divelab/Sys2Bench huggingface dataset:
Question: On a map, 1 centimeter represents 25 kilometers. Two cities 425 kilometers apart would be separated on the map by how many centimeters?
Options:
A)25
B)17
C)19
D)310
E)280
Rationale: X=425/25= 17
Answer: B
Answer: B
Question: Three numbers are in the ratio 5 : 6 : 8. The sum of its longest and smallest numbers equals the sum of the third number and 49. Find the third number?
Options:
A)A)54
B)B)75
C)C)48
D)D)42
E)E)63
Rationale: Let the numbers be 5x, 6x, 8x.
Largest number = 8x.
Smallest number = 5x.
Third number = 6x.
8x + 5x = 6x + 49
7x = 49 =>x=7
6x=42=> third number is 42.
Answer:D
Answer: D
Question: The total of 336 of 20 paise and 25 paise make a sum of Rs. 71. The no of 20 paise coins is
Options:
A)238
B)277
C)278
D)260
E)288
Rationale: Explanation:
Let the number of 20 paise coins be x. Then the no of 25 paise coins = (336 - x).
0.20 * (x) + 0.25 (336 - x) = 71 => x = 260..
Answer: D) 260
Answer: D
Question: A train running at the speed of 60 km/hr crosses a pole in 18 seconds. What is the length of the train?
Options:
A)120 metres
B)180 metres
C)324 metres
D)300 metres
E)180 metres
Rationale: Speed=(60 x 5/18)/m/sec	=	50/3	m/sec.
Length of the train = (Speed x Time).
Length of the train =	50 x 18/3 m = 300 m.
ANSWER : OPTION D
Answer: D
Question: In a game of billiards, A can give B 30 points in 80 and he can give C 40 points in 80. How many points can B give C in a game of 100?
Options:
A)23
B)24
C)25
D)20
E)28
Rationale: A scores 80 while B score 50 and C scores 40.
The number of points that C scores when B scores 100 = (100 * 40)/50 = 80.
In a game of 100 points, B gives (100 - 80) = 20 points to C
Answer:D
Answer: D
Question: Two trains, each 100 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is?
Options:
A)17 km/hr
B)18 km/hr
C)60 km/hr
D)16 km/hr
E)11 km/hr
Rationale: Let the speed of the slower train be x m/sec.
Then, speed of the train = 2x m/sec.
Relative speed = ( x + 2x) = 3x m/sec.
(100 + 100)/8 = 3x => x = 25/3.
So, speed of the faster train = 50/3 = 50/3 * 18/5
= 60 km/hr.
Answer: C
Answer: C
Question: An urn contains 8 black and 2 white balls. Two balls are drawn from the urn one after the other
without replacement. What is the probability that both drawn balls are black?
Options:
A)1/5
B)28/45
C)2/5
D)3/5
E)2/7
Rationale: Let E and F denote respectively the events that first and second ball drawn
are black. We have to find P(E n F) or P (EF).
Now P(E) = P (black ball in first draw) = 8/10
Also given that the first ball drawn is black, i.e., event E has occurred, now there are 7 black balls and two white balls left in the urn. Therefore, the probability that the second ball drawn is black, given that the ball in the first draw is black, is nothing but the conditional probability of F given that E has occurred.
That is P(F|E) = 7/9
By multiplication rule of probability, we have
P (E n F) = P(E) P(F|E)
= 8/10 × 7/9 = 28/45
B
Answer: B
Question: If × stands for 'addition', ÷ stands for 'subtraction', + stands for 'multiplication' and-stands for 'division', then 20 × 8 ÷ 8 - 4 + 2 = ?
Options:
A)33
B)77
C)24
D)23
E)21
Rationale: Explanation:
By the Given data , We have the expression:
20 + 8 - 8 ÷ 4 × 2 = 20 + 8 - 2 × 2 = 20 + 8 - 4 = 24
Answer: C) 24
Answer: C
Question: In March, Kurt ran an average of 1.5 miles an hour. If by June he had increased his pace by 10 seconds per mile, then which of the following expresses the number of hours it would take Kurt to complete one mile in June?
