divelab/Sys2Bench huggingface dataset:
Question: If n is a positive integer and n^2 is divisible by 264, then the largest positive integer that must divide n is
Options:
A)6
B)12
C)24
D)36
E)48
Rationale: The question asks aboutthe largest positive integer that MUST divide n, not COULD divide n. Since the least value of n for which n^2 is a multiple of 72 is 12 then the largest positive integer that MUST divide n is 12.
Complete solution of this question is given above. Please ask if anything remains unclear.
I spent a few hours on this one alone and I'm still not clear. I chose 12 at first, but then changed to 48.
I'm not a native speaker, so here is how I interpreted this question:the largest positive integer that must divide n=the largest positive factor of n. Since n is a variable (i.e. n is moving), so is its largest factor. Please correct if I'm wrong here.
I know that if n = 12, n^2 = 144 = 2 * 72 (satisfy the condition). When n = 12, the largest factor of n is n itself, which is 12. Check: 12 is the largest positive number that must divide 12 --> true
However if n = 48, n^2 = 48 * 48 = 32 * 72 (satisfy the condition too). When n = 48, the largest factor of n is n itself, which is 48. Check: 48 is the largest positive number that must divide 48 --> true
So, I also notice that the keyword isMUST, notCOULD. The question is, why is 48 notMUST divide 48, but instead onlyCOULD divide 48? I'm not clear right here. Why is 12MUST divide 12? What's the difference between them?
Only restriction we have on positive integer n is that n^2 is divisible by 72. The least value of n for which n^2 is divisible by 72 is 12, thus nmustbe divisible by 12 (n is in any case divisible by 12). For all other values of n, for which n^2 is divisible by 72, n will still be divisible by 12. This means that n is always divisible by 12 if n^2 is divisible by 72.
Now, ask yourself: if n=48, is n divisible by 48? No. So, n is not always divisible by 48.
E
Answer: E
Question: A car travels uphill at 30 km/hr and downhill at 40 km/hr. It goes 100 km uphill and 50 km downhill. Find the average speed of the car?
Options:
A)32kmph
B)33kmph
C)34kmph
D)35kmph
E)36kmph
Rationale: avg speed=total distance/total time.
total distance traveled=100+50=150km;
time taken for uphill journey=100/30=10/3;
time taken for down hill journey=50/40=5/4;
avg speed=150/(10/3+5/4)=33kmph
ANSWER:B
Answer: B
Question: In a certain pond, 80 fish were caught, tagged, and returned to the pond. A few days later, 80 fish were caught again, of which 2 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what`s the approximate number of fish in the pond?
Options:
A)400
B)625
C)1250
D)3200
E)10 000
Rationale: The percent of tagged fish in the second catch is 2/80*100 = 2.5%.
We are told that 2.5% approximates the percent of tagged fish in the pond. Since there are 80 tagged fish, then we have 0.025x = 80 --> x = 3,200.
Answer: D.
Answer: D
Question: An empty fuel tank to a car was filled with A type of petrol. When the tank was half empty, it was filled with B type of petrol. Again when the tank was half empty, it was filled with A type of petrol. When the tank was half empty again,it was filled
Options:
A)50%
B)40%
C)33.5%
D)37.5%
E)None of these
Rationale: Now, amount of petrol A = A⁄4 + A⁄8 = 3A⁄8
∴ required% = 3A⁄ (8 × A) × 100 = 37.50%
Answer D
Answer: D
Question: The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 10 and 12. The larger of the two numbers is:
Options:
A)276
B)295
C)322
D)345
E)354
Rationale: Clearly, the numbers are (23 x 10) and (23 x 12).
Larger number = (23 x 12) = 276.
Answer: Option A
Answer: A
Question: A student has to read one history book of 200 pages and one science book of 300 pages . At the end of first day, if 57 percent of the pages in history book and 42 percent of the pages in science book were read, what percent of the total number of pages were read ?
Options:
A) 45.5%
B) 46.5%
C) 48.0%
D) 49.5%
E) 51.0%
Rationale: 57% of 200 pages in history book, hence 0.57*200 = 114 pages read.
42% of 300 pages in science book, hence 0.42*300 = 126 pages read
Thus (total read)/(total) = (114 + 126)/(200 + 300) = 240/500 =
48% pages read
Answer: C.
Answer: C
Question: The population of a town is 8000. It decreases annually at the rate of 20% p.a. What will be its population after 2 years?
