
Total = 10 * 10 * 10 * 10 * 10 --> 10^5 --> Notice that there is no restriction to avoid a hotel.
Number of ways so that no person stays together with another friend = 10 * 9 * 8 * 7 * 6 = 10P5 = 10C5 * 5!
Number of ways can 5 friends stay in these hotels if at least two of them stay together = 10^5 - (10C5 * 5!)
Answer: D
Answer: D
Question: If nn is a positive integer and (n+1)(n+3)(n+1)(n+3) is odd, then (n+2)(n+4)(n+2)(n+4) must be a multiple of which one of the following?
Options:
A)5
B)7
C)6
D)8
E)9
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: Simple interest on a certain sum is 16 over 25 of the sum. Find the rate per cent and time, if both are equal.
Options:
A)8% and 8 years
B)6% and 6 years
C)10% and 10 years
D)12 % and 12 years
E)None of these
Rationale: 16⁄25P = P×R×R/100
⇒ R2 = 1600⁄25 ⇒ R = 40⁄5 = 8%
Also, time = 8 years
Answer A
Answer: A
Question: Ajay marked the price of his goods 30% more than his C.P. He then sells 1/4th of his stock at a discount of 15%, and half of the stock at the marked price, and the rest at a discount of 30%. Find his gain percentage.
Options:
A)16.5%
B)15.375%
C)14.20%
D)13.37%
E)None of these
Rationale: If C.P = 100, M.P = 130
S.P = (1/4) x 110.5 + (1/2) x 130 + (1/4) x 91
S.P = 27.625 + 65 + 22.75 = 115.375
Hence , Profit = 15.375%
ANSWER:B
Answer: B
Question: At a certain school, the ratio of the number of English majors to the number of Sociology majors is 5 to 2, and the ratio of the number of Psychology majors to the number of Sociology majors is 3 to 4. If the ratio of the number of History majors to the number of English majors is 5 to 3, what is the ratio of the number of Psychology majors to the number of History majors
Options:
A)25 to 3
B)20 to 9
C)9 to 50
D)6 to 25
E)3 to 10
Rationale: Correct B
Answer: B
Question: John can do a piece of work in 30 days while michael can do it in 40 days. In how many days will they finish it together?
Options:
A)17 1/7 days
B)27 1/7 days
C)23 2/7 days
D)16 4/11 days
E)17 5/11 days
Rationale: Explanation:
1/30 + 1/40 = 7/120
120/7 = 17 1/7 days
Answer: A
Answer: A
Question: A and B can finish a piece of work in 30 days. They worked at it for 20 days and then B left. The remaining work was done by A alone in 20 more days. A alone can finish the work in
Options:
A)48 days
B)50 days
C)54 days
D)60 days
E)65 days
Rationale: Explanation:
(A + B)’s 1 day’s work = 1/30
Their 20day’s work = 1/30 × 20 = 2/3
Remaining 1/3 work is done by A in 20 days
Therefore, A alone can finish the work in 3 × 20 = 60 days.
Answer: Option D
Answer: D
Question: A and B undertake to do a piece of work for $120. A alone can do it in 4days while B alone can do it in 6days. With the help of C, they finish it in 2days. Find the share of B?
Options:
A)$150
B)$100
C)$200
D)$50
E)$40
Rationale: C's 1day work = (1/2)-(1/4 + 1/6) = 1/12
A:B:C= 1/4 : 1/6: 1/12 = 3:2:1
B's share = 120*2/6 = $40
Answer is E
Answer: E
Question: A and B can finish a work in 10 days while A alone can do the same work in 20 days. In how many days B alone will complete the work?
Options:
A)20 days
B)48 days
C)98 days
D)31 days
E)22 days
Rationale: B = 1/10 – 1/20 = 1/20 => 20 days
Answer: A
Answer: A
Question: It takes ten minutes to fry a steak (five minutes for each side). You are frying the steaks in a pan that can accommodate only two steaks at one time. What is the least amount of time by which you can fry all the three steaks you have?