Options:
A)3590/60^2
B)2410/60^2
C)2390/60^2
D)3586/60
E)60^2/3590
Rationale: 1500 in 3600 sec
1000 in x sec
x = 2400
In june = 2400-10 = 2390
so 2390 / 60 * 60
2390/60^2
ANSWER:C
Answer: C
Question: Which fraction should be added to:
1/(2 Ã— 3) + 1/(3 Ã— 4) + 1/(4 Ã— 5) + ....... + 1/(31 Ã— 32)
so that the result is equal to 1?
Options:
A)11/32
B)13/32
C)15/32
D)17/32
E)19/32
Rationale: The given expression
= 1/(2 Ã— 3) + 1/(3 Ã— 4) + 1/(4 Ã— 5) + ...... + 1/(31 Ã— 32)
= (1/2 - 1/3) + (1/3 - 1/4) + (1/4 - 1/5) + .......... + (1/31 - 1/32)
= 1/2 - 1/32 = 15/32
Thus, the fraction we should add = 1 - 15/32 = 17/32
The answer is D.
Answer: D
Question: In a renowned city, the average birth rate is 4 people every two seconds and the death rate is 2 people every two seconds. Estimate the size of the population net increase that occurs in one day.
Options:
A)86,400
B)172,800
C)468,830
D)338,200
E)259,200
Rationale: Every 2 seconds, 2 persons are added (4-2). Every second 1 person are added.
In a day 24hrs = 24 * 60 Minutes = 24 * 60 * 60 = 86400 seconds.
86400 * 1 = 86400
Option A
Answer: A
Question: In what time will a train 200 m long cross an electric pole, it its speed be 216 km/hr?
Options:
A)2.5 sec
B)2.8 sec
C)8.5 sec
D)3.3 sec
E)4.5 sec
Rationale: Speed = 216 * 5/18
= 60 m/sec
Time taken = 200/60
= 3.3 sec.
Answer:D
Answer: D
Question: A certain debt will be paid in 52 installments from January 1 to December 31 of a certain year. Each of the first 25 payments is to be $500; each of the remaining payments is to be $100 more than each of the first 25 payments. What is the average (arithmetic mean) payment that will be made on the debt for the year?
Options:
A)500
B)450
C)552
D)600
E)400
Rationale: Total = 500(25) + 600(27)
Number of installments = 52
Average = Total/Number of installments = 552 approximately
Answer: C
Answer: C
Question: In the first week of the Year, Rancy saved $1. In each of the next 51 weeks, she saved $1 more than she had saved in the previous week. What was the total amount that Rancy saved during the 52 weeks?
Options:
A)$1,326
B)$1,352
C)$1,378
D)$2,652
E)$2,756
Rationale: In the first week of the Year, Rancy saved $1.If you don't recall the formula, there is one method:
1 + 2 + 3 + 4 + 5 ........ + 26 + 27 + ............ + 48 + 50 + 51 + 52
Sum of 1stlast digit = 1 + 52 = 53
Sum of 2nd2nd last digit = 2 + 51 = 53
Sum of 3rd3rd last digit = 3 + 50 = 53
.
.
.
.
This is repeated 26 times
So, 26 * 53 = 1378
Answer = C
Answer: C
Question: A truck covers a distance of 200 metres in 1 minute whereas a bus covers a distance of 100kms in 50minutes. The ratio of their speeds is?
Options:
A)2:3
B)1:5
C)ratio 1:10
D)9:13
E)7:15
Rationale: Ratio of speeds = (200/60) 18/5 : 60*100/50 = 12:120 = 1:10
Answer is C
Answer: C
Question: A circular logo is enlarged to fit the lid of a jar. The new diameter is 10 per cent larger than the original. By what percentage has the area of the logo increased?