Options:
A)4300
B)4500
C)5120
D)5230
E)5366
Rationale: Formula :
( After =100 denominator
Ago = 100 numerator)
8000 × 80/100 × 80/100 = 5120
C
Answer: C
Question: A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 900 m long?
Options:
A)200 Sec
B)210 Sec
C)167 Sec
D)197 Sec
E)179 Sec
Rationale: L = S*T
S= 1200/120
S= 10 m/Sec.
Total length (D)= 2100 m
T = D/S
T = 2100/10
T = 210 Sec
Answer: B
Answer: B
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is?
Options:
A)3/7
B)3/2
C)3/5
D)3/6
E)3/1
Rationale: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x meters, and length of the second train = 17 y meters. (27 x + 17 y) / (x + y) = 23 ==> 27 x + 17 y = 23 x + 23 y ==> 4 x = 6 y ==> x/y = 3/2.
Answer:B
Answer: B
Question: The base of a parallelogram is twice its height. If the area of the parallelogram is 72 sq. cm, find its height
Options:
A)6
B)8
C)9
D)9
E)2
Rationale: Explanation:
Let the height of the parallelogram be x. cm. Then, base = (2x) cm.
Answer: A) 6
Answer: A
Question: A and B can do a work in 20days, B and C can do it in 30days; A,B and C together can finish it in 40days. A and C together will do it in?
Options:
A)25days
B)30days
C)20days
D)15days
E)10days
Rationale: A+B+C 1day work = 1/40
A+B 1day work = 1/20
B+C 1day work = 1/30
A+C 1day work = 2*1/40 - 1/20+1/30 = 1/30
A and C together will do the work in 30 days.
Answer is B
Answer: B
Question: Which of the following describes all values of x for which 25–x^2 >= 0?
Options:
A) x >= 1
B) x <= –1
C) 0 <= x <= 1
D) x <= –1 or x >= 1
E) –5 <= x <= 5
Rationale: 25 - x^2 >=0
means x^2 - 25 <=0
=> (x-5)(x+5) <= 0
=> -5 <= x <= 5
Answer - E
Answer: E
Question: A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 4 employees to 2 different offices?
Options:
A)5
B)16
C)7
D)8
E)9
Rationale: Ans. Each employee can go into any of the two offices. Thus we have
=> 2 * 2 * 2 * 2= 16
Answer : B
Answer: B
Question: At what rate percent on simple interest will Rs.750 amount to Rs.900 in 5 years?
Options:
A)5
B)4
C)5 1/2
D)7
E)8
Rationale: 150 = (750*5*R)/100
R = 4%
ANSWER B
Answer: B
Question: The length of a rectangle is increased by 15% and its breadth is decreased by 20%. What is the effect on its area?
Options:
A)1288
B)1299
C)1000
D)10000
E)9200
Rationale: 100 * 100 = 10000
115 * 80 = 9200
Answer: E
Answer: E
Question: find two integers, neither of which ends in a zero, and whose product is exactly 10,000,000
Options:
A)64 and 15,625
B)60 and 15,625
C)64 and 15,620
D)64 and 15,635
E)128 and 78,125
Rationale: 10,000,000=10^7
=10x10x10x10x10x10x10
=(2x5)x(2x5)x(2x5)x(2x5)x(2x5)x(2x5)x(2x5)
=(2^7)x(5^7)
= 128x78125
so the numbers are 128 and 78,125
ANSWER:E
Answer: E
Question: The prices for five dresses Susan was considering were $60, $125, $80, $70 and $x. If the median price was $5 lower than the average (arithmetic mean) price, which of the following could be $x?
Options:
A)$80
B)$85
C)$90
D)$95
E)$100
Rationale: Look at the options available
Value of x seems to $80 < = $x < = $100
A. $80
B. $85
C. $90
D. $95
E. $100
So position of $x is fourth
$60 , $70 , $80 , $x , $125
Median = $80
Median price was $5 lower than the average, so average = $85
$60 + $70 + $80 + x + $125 = $425
$x = $90 = Answer = C
Answer: C
Question: How many minimum number's of whole square slabs are required for paving the floor 12.96 meters long and 3.84 meters side?
Options:
A)216
B)192
C)108
D)256
E)356
Rationale: HCF of 384, 1296 = 48
48 * 48 * x = 384 * 1296
x = 216
ANSWER:A
Answer: A
Question: A football player scores 2 goals in his fifth match thus increasing his average goals score by 0.3. The total number of goals in his 5 matches would be
Options:
A)4
B)6
C)8
D)10
E)12
Rationale: While this question can be solved with a rather straight-forward algebra approach (as the other posters have noted), it can also be solved by TESTing THE ANSWERS. One of those numbers MUST be the total number of goals...