Options:
A)14 Minutes
B)15 Minutes
C)16 Minutes
D)17 Minutes
E)19 Minutes
Rationale: Solution:
Fifteen Minutes.
After frying for five minutes, you can take out one steak and put the third one inside while turning the other one inside. After five more minutes, one steak is fried from both sides and you can take it out. Now put in the steak that we removed and turn the other one inside. After five more minutes, they both will also be fried from both sides.
Answer B
Answer: B
Question: A rectangular plot measuring 40 meters by 50 meters is to be enclosed by wire fencing. If the poles of the fence are kept 5 meters apart. How many poles will be needed?
Options:
A)46m
B)36m
C)26m
D)56m
E)25m
Rationale: Perimeter of the plot = 2(40+50) = 180m
no of poles =180/5 =36m
Answer: B
Answer: B
Question: There are two circles of different radii. The are of a square is 784 sq cm and its side is twice the radius of the larger circle. The radius of the larger circle is seven - third that of the smaller circle. Find the circumference of the smaller circle.
Options:
A)19∏ cm
B)10∏ cm
C)12∏ cm
D)11∏ cm
E)13∏ cm
Rationale: Explanation:
Let the radii of the larger and the smaller circles be l cm and s cm respectively. Let the side of the square be a cm.
a2 = 784 = (4)(196) = (22).(142)
a = (2)(14) = 28
a = 2l, l = a/2 = 14
l = (7/3)s
Therefore s = (3/7)(l) = 6 Circumference of the smaller circle = 2∏s = 12∏ cm.
Answer: Option C
Answer: C
Question: In a camp, there is a meal for 120 men or 200 children. If 150 children have taken the meal, how many men will be catered to with remaining meal?
Options:
A)50
B)30
C)40
D)10
E)20
Rationale: Explanation :
Meal for 200 children = Meal for 120 men
Meal for 1 child = Meal for 120/200 men
Meal for 150 children = Meal for (120×150)/200 men=Meal for 90 men
Total mean available = Meal for 120 men
Renaming meal = Meal for 120 men - Meal for 90 men = Meal for 30 men . Answer : Option B
Answer: B
Question: Four extra-large sandwiches of exactly the same size were ordered for m students, where m > 7. Three of the sandwiches were evenly divided among the students. Since 4 students did not want any of the fourth sandwich, it was evenly divided among the remaining students. If Carol ate one piece from each of the four sandwiches, the amount of sandwich that she ate would be what fraction of a whole extra-large sandwich?
Options:
A)(6m-21)/[m(m-7)]
B)(4m-21)/[m(m-7)]
C)(8m-21)/[m(m-5)]
D)(10m-21)/[m(m-5)]
E)(4m-15)/[m(m-5)]
Rationale: Three of the sandwiches were evenly divided among the students
i.e. Amount of Sandwiches with each students = 3/m
Amount of 4th Sandwich with remaining (m-7) students = 1/(m-7)
The amount of Sandwich that carol ate = 3/m + 1/(m-7) = (3m-21+m)/[m(m-7)] = (4m-21)/[m(m-7)]
Answer: B
Answer: B
Question: If 2|2 –f| = 5, what is the sum of all the possible values for f ?
Options:
A)1/2
B)2
C)5/2
D)4
E)5
Rationale: if f<2, then 2-f=5/2; f=-1/2
if f>2 , then f-2=5/2; f=9/2
9/2-1/2=8/2=4=D
Answer: D
Question: Enrollment in City College in 1980 was 42 percent of enrollment in 1990. What was the percent increase in the college’s enrollment from 1980 to 1990?
Options:
A)10%
B)138.09 %
C)20%
D)25%
E)183 1/3%
Rationale: Assume 100 enrollments present in 1990
42 % of 1990 = enrollments on 1980
enrollments on 1980 = 42
% change = (enrollment in 1990 - enrollment in 1980)*100/(enrollment in 1980)
=(100 - 42) *100 / 42
= 5800 / 42
= 138.09 %
Ans - B
Answer: B
Question: Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S last month, 2/3 were basic and the rest were deluxe. If it takes 1.1 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos?