Options:
A)50
B)80
C)100
D)125
E)21
Rationale: Let old diameter be 4 , so radius is 2
Old area = 4π
New diameter is 4.4 , so radius is 2.2
New area = 4.84π
Increase in area is 0.84π
% increase in area = 0.84/4*100
So, % increase is 21%
Answer will be (E)
Answer: E
Question: Two pipes P and Q can fill a cistern in 12 and 13 minutes respectively. Both are opened together, but at the end of 3 minutes the first is turned off. How much longer will the cistern take to fill?
Options:
A)1/8
B)1/4
C)2/4
D)1/4
E)3/4
Rationale: 3/12 + x/13
= 1
x= 7 3/4
Answer: E
Answer: E
Question: Find the compound interest accrued on an amount of Rs.14,800 at 13.5% p.a at the end of two years. (Round off your answer to nearest integer?
Options:
A)Rs.4268
B)Rs.4290
C)Rs.4566
D)Rs.4266
E)Rs.4208
Rationale: CI = 14800{ [ 1 + 13.5/100]2 - 1 }
= 14800 { [1 + 27/200]2 - 1
= 14800 { 2 + 27/200}{27/200}
= (74)[2 + 27/200](27) =
1998[2 + 27/200] = 3996 + 269.73 = Rs.4266
Answer:D
Answer: D
Question: Which one of the following is the common factor of (4743 + 4343) and (4747 + 4347) ?
Options:
A)47-43
B)47+43
C)(47^43)+(43^47)
D)None of these
E)(47^2)+(43^2)
Rationale: When n is odd, (xn + an) is always divisible by (x + a).
Each one of (4743 + 4343) and (4747 + 4347) is divisible by (47 + 43).
Option B
Answer: B
Question: The rate of a certain chemical reaction is directly proportional to the square of the concentration of chemical B present and inversely proportional to the concentration of chemical A present. If the concentration of chemical B present is increased by 100 percent, which of the following is closest to the percent change in the the concentration of chemical B required to keep the reaction rate unchanged.
Options:
A)100 % decrease
B)60% decrease
C)40% decrease
D)30% increase
E)50% increase
Rationale: Let's say here is the formula of how B and A affects the reaction speed:
rate = B^2/A
After the concentration A is increased by 100%, the percentage of A
become 2A, to keep 'rate' the same, need to have B^2 being doubled.
Which means A increased by 2^(1/2) times.
Answer : C
Answer: C
Question: 10 books are placed at random in a shelf. The probability that a pair of books will always be together is?
Options:
A)1/7
B)1/8
C)1/5
D)1/1
E)1/2
Rationale: 10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2!
Required probability
= 1/5
Answer:C
Answer: C
Question: In a T.V. factory, an average of 60TVs are produced per day for the fist 25days of the months. A few workers fell ill for the next five daysreducing the daily avg for the month to 58 sets/day . The average production per day for day last 5days is ?
Options:
A)30
B)42
C)48
D)50
E)54
Rationale: Production during these 5 days = Total production in a month - production in first 25 days.
= 30 x 58 - 25 x 60
= 240
∴ Average for last 5 days = 240 / 5
= 48
C
Answer: C
Question: In covering a distance of 18 km, Abhay takes 2 hours more than Sameer. If Abhay doubles his speed, then he would take 1 hour less than Sameer. Abhay's speed is:
Options:
A)3 kmph
B)6 kmph
C)6.25 kmph
D)7.5 kmph
E)7.8 kmph
Rationale: Let Abhay's speed be x km/hr.
Then,	18/X	-	18/2X	= 3
6x = 18
x = 3 km/hr. Answer: Option A
Answer: A
Question: Ratio between Rahul and Deepak is 4:2, After 6 Years Rahul age will be 22 years. What is Deepak present age
Options:
A)9
B)3
C)5
D)2
E)7
Rationale: Explanation:
Present age is 4x and 2x,
=> 4x + 22 = 26 => x = 1
So Deepak age is = 2(1) = 2
Answer: Option D
Answer: D
Question: 12,31,68,?,220,347,516
Options:
A)199
B)220
C)347
D)129
E)520
Rationale: 2*2*2 + 4 = 12
3*3*3 +4 = 31
4*4*4 + 4 = 68
6*6*6 + 4 = 220
7 *7 *7 + 4 = 347
8 *8 *8 + 4 = 516.