From a tactical standpoint, it's best to TEST either Answer B or Answer D, so if the answer is not correct, then you would have a gauge for whether you should gohigherorlowerwith your next TEST.
Here, I'll start with Answer A = 4 goals
If....
Total goals = 4 goals
5th game = 2 goals
1st 4 games = 2 goals
Avg. for 1st 4 games = 2/4 = 0.5 goal/game
Avg. for all 5 games = 4/5 =0.8 goals/game
This is an EXACT MATCH for what we're told in the prompt, so Answer A MUST be the answer.
Answer: A
Question: In the coordinate plane, points (x, 3) and (5, y) are on line k. If line k passes through the origin and has slope 3/5, then x + y =
Options:
A)9
B)8
C)7
D)5
E)6
Rationale: Line k passes through the origin and has slope 3/5 means that its equation is y=3/5*x.
Thus: (x, 3)=(3, 5) and (5, y) = (3, 5) --> x+y=3+5=8.
Answer: B
Answer: B
Question: The value of x + x(xx) when x = 4
Options:
A)A) 60
B)B) 66
C)C)68
D)D) 56
E)E) 64
Rationale: x + x(xx)
Put the value of x = 4 in the above expression we get,
4 + 4(44)
= 4 + 4(4 Ã— 4)
= 4 + 4(16)
= 4 + 64
= 68 The answer is (C)
Answer: C
Question: If the average (arithmetic mean) of a list of numbers is 12 and the standard deviation of that list of numbers is 1.3, then which of the following numbers is more than two standard deviations from the mean?
I. 14.7
II. 15.3
III. 9.5
Options:
A)I only
B)I and II only
C)II only
D)III only
E)I and III only
Rationale: Mean = 12
SD = 1.3
2 SD above mean = 12+2*1.3 = 14.6
2 SD below mean = 12-2*1.3 = 9.4
only 9.5 lies in the range of 2SD from mean
Answer: Option B
Answer: B
Question: The sum of the present age of Henry and Jill is 41. What is their present ages if 7 years ago Henry was twice the age of Jill?
Options:
A)and 25
B)and 24
C)and 22
D)and 29
E)of these
Rationale: Let the age of Jill 7 years ago be x, age of Henry be 2x
x+7 + 2x+7 = 41
x = 9
Present ages will be 16 and 25
Answer : A
Answer: A
Question: Which of the following options is the possible total number of people in a hall given that the number of people is a multiple of both 4 and 20.?
Options:
A)28
B)60
C)32
D)36
E)44
Rationale: the number of people are a multiple of both 7 and 13, so it must be divisible by 7 and 13.
using the elimination method look for a number that is both divisible by 7 and 13,
of all the options only 60 is divisible by 4 and 20.
[ 60/4=15 and 60/20=3]
answer :B
Answer: B
Question: The length of the bridge, which a train 145 metres long and travelling at 45 km/hr can cross in 30 seconds, is:
Options:
A)200 m
B)230 m
C)245 m
D)250 m
E)270 m
Rationale: Let the length of the bridge:L
The equation now is L+145/12.5m/s(45km/hr or12.5m/s)=30
Solving, L =230m
ANSWER:B
Answer: B
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are picked at random, what is the probability that they are either blue or yellow?
Options:
A)3/22
B)4/21
C)2/21
D)1/14
E)None of these
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability that both marbles are blue = ³C₂/¹⁵C₂ = (3 * 2)/(15 * 14) = 1/35
Probability that both are yellow = ²C₂/¹⁵C₂ = (2 * 1)/(15 * 14) = 1/105
Probability that one blue and other is yellow = (³C₁ * ²C₁)/¹⁵C₂ = (2 * 3 * 2)/(15 * 14) = 2/35
Required probability = 1/35 + 1/105 + 2/35
= 3/35 + 1/105 = 1/35(3 + 1/3)
= 10/(3 * 35) = 2/21
ANSWER:C
Answer: C
Question: There are five same model cars parked in the same direction in parking. If 3 cars are red, 1 is black and 1 is green, in how many ways they can be arranged in the parking?
Options:
A)10 ways.
B)20 ways.
C)30 ways.
D)40 ways.
E)50 ways.
Rationale: 5!/(3!*1!*1!) = (5*4*3*2*1)/(3*2*1) = 120/6 = 20 ways.