Options:
A)7/17
B)14/31
C)7/15
D)11/31
E)1/2
Rationale: The easiest way for me is to plug in numbers.
Let the number of basic stereos produced be 40, and number of delux stereos produced be 20. Total of 60 stereos.
If it takes an hour to produce a basic stereo then it will take 1.4 hours to produce a deluxe stereo.
40 basic stereos = 40 hours.
20 delux stereos = 22 hours.
Total hours = 62.
Then the fraction would be 22/62 = 11/31. Therefore answer
D.
Answer: D
Question: Two pumps are connected to an empty tank. Pump X fills the tank with water at a constant rate, while pump Y drains water out of the tank at a constant rate. The two pumps finish filling the tank in six times the duration it would take pump X alone to fill the tank. If pump Y alone can empty a whole tank in 48 minutes, then how many minutes does it take pump X alone to fill the tank?
Options:
A)32
B)34
C)36
D)38
E)40
Rationale: Let V be the volume of the tank.
Let R be the rate per minute that pump X fills the tank.
Let T be the time it takes pump X to fill the tank.
The rate at which pump Y empties the tank is V/48 per minute.
(R - V/48)*6T=V=RT.
(R-V/48)*6=R
5R=V/8.
R=V/40.
It takes pump X 40 minutes to fill the tank.
The answer is E.
Answer: E
Question: A garrison of 400 men had a provision for 31 days. After 28 days 280 persons re-enforcement leave the garrison. Find the number of days for which the remaining ration will be sufficient?
Options:
A)22
B)28
C)10
D)66
E)23
Rationale: 400 --- 31
400 --- 3
120 --- ?
400*3 = 120*x => x =10 days
Answer: C
Answer: C
Question: Of 32 applicants for a job, 14 had at least 4 years' experience, 18 had degrees, and 7 had less than 4 years' experience and did not have a degree. How many of the applicants had at least 4 years' experience and a degree?
Options:
A) 14
B) 13
C) 9
D) 7
E) 5
Rationale: set A : people with more than 4 years exp
set B : people with degree
AUB = total - (less than 4 exp and no degree)
AUB = 32-7=25
AUB = A + B - AiB
AiB = 18+14-25
=7
Answer D
Answer: D
Question: A car covers a certain distance at aspeed of 60 kmph in 5 hours. To cover the same distance in 4 hrs, it must travel at a speed of?
Options:
A)567 km/hr
B)75 km/hr
C)782 km/hr
D)789 km/hr
E)720 km/hr
Rationale: Distance = (60 x 5) = 300 km.
Speed = Distance/Time
Speed = 300/4 = 75 kmph
Answer : B
Answer: B
Question: A sports equipment store sold ping pong rackets for a total of $490. If the average (arithmetic mean) price of a pair of rackets is $9.8, how many pairs were sold?
Options:
A)50
B)100
C)490
D)500
E)980
Rationale: Average price for a pair of rackets = $9.8
Total cost = $9.8*x = $490
x = 50 pairs were sold.
ANSWER:A
Answer: A
Question: How many seconds will a 300 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
Options:
A)12 sec
B)30 sec
C)86 sec
D)15 sec
E)18 sec
Rationale: Speed of train relative to man = 63 - 3
= 60 km/hr.
= 60 * 5/18 = 50/3 m/sec.
Time taken to pass the man = 300 * 3/50
= 18 sec.
Answer: E
Answer: E
Question: By walking at 4/5 of his usual speed, Mohan is 6 minute late to his office. find his usual time to cover the distance.
Options:
A)25 minutes
B)23 minutes
C)24 minute
D)26 minute
E)None of these
Rationale: Here, Change in time = 6 and a/b = 4/5
We have, change in time = (b/a - 1) x original time
=> Original time = Change in time/(b/a - 1)
=>6(5/4 - 1) = 24 minute.
ANSWER:C
Answer: C
Question: A farm has only chickens and pigs. When the manager of the farm counted the heads of the animals on the farm, the number totaled up to 50. When the number of legs was counted, the number totaled up to 120. How many more chickens than pigs are there on the farm? Note: Each pig has 4 legs and each chicken had 2 legs.