5*5*5 + 4 = 129
ANSWER : D
Answer: D
Question: The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 6 minutes, then the area of the park (in sq. m) is:
Options:
A)153601
B)153600
C)86400
D)153603
E)153604
Rationale: Perimeter = Distance covered in 6 min. =(12000/60) x 6m = 1200 m.
Let length = 3x metres and breadth = 2x metres.
Then, 2(3x + 2x) = 1200 or x = 120.
Length = 360 m and Breadth = 240 m.
Area = (360 x 240) m2 = 86400 m2.
Answer: C
Answer: C
Question: John and Ingrid pay 30% and 40% tax annually, respectively. If John makes $56000 and Ingrid makes $73000, what is their combined tax rate?
Options:
A)32%
B)34.4%
C)35%
D)35.6%
E)36.4%
Rationale: (1) When 30 and 40 has equal weight or weight = 1/2, the answer would be 35.
(2) When 40 has larger weight than 30, the answer would be in between 35 and 40. Unfortunately, we have 2 answer choices D and E that fit that condition so we need to narrow down our range.
(3) Get 73000/129000 = 73/129 is a little above 1/2. Thus, our answer is just a little above 35.
Answer: D
Answer: D
Question: Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 36 kmph. Of how many minutes does the train stop per hour?
Options:
A)E982
B)27
C)12
D)121
E)28
Rationale: Explanation:
T = 9/45 * 60 = 12
Answer: Option C
Answer: C
Question: What decimal of an hour is a second
Options:
A)0028
B)0027
C)2787
D)2788
E)2992
Rationale: Explanation:
1 / (60 * 60) = 1 / 3600 = .0027
Answer: B) .0027
Answer: B
Question: A car covers a distance of 1080 km in10 hrs. What is its speed in mps.
Options:
A)40 m/s
B)25 m/s
C)20 m/s
D)15 m/s
E)30 m/s
Rationale: Explanation:
Distance = Speed x Time
Speed = (1080/10) = 108 kmph
Spees in mps = 108 x 5/18 = 6 x 5 = 30 mps.
Answer: Option E
Answer: E
Question: Tim and Élan are 120 miles away from one another. They are starting to move towards each other simultaneously, Tim at a speed of 10 Mph and Élan at a speed of 5 Mph. If every hour they double their speeds, what is the distance that Tim will pass until he meets Élan?
Options:
A)30 miles.
B)35 miles.
C)45 miles.
D)60 miles.
E)80 miles.
Rationale: Tim and Elan will meet at the same time while their ratio of speed is 2:1 respectively.So their individual distance traveled ratio will be same.
Plugging in the answer choice Only Answer Choice E meet the 2:1(Tim:Elan=80:40) ratio of maintaining total distance traveled 120 miles
So Correct answer E
Answer: E
Question: The average temperature of Monday, Tuesday, Wednesday and Thursday was 38∘ and that of Tuesday, Wednesday, Thursday and Friday was 40∘. If the temperature on Monday was 34∘, the temperature of Friday was :
Options:
A)42∘
B)39∘
C)38∘
D)30∘
E)None of these
Rationale: Explanation:
M+T+W+Th=(4×38)=152
Monday temperature is 34. So T+W+Th=(152-34)=118
T+W+Th+F=(4×40)=160
F = (160-118)=42∘
Correct Option: A
Answer: A
Question: Out of 17 applicants, there are 8 boys and 9 girls. Two persons are to be selected for the job. Find the probability that at least one of the selected persons will be a girl.
Options:
A)25/34
B)19/34
C)21/34
D)27/34
E)37/34
Rationale: The events of selection of two person is redefined as (i) first is a girl AND second is a boy OR (ii) first is boy AND second is a girl OR (iii) first is a girl and second is a girl.
So the required probability:
= (8/17 x 9/16) + (9/17 x 8/16) + (9/17 x 8/16)
= 9/34 + 9/34 + 9/34
= 27/34.