ANSWER:B
Answer: B
Question: A constructor estimates that 10 people can paint Mr khans house in 4 days. If he uses 5 people instead of 10,how long will they take to complete the job?
Options:
A)10
B)4
C)5
D)8
E)6
Rationale: Explanation:
Use formula For a work Members Ã— days = constant
10 Ã— 4 = 5Ã— a
a = 8
so answer is 8 days
Answer: D
Answer: D
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train?
Options:
A)150
B)277
C)299
D)662
E)181
Rationale: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 9 = 150 meter
Answer: A
Answer: A
Question: 1/2+[(2/3*3/8)+4]-3/16=
Options:
A)29/16
B)61/16
C)15/16
D)9/13
E)0
Rationale: 1/2+[(2/3*3/8)+4]-3/16=
1/2+[(1/4)+4]-3/16=
1/2+[17/4]-3/16=
8/16 + 68/16 - 3/16 = 61/16
B
Answer: B
Question: Excluding stoppages, the average speed of a bus is 60 km/hr and including stoppages, the average speed of the bus is 40 km/hr. For how many minutes does the bus stop per hour?
Options:
A)18 min
B)17 min
C)19 min
D)20 min
E)21 min
Rationale: In 1hr, the bus covers 60 km without stoppages and 40 km with stoppages.
Stoppage time = time take to travel (60 - 40) km i.e 20 km at 60 km/hr.
stoppage time = 20/60 hrs =20 min.
Answer: D
Answer: D
Question: A toothed wheel of diameter 50 cm is attached to a smaller wheel of diameter 30 cm. How many revolutions will the smaller wheel make when the larger one makes 15 revolutions?
Options:
A)18
B)20
C)22
D)25
E)27
Rationale: Solution
Distance covered by smaller wheel in 1 revolution = (2Π x 15) cm
= (30 Π) cm.
Distance covered by larger wheel in 1 revolution = (2Π x 25) cm
= (50 Π) cm.
Let k x 30 Π = 15 x 50 Π.
Then, k = [15 x 50 Π / 30 Π] = 25.
∴ Required number of revolutions = 25.
Answer D
Answer: D
Question: In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 46, the dividend is:
Options:
A)5336
B)5340
C)5342
D)5344
E)5346
Rationale: Divisor = (5 * 46) = 230
= 10 * Quotient = Divisor
=> Quotient = 230/10 = 23
Dividend = (Divisor * Quotient) + Remainder
Dividend = (230 * 23) + 46 = 5336.
A
Answer: A
Question: To apply for the position of photographer at a local magazine, a photographer needs to include four or five photos in an envelope accompanying the application. If the photographer has pre-selected seven photos representative of her work, how many choices does she have to provide the photos for the magazine?
Options:
A)48
B)50
C)52
D)54
E)56
Rationale: 7C4 + 7C5 = 35 + 21 = 56
The answer is E.
Answer: E
Question: The cost of the paint is Rs. 36.50 per kg. If 1 kg of paint covers 16 square feet, how much will it cost to paint outside of a cube having 8 feet each side.
Options:
A)Rs. 850
B)Rs. 860
C)Rs. 876
D)Rs. 886
E)None of these
Rationale: Explanation:
We will first calculate the Surface area of cube, then we will calculate the quantity of paint required to get answer.
Here we go,
Surface area =6a2=6∗8(2)=384sq feet
Quantity required =38416=24kg
Cost of painting =36.50∗24=Rs.876
Option C
Answer: C
Question: The exam scores of all 500 students were recorded and it was determined that these scores were normally distributed. If Jane's score is 0.8 standard deviation above the mean, then how many, to the nearest unit, students scored above Jane?
Options:
A)394
B)250
C)400
D)106
E)None
Rationale: Solution
Let m be the mean and s be the standard deviation and find the z score.
z = (x - m) /s = (0.8 s + m - m) / s = 0.8
The percentage of student who scored above Jane is (from table of normal distribution).
1 - 0.7881 = 0.2119 = 21.19%
The number of student who scored above Jane is (from table of normal distribution).
21.19% 0f 500 = 106
Answer D
Answer: D
Question: A jeep takes 7 hours to cover a distance of 420 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
Options:
A)48 Kmph
B)52 Kmph
C)40 Kmph
D)63 Kmph
E)65 Kmph
Rationale: Time = 7
Distance = 420
3/2 of 7 hours = 7 * 3/2 = 10.5 Hours
Required speed = 420/10.5 = 40 Kmph
C)
Answer: C
Question: What will be the fraction of 12.5%
Options:
A)1/4
B)1/5
C)1/10
D)1/8
E)None of above
Rationale: Explanation:
It will 12.5*1/100 = 1/8
Answer: Option D
Answer: D
Question: What comes next?