Options:
A)30
B)32
C)34
D)36
E)38
Rationale: Let x be the number of chickens.
Then 50-x is the number of pigs.
2x+4(50-x)=120
2x=80
x=40 (chickens)
50-x=10 (pigs)
There are 40-10=30 more chickens on the farm.
The answer is A.
Answer: A
Question: If the operation ∆ is defined by a ∆ b = (b - a)^2/a^2 for all numbers a and b, and a ≠ 0, then what is the result when we evaluate this expression: (-5) ∆ (5 ∆ −5) ?
Options:
A)49/9
B)49/16
C)81/16
D)81/25
E)100/81
Rationale: (-5) ∆ (5 ∆ −5) =
(-5) ∆ (10^2/5^2) =
(-5) ∆ (4) =
(-9^2) / (-5)^2 = 81/25
The answer is D.
Answer: D
Question: A bag marked at $150 is sold for $120. The rate of discount is?
Options:
A)10%
B)25%
C)20%
D)50%
E)45%
Rationale: Rate of discount = 30/150 * 100 = 20%
Answer is C
Answer: C
Question: Arabica coffee costs $0.5 per ounce while Robusta coffee costs $0.4 per ounce. If the blend of Arabica and Robusta costs $0.44 per ounce, what is the share of Arabica in this blend?
Options:
A)20%
B)24%
C)30%
D)33%
E)40%
Rationale: a= amount of arabica coffee
1-a = amount of robusta coffee. because if you subtract a from the 1 ounce, the remaining amount is robusta
therefore:
.5a + .4(1-a) = .44
.5a + .4 - .4a = .44
a= .4
therefore: .4/1 ounce = 40%. Therefore, the answer should be E
Answer: E
Question: A family consists of grandparents, parents and three grandchildren. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family ?
Options:
A)31( 5/7)
B)31( 5/9)
C)31( 5/2)
D)31( 4/7)
E)41( 5/7)
Rationale: Required average = (67 * 2 + 35 * 2 + 6 * 3) / (2 + 2 + 3)
= (134 + 70 + 18) / 7 = 222 / 7
= 31(5/7) years.
Answer: A
Answer: A
Question: Simplify:12345679 x 72
Options:
A)888888888
B)888888881
C)888888887
D)888888886
E)888888885
Rationale: 12345679 x 72	= 12345679 x (70 +2)
= 12345679 x 70 + 12345679 x 2
= 864197530 + 24691358
= 888888888
Answer is A
Answer: A
Question: A man is walking at a speed of 10 km per hour. After every kilometre, he takes rest for 7 minutes. How much time will be take to cover a distance of 7 kilometres?
Options:
A)80 min.
B)70 min.
C)84 min.
D)55 min.
E)None of these
Rationale: Rest time = Number of rest Ã— Time for each rest
= 6 Ã— 7 = 42 minutes
Total time to cover 7 km
= (7â„10 Ã— 60)minutes + 42 minutes = 84 minutes
Answer C
Answer: C
Question: The first year, two cows produced 8100 litres of milk. The second year their production increased by 15% and 10% respectively, and the total amount of milk increased to 9100 litres a year. How many litres were milked from one cow?
Options:
A)2178 lt
B)3697 lt
C)6583 lt
D)4370 lt
E)5548 lt
Rationale: Let x be the amount of milk the first cow produced during the first year. Then the second cow produced (8100−x) litres of milk that year. The second year, each cow produced the same amount of milk as they did the first year plus the increase of 15%15% or 10%
So 8100+15100⋅x+10100⋅(8100−x)=9100
Therefore 8100+320x+110(8100−x)=9100
120x=190
x=3800
Therefore, the cows produced 3800 and 4300 litres of milk the first year, and 4370 and 4730 litres of milk the second year, => one cow produced 4370 litres
correct answer is D)4370 lt
Answer: D
Question: Three consecutive odd integers are in increasing order such that the sum of the last two integers is 13 more than the first integer. Find the three integers?