ANSWER:D
Answer: D
Question: A man sells a horse for Rs.800 and loses something, if he had sold it for Rs.980, his gain would have been double the former loss. Find the cost price of the horse?
Options:
A)198
B)268
C)267
D)860
E)727
Rationale: CP = SP + 1CP = SP - g
800 + x = 980 - 2x
3x = 180 => x = 60
CP = 800 + 60 = 860
Answer: D
Answer: D
Question: At what price must an article costing Rs.95 be marked in order that after deducting 5% from the list price. It may be sold at a profit of 25% on the cost price?
Options:
A)130
B)125
C)145
D)135
E)144
Rationale: CP = 95
SP = 47.50*(125/100) = 118.125
MP*(95/100) = 118.125
MP = 125
Answer:B
Answer: B
Question: A tank of 425 litres capacity has been filled with water through two pipes, the
first pipe having been opened five hours longer than the second. If the first pipe
were open as long as the second, and the second pipe was open as long as the
first pipe was open, then the first pipe would deliver half the amount of water
delivered by the second pipe; if the two pipes were open simultaneously, the
tank would be filled up in 17 hours. How long was the second pipe open?
Options:
A)13
B)14
C)15
D)16
E)17
Rationale: Let the 1st and 2nd pipe be x and y respectively
and time = z hours
A/Q
y=2x (since first pipe would deliver half the amount of water
delivered by the second pipe)
(x+y)*17 =425
x+y =25
putting the value of y then we get
3x=25
x=25/3 and y =50/3
(z+5)25/3 + z(50/3) =425
from you can find z which = 15.3 so ans is 15
ANSWER:C
Answer: C
Question: If x > y and y > z, which of the following represents the greatest number T?
Options:
A) x − z
B) x − y
C) y − x
D) z − y
E) z − x
Rationale: Because x>y>z
thus T=x- z wil lbe greatest
Ans: A
Answer: A
Question: A, B, C, D, E are the five electronic shops in the Naza market, which have 20, 30, 60, 80 and 50 T. V . sets with them respectively, then the average number of T. V. sets in each shop is
Options:
A)24
B)48
C)50
D)60
E)None
Rationale: Answer
Average number of T. V. sets
= ( 20 + 30 + 60 + 80 + 50 ) / 5
= 48
Correct Option: B
Answer: B
Question: The cost of 3 pens and 5 pencils is Rs.240. Also the cost of one pen and one pencil is in the ratio of 5:1 respectively. What is the cost of one dozen pens?
Options:
A)Rs.200
B)Rs.720
C)Rs.300
D)Rs.150
E)None of these
Rationale: Explanation:
Let the cost of one pen is ‘5x’ and pencil is ‘x’
3 X 5x + 5x = Rs.240
15x + 5x = Rs.240
X = 240/20 = 12
:. Cost of 1 pen = 5x = 5 x 12 = 60
:. Cost of 12 pens, i.e. (one dozen) = 60 x 12 = Rs.720
Answer: Option B
Answer: B
Question: what is the minimum value of f(x) where
f(x)=(logax+logbx+logcx) and a>b>c>1..
Options:
A)3
B)2
C)1
D)4
E)5
Rationale: here a,b,c are base for log..they aren't multiplied with x.
so logax=logex/logea;
f(x)= (logx/loga + logx/logb+ logx/logc);
= logx * (1/loga + 1/logb + 1/logc);
for minimum value of f(x) log values must me max 1
=1*3
= 3
ANSWER:A
Answer: A
Question: Suppose you have access to a large vat of distilled water, several gallons large. You have two precise measuring pipettes, one to measure exactly 1/6 of an ounce and one to measure exactly 1/7 of an ounce. You can pour precisely measured amounts into a beaker, which initially is empty. You can use either pipette to remove distilled water from the vat or from the beaker and use either pipette to dispense water into either of those receptacles, but you cannot use either pipette to take any quantity of distilled water other than the amount for which it is designed. Which of the following represents, in ounces, a precise amount of distilled water you can transfer from the vat to the beaker?