2, 7, 22, 67, 202, ?
Options:
A)765
B)345
C)798
D)607
E)567
Rationale: D
607
x 3 + 1 at each stage.
Answer: D
Question: What is the median of a set of consecutive integers if the sum of nth number from the beginning and nth number from the end is 120?
Options:
A)60
B)25
C)50
D)75
E)100
Rationale: Surprisingly no one answered this easy one.
property of a set of consecutive integerz.
mean=median=(first element+last element)/2 = (second element+last but one element)/2 =(third element+ third last element)/2 Etc. Etc.
So mean=median=120/2=60
Answer is A
Answer: A
Question: If a farmer sells 5 of his goats, his stock of feed will last for 4 more days than planned, but if he buys 10 more goats, he will run out of feed 3 days earlier than planned. If no goats are sold or bought, the farmer will be exactly on schedule. How many goats does the farmer have?
Options:
A)12
B)20
C)48
D)55
E)60
Rationale: Say farmer has n goat and he is good for d days.:-
We have 3 equations given in question:-
(n-5) * d+4 =(n+10) *(d-3) = n * d
Solving these: (You can solve 1st and 3rd and 2nd and 3rd together)
We get:
10d-3n=30
4n-5d =20
=> n=20
Ans B it is!
Answer: B
Question: If the simple interest on a sum of money for 2 years at 5% per annum is Rs.50, what will be the compound interest on same values
Options:
A)Rs.51.75
B)Rs 51.50
C)Rs 51.25
D)Rs 51
E)None of these
Rationale: Explanation:
S.I.=P∗R∗T/100P
=50∗100/5∗2=500
Amount=500(1+5100)2
500(21/20∗21/20)=551.25
C.I.=551.25−500=51.25
Option C
Answer: C
Question: The mean of 50 observations is 200. But later he found that there is decrements of 6 from each observations. what is the the updated mean is ?
Options:
A)165
B)185
C)190
D)198
E)194
Rationale: 194
Answer is E
Answer: E
Question: If log 27 = 1.431, then the value of log 9 is:
Options:
A)0.954
B)0.93
C)0.933
D)0.96
E)0.974
Rationale: If log 27 = 1.431, then the value of log 9 is:
A.	0.934
B.	0.945
C.	0.954
D.	0.958
Answer: Option C
Explanation:
log 27 = 1.431
log (33 ) = 1.431
3 log 3 = 1.431
log 3 = 0.477
log 9 = log(32 ) = 2 log 3 = (2 x 0.477) = 0.954.
ANSWER A
Answer: A
Question: Whats the reminder when 65,985,241,545,898,754,582,556,898,522,454,889 is divided by 16
Options:
A)1
B)7.
C)2.
D)3
E)9
Rationale: A number ending in a 0 is divisible by 2. A number ending in 2 zeroes is divisible by 4. A number ending in 3 zeroes is divisible by 8. A number ending in 4 zeroes in divisible by 16.
Given the obscene number, you should immediately be convinced that you will need to focus on a very small part of it.
65,985,241,545,898,754,582,556,898,522,454,889 = 65,985,241,545,898,754,582,556,898,522,450,000+4,889
The first number is divisible by 16. You just have to find the remainder when you divide 5287 by 16. That will be the remainder when you divide the original number by 16.
4889/16 gives remainder 9.
Answer (E)
Answer: E
Question: Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes and 10 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P, Q and R respectively. What is the proportion of solution R in the liquid in the tank after 3 minutes?
Options:
A)6/15
B)6/11
C)6/14
D)6/12
E)6/13
Rationale: Part filled by (A + B + C) in 3 minutes = 3(1/30 + 1/20 + 1/10) = 11/20
Part filled by C in 3 minutes = 3/10
Required ratio = 3/10 * 20/11 = 6/11
Answer: B
Answer: B
Question: Kevin, David, and Catherine each try independently to solve a problem. If their individual probabilities for success are 1/2, 2/9 and 3/4, respectively, what is the probability all three will solve the problem?