Options:
A)9, 11, 13
B)11, 13, 15
C)13, 15, 17
D)7, 9, 11
E)None of these
Rationale: Let the three consecutive odd integers be x, x + 2 and x + 4 respectively.
x + 4 + x + 2 = x + 13 => x = 7
Hence three consecutive odd integers are 7, 9 and 11.
ANSWER:D
Answer: D
Question: Suzie’s Discount Footwear sells all pairs of shoes for one price and all pairs of boots for another price. On Monday the store sold 22 pairs of shoes and 16 pairs of boots for $508. On Tuesday the store sold 8 pairs of shoes and 32 pairs of boots for $656. How much more do pairs of boots cost than pairs of shoes at Suzie’s Discount Footwear?
Options:
A)10
B)12
C)14
D)16
E)8
Rationale: Let X be pair of shoes and Y be pair of boots.
22x+16y = 508 ... eq1
8x +32y = 656....eq 2.
Now multiply eq 1 by 2 and sub eq 2.
44x =1016
8x = 656.
36x = 360 => x = 10.
Sub x in eq 2.... we get 80 + 32y = 656... then we get 32y = 576 then y = 18
Differenece between X and Y is 8
Answer : E
Answer: E
Question: If A speaks the truth 80% of the times, B speaks the truth 60% of the times. What is the probability that at least one will tell the truth
Options:
A)0.8
B)0.92
C)1.02
D)1.2
E)1.3
Rationale: probability of A speaks truth p(A)=8/10;false=2/10
probability of B speaks truth p(B)=6/10;false=4/10.For given qtn
Ans=1-(neither of them tell truth).Because A & B are independent events
=1-[(2/10)*(4/10)]=1-8/10=1-0.08=0.92
ANSWER:B
Answer: B
Question: A certain sum of money doubles itself in 10 years in how much many years will it trible itself at the same rate?
Options:
A)20 years
B)76 years
C)88 years
D)44 years
E)11 years
Rationale: 100 ---- 100 --- 10
100 --- 10
--------------------
300 ---- 20 years
Answer: A
Answer: A
Question: if deepak has 5 pants and 3 shirts how many combinations can deepak make?
Options:
A)10
B)9
C)15
D)20
E)25
Rationale: If deepak can only choose one of each, there are 5*3 = 15 possible combinations.
Answer:C
Answer: C
Question: How many possible ways can 1 girls (Rebecca, Kate, Ashley) go on a date with 3 boys (Peter, Kyle, Sam)?
Options:
A) 3
B) 4
C) 5
D) 6
E) 8
Rationale: Any one girl can go with 3 boys.
3 (A) is the answer
Answer: A
Question: A painter intends to mixed two jars of paint to create a new color. He chooses one paint jar randomly from a display containing 3 red and 2 blue samples, and a second jar is chosen at random from a different display containing 3 red and 2 blue samples. If he plans on mixing the two chosen jars together, what is the probability that when mixed together, the result will be purple paint? (The color purple is created with 1 part red and 1 part blue.)
Options:
A)1/5
B)1/2
C)2/3
D)4/5
E)6/5
Rationale: Painter has two buckets he has to randomly pick from 2 different lists ... Let these Lists be A and B ... He has to choose the first bucket from List A , and the second bucket from List B
FOR THE FIRST BUCKET ...
Red color - 2
Blue color - 2
FOR THE SECOND BUCKET
Red color - 3
Blue color -2
In order to get Purple he has to mix red with blue .. Both the LISTS contain either blue or red , therefore we have two scenarios :
Scenario I - He picks Red color from List A and Blue color from List B
Scenario II - He picks Blue color from List A and Red color from List B
Scenario I - Odds for red color from List A are 1/2 .. and for Blue color from List B are 2 /5 .. Multiplying them (because we have to find the odds that both colors are selected from their respective lists together (this is a AND not an OR problem) we get 1/5
Scenario II - Odds for blue color from List A are 1/2 , and for Red color from List B are 3/5 ... Multiplying them we get 3/10 ...
Both the scenarios are equally possible therefore we must ADD the two (not multiply ) because both of them do not have to hold true together (have to independently) for our desired result to be achieved ...