I. 1/6
II. 1/7
III. 1/12
Options:
A)I only
B)III only
C)I and III only
D)1/42 and 13/42
E)I, II, and III
Rationale: Looking at the potential answer choices, 1/7 is immediately out as 7 is a prime that cannot be created from either 4 or 3.
1/6-1/7=1/42
1/6+1/7=13/42
Answer:D
Answer: D
Question: A trader mixes 80 kg of tea at 15 per kg with 20 kg of tea at cost price of 20 per kg. In order to earn a profit of 50%, what should be the sale price of the mixed tea?
Options:
A)23.75
B)22
C)20
D)19.2
E)None of these
Rationale: C.P. of mixture = 80×15+20×20 /80+20=16
∴ S.P. = (100+50)/100×16=24
Answer E
Answer: E
Question: Mala had a stock of 1200 balls in his bookshop. He sold 50 on Monday, 100 on Tuesday, 120 on Wednesday, 150 on Thursday and 200 on Friday. What percentage of the balls were not sold?
Options:
A)26.3%
B)42.5%
C)38.6%
D)48.3%
E)52.8%
Rationale: Let N be the total number of balls sold. Hence
N = 50+ 100 + 120 + 150 + 200= 620
Let M be the balls NOT sold
M = 1200 - N = 1200 - 620 = 580
Percentage
Balls not sold / total number of balls = 580/1200 = 0.483 =48.3%
correct answer D
Answer: D
Question: The difference between the compound interest compounded annually and simple interest for 2 years at 20% per annum is Rs.144. Find the principal?
Options:
A)3627
B)3622
C)3600
D)3618
E)3620
Rationale: P = 144(100/5)2
=> P = 3600
Answer: C
Answer: C
Question: Find the highest common factor of 36 and 84?
Options:
A)4
B)6
C)12
D)18
E)None of these
Rationale: 36=2^2*3^2; 84=2^2*3*7
H.C.F=2^2*3=12.
Correct Option: C
Answer: C
Question: There are 9 balls in a jar: 3 red, 2 blue and 4 green. If a single ball is drawn from the jar, what is the probability of that it is either blue or red?
Options:
A)1/12
B)1/4
C)5/9
D)2/3
E)3/4
Rationale: Blue + Red =5
Total number of balls is 3+2+4=9
So the answer is 5/19=5/9
Answer C
Answer: C
Question: A painting is painted on a cardboard 19 cm and 14 cm wide, such that there is a margin of 1.5 cm along each of its sides. Find the total area of the margin.
Options:
A)70 cm²
B)80 cm²
C)90 cm²
D)95 cm²
E)98 cm²
Rationale: Length of the cardboard = 19 cm
Breadth of the cardboard = 14 cm
Area of the cardboard = 19 × 14 cm² = 266 cm²
Length of the painting excluding the margin = [19 - (1.5 + 1.5)] cm = 16 cm
Breadth of the painting excluding the margin = 14 - (1.5 + 1.5) = 11 cm
Area of the painting excluding the margin = (16 × 11) cm² = 176 cm²
Therefore, area of the margin = (266 - 176) cm² = 90 cm²
ANSWER : C
Answer: C
Question: What is the measure of the angle Q made by the diagonals of the any adjacent sides of a cube.
Options:
A)30
B)45
C)60
D)75
E)90
Rationale: C.. 60 degrees
All the diagonals are equal. If we take 3 touching sides and connect their diagonals, we form an equilateral Triangle. Therefore, each angle would be Q=60.C
Answer: C
Question: A set consist of 2n-1 element. What is the number of subsets of this set which contain at most n-1 elements?
Options:
A)2^(2n-2)
B)2^(2n) - 2
C)2^(2n) -1
D)2^(2n)
E)2^(2n-1)
Rationale: I took n=2 so total terms becomes 2n-1 = 3 and at most you can take n-1 = 1 term.
so the ans should be 3, but if you put n=2 in all the equations you wont get the ans. That means they have considered empty set as well, thus the total number of subsets with at most one is a1,a2,a3,0
so ans is 4.
put n=2 in all the equations , you will get A=4 hence A.