Options:
A)1/12
B)1/8
C)1/3
D)1/4
E)1/6
Rationale: P(Kevin will solve)= 1/2
P(David will solve)= 2/9
P(Catherine will solve) = 3/4
P= (1/2)*(2/9)*(3/4) = 6/72 = 1/12
Answer:A
Answer: A
Question: A and B enter into partnership with capital as 7:9. At the end of 8 months, A withdraws. If they receive the profits in the ratio of 8:9 find how long B's capital was used?
Options:
A)6 months
B)8 months
C)10 months
D)7 months
E)9 months
Rationale: 7 * 8 : 9 * x = 8:9 => x= 7
ANSWER:D
Answer: D
Question: A is a working partner and B and C is a sleeping partner in a business. A puts in 45,000 and B 60,000 and C 75000. A gets 20000% of the profit for managing the business, and the rest is divided in proportion to their capitals. Find the share of A in profit of 30000.
Options:
A)9000
B)15000
C)14000
D)10000
E)None of these
Rationale: The amount A gets for managing
= 20% of Rs. 30000 = 6000
Remaining profit = 30000 – 6000 = 24000
This is to be divided in the ratio 3 : 4 : 5.
Share of A = 3/12 of 24000 = 6000
⇒ Total share of A = 6000 + 6000 = 12000.
Answer E
Answer: E
Question: A shopkeeper sold a TV set for 17940, at a discount of 8 % and gained 19.6 %.If no discount is allowed, what will be his gain per cent?
Options:
A)25 %
B)36.4 %
C)24.8 %
D)Can’t be determined
E)None of these
Rationale: If no discount is given,selling price of TV
= 17940 × 100⁄92 = 19500
Cost price of TV = 17940×100/119.60x15000
Gain % = 19500−15000/15000×100= 30 %
Answer E
Answer: E
Question: Which of the following is equal to 10^-(-2)^3?
Options:
A)1/(10^8)
B)1/(10^9)
C)1/(10^5)
D)1/(10^4)
E)1/(10^3)
Rationale: 10^-(-2)^3 => 10^-(-2^3) => 10^-(8) = 1/(10^8)
Answer : A
Answer: A
Question: Find the odd man out. 1, 5, 11, 17, 23, 29
Options:
A)29
B)17
C)11
D)1
E)2
Rationale: Explanation :
All given numbers except 1 are prime numbers.
One is not a prime number because it does not have two factors. It is divisible by only 1.. Answer : Option D
Answer: D
Question: Pane and Thomas are among the 8 people from which a committee of 4 people is to be selected. How many different possible committees of 4 people can be selected from these 8 people if at least one of either Pane or Thomas is to be selected?
Options:
A)28
B)46
C)55
D)63
E)70
Rationale: Ans:C
Solution:
P+T+6 = total 8 ,
we need to select at least one of the P and T or both= total 4 out of 8 - 4 out of 6
8C4 - 6C4
=55
Answer: C
Question: If each digit in the set A = {1, 2, 3, 4, 5, 6, 7, 8} is used exactly once, in how many ways can the digits be arranged?
Options:
A)36,100
B)38,210
C)40,320
D)42,430
E)44,540
Rationale: 8! = 40,320
The answer is C.
Answer: C
Question: A painting at an art gallery is framed such that the area of the square frame is 1/5 the area of the painting itself. If the diagonal line connecting corners of the frame has a length of 12, what is the area of the painting inside the frame?
Options:
A)10
B)20
C)30
D)40
E)60
Rationale: Suppose side of the painting(which is a square) is a and side of the outer square(painting+frame) is b
Area of painting = a^2 and we know that the area of the frame is (1/5) of that of the painting so
Area of frame = (1/5) * a^2
Area of Frame + Painting = a^2 + (1/5)*a^2 = (6/5)*a^2 which is equal to b^2
Line connecting the corners of the frame is the diagonal of the outer square which is equal to b*sqrt2
so, b * sqrt2 = 12
so, b = 6 * sqrt2
b^2 = 72
we know that b^2 = (6/5)*a^2
so, a^2 = (5/6)*b^2 = (5/6)*72 = 60
And area of painting = a^2 = 60
So, answer will be E.
Answer: E
Question: The average age of a group of persons going for picnic is 16 years. Twenty new persons with an average age of 15 years join the group on the spot due to which their average age becomes 15.5 years. The number of persons initially going for picnic is?
Options:
A)10
B)20
C)37
D)26
E)22
Rationale: Let the initial number of persons be x. Then,
16x + 20 * 15 = 15.5 (x + 20) <=> 0.5x
= 10 <=> x = 20.
Answer: B
Answer: B