We get 1/5 + 3/10 = 2/3 (C)
Answer: C
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 66 kg. What is the correct weight?
Options:
A)58kgs
B)58.85kgs
C)58.9kgs
D)59kgs
E)59.85kgs
Rationale: Actual total weight is (20X 58.4 - 56 + 66) = 1178 Kgs
Actual average weight is 1178/20 = 58.9kgs
C
Answer: C
Question: What is the value of 3x^2 − 1.8x + 0.7 for x = 0.6?
Options:
A)−0.3
B)0
C)0.3
D)0.7
E)2.46
Rationale: 3x^2-1.8x+0.7 for x=0.6
=3(0.6*0.6)-3*0.6*(0.6)+0.7
=0+0.7
=0.7
ANSWER:D
Answer: D
Question: The number of timeshare condos available at Sunset Beach is 3/5 the number of timeshare condos available at Playa del Mar. If the total number of timeshare condos available at the two beaches combined is 400, 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)100
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 + 3/5 x = 400
Hence, x = 250. So, number of timeshare condos available at Playa del Mar = 250
the difference between the number of condos available at Sunset Beach and the number of condos available at Playa del Mar = x - 3/5x = 2/5x = 2/5(250) = 100
The correct answer is D
Answer: D
Question: Find the next no.
82, 51, 28, 20, ?
Options:
A)10
B)11
C)12
D)13
E)14
Rationale: 82=9^2+1
51=7^2+2
28=5^2+3
20=4^2+4
then next no is
3^2+5=14
ANSWER:E
Answer: E
Question: If a is a positive integer, then 2^a + 2^(a + 1) + 2^(a + 2)=
Options:
A)3^(a + 1)
B)2^(a + 1)
C)2a
D)2a^(a + 1)
E)7(2^a)
Rationale: If a is a positive integer, then 2^a + 2^(a + 1) =
2^a + 2^(a + 1)+2^(a + 2)
2^a(1+2+4)
2^a(7)
E. 7(2^a)
Answer: E
Question: A reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.600, what is the reduced price for kg?
Options:
A)30
B)60
C)70
D)80
E)20
Rationale: A
600*(25/100) = 150 ---- 5
? ---- 1 => Rs.30
Answer: A
Question: A is three times as old as B. C was twice-as old as A four years ago. In four years' time, A will be 31. What are the present ages of B and C ?
Options:
A)9, 46
B)9, 50
C)10, 46
D)10, 50
E)10, 60
Rationale: B = x
A = 3x-4
c = 6x-4
so. given A=3x-4 = 31
after 4 year A=3x = 31 -4 =27
B= x = 9
c = 6*9 -4 = 50
ANSWER:B
Answer: B
Question: A fifth of Arunâ€™s marks in mathematics exceed a third of his marks in English by 20.If he got 260 marks in two subjects together how many marks did he got in English?
Options:
A)120,80
B)180,60
C)200,60
D)200,40
E)None of them
Rationale: Let Arunâ€™s marks in mathematics and english be x and y
Then (1/5)x-(1/3)y=20
3x-5y=300â€¦â€¦>(1)
x+y=260â€¦â€¦.>(2)
solving (1) and (2)
x=200
and y=60
Answer is C.
Answer: C
Question: Which of the following is closest in value to (9^10)-(9^2)?
Options:
A)9^10
B)9^8
C)9^7
D)9^6
E)9^5
Rationale: 9^10 is much larger number than 9^2 and as we need approximate value then it's pretty much negligible in this case, so: (9^10)-(9^2) = ~9^10.
Answer: A.
Similar questions to practice:
Hope it helps.
Answer: A
Question: The arithmetic mean and standard deviation of a certain normal distribution are 15 and 1.5, respectively. What value is exactly 2 standard deviations less than the mean?
Options:
A)10.5
B)11
C)11.5
D)12
E)12.5
Rationale: The value which isexactlytwo SD less than the mean is:mean-2*SD=15-2*1.5=12.
Answer: D.
Answer: D