Answer: A
Question: A man can swim in still water at 4.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
Options:
A)1.7
B)1.4
C)1.1
D)1.5
E)1.9
Rationale: M = 4.5
S = x
DS = 4.5 + x
US = 4.5 + x
4.5 + x = (4.5 - x)2
4.5 + x = 9 -2x
3x = 4.5
x = 1.5
Answer:D
Answer: D
Question: A man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is?
Options:
A)1 kmph
B)4 kmph
C)8 kmph
D)5 kmph
E)9 kmph
Rationale: DS = 6
US = 4
S = ?
S = (6 - 4)/2 = 1 kmph
Answer: A
Answer: A
Question: A customer pays 40 dollars for a coffee maker after a discount of 20 dollars
What is the original price of the coffe maker?
Options:
A)A)$50
B)B)$60
C)C)$70
D)D)$80
E)E)$90
Rationale: Let x be the original price.
x - 20 = 40
x - 20 + 20 = 40 + 20
x + 0 = 60
x = 60
correct answer is B)$60
Answer: B
Question: What is the smallest integer c for which 27^c> 3^24?
Options:
A)7
B)8
C)9
D)10
E)12
Rationale: 27^c> 3^24
Converting into the same bases:
27^c> 27^8
Therefore for the equation to hold true, c > 8 or c= 9
Option C
Answer: C
Question: Each of the 42 points is placed either inside or on the surface of a perfect sphere. If 65% or fewer of the points touch the surface, what is the maximum number of segments which, if connected from those points to form chords, could be the diameter of the sphere?
Options:
A)7
B)11
C)13
D)23
E)38
Rationale: Maximum number of points on the surface is 65%*42 = 27.3 ... or 27 since it has to be an integer
Now note that if two points form a diameter, they cannot be part of any other diameter.
So in the best case we can pair up the points
We have 27 points, so at best we can form 13 pairs (26).
So, answer is (C)
Answer: C
Question: In how many different ways can 4 physics, 2 math, and 2 chemistry books be arranged in a row so that all books of the same subject are together?
Options:
A)378
B)432
C)456
D)524
E)576
Rationale: Let's think of each subject as a group so there are 3 groups.
The number of ways to arrange these 3 groups is 3!
Within each subject the books can be re-arranged.
So we need to multiply 3! by 4!*2!*2! which is 3!*4!*2!*2! = 576
The answer is E.
Answer: E
Question: Even after reducing the marked price of a transistor by Rs. 32, a shopkeeper makes a profit of 15%. If the cost price be Rs.320, what percentage of profit would he have made if he had sold the transistor at the marked price?
Options:
A)18 %
B)20 %
C)25 %
D)30 %
E)None
Rationale: Sol.
C.P. = Rs. 320, Profit = 15%
S.P. Rs. [115/100 * 320] = Rs. 368. Marked price = Rs. (368 + 32) = Rs. 400.
∴ Required profit% = [80/320 * 100] % = 25%.
Answer C
Answer: C
Question: A ball is bought for Rs.400 and sold at a gain of 40% find its selling price?
Options:
A)A)Rs.560/-
B)B)Rs.490/-
C)C)Rs.500/-
D)D)Rs.520/-
E)E)Rs.540/-
Rationale: 100 % ------> 400 (100 * 4 = 400)
140 % ------> 560 (140 * 4 = 560)
Selling price = Rs.560/-
A
Answer: A
Question: The population of a city increases @ 4% p.a. There is an additional annual increase of 4% of the population due to the influx of job seekers, find the % increase in population after 2 years ?
Options:
A)14.64%
B)15.64%
C)16.64%
D)17.64%
E)18.64%
Rationale: total annual increament in population = 4+4 = 8%
let the population be x
Population after 2 years = 1.08x +.0864x
Population increase = 1.08x + .0864x - x
%increase = ((1.08x + .0864x - x)/x )*100
= ( 1.08 + .0864 - 1 )*100
=.1664*100
=16.64%
ANSWER:C
Answer: C