divelab/Sys2Bench huggingface dataset:
Question: Mr. Shah decided to walk down the escalator of a tube station. He found Â that if he walks down 26 steps, he requires 30 seconds to reach the bottom. However, if he steps down 34 stairs he would only require 18 seconds to get to the bottom. If the time is measured from the moment the top step begins Â to descend to the time he steps off the last step at the bottom, find out the height of the stair way in steps?
Options:
A)44
B)45
C)46
D)47
E)48
Rationale: (s1*t2~s2*t1)/(t2~t1)=(26*18~34*30)/(18~30)=46
ANSWER:C
Answer: C
Question: If a certain sample of data has a mean of 35.0 and a standard deviation of 2.0, which of the following pairs contain two values that are each at least 2.5 standard deviations from the mean?
Options:
A)(14.0; 16.5)
B)(14.5; 21.0)
C)(14.0; 26.5)
D)(16.5; 26.0)
E)(28.0; 46.5)
Rationale: 2.5 standard deviation equals to 2.5*2=5;
2.5 standard deviations from the mean, so5 points, from the mean is the range from {mean-5} to {mean+5}, so from 30 40.
The correct answer choice must cover all this range: only answer choice E does this.
Answer:E.
Answer: E
Question: Three people each took 3 tests. If the ranges of their scores in the 3 practice tests were 17, 28 and 35, what is the minimum possible range in scores of the three test-takers?
Options:
A)a 17
B)b) 28
C)c) 35
D)d) 45
E)e) 80
Rationale: It is finding the minimum range between all their scores, if all test taker scores are between 0 and maximum range we will have:
A- 0 and 17
B- 0 and 28
therefore the minimum range is 35, it cant be any lower however you play with the numbers.
B
Answer: B
Question: If (a-b) is 6 more than (c+d) and (a+b) is 3 less than (c-d), then (a-c)
Options:
A)0.5
B)1.5
C)2.5
D)1.0
E)2.0
Rationale: (a-b)-(c-d)=6 and (c-d)-(a+b)=3
(a-c)-(b+d)=6 and (c-a)-(b+d)=3
(b+d)= (a-c)-6 and (b+d)=3-(c-a)
2(a-c)=3
(a-c)=1.5
ANSWER B 1.5
Answer: B
Question: Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 90 kmph and 72 kmph. After how much time will the trains meet?
Options:
A)27/7 sec
B)20/9 sec
C)33/7 sec
D)21/7 sec
E)32/7 sec
Rationale: They are moving in opposite directions, relative speed is equal to the sum of their speeds.
Relative speed = (90 + 72)*5/18 = 9*5 = 45 mps.
The time required = d/s = 100/45 = 20/9 sec.
Answer : B
Answer: B
Question: What will be the compound interest on a sum of Rs. 26000 after 3 years at the rate of 12% p.a.?
Options:
A)s.10123.22
B)s.10823.20
C)s.10123.20
D)s.10123.29
E)s.10528.13
Rationale: Explanation:
Amount = [26000 * (1 + 12/100)3]
= 26000 * 28/25 * 28/25 * 28/25 = Rs. 35123.20
C.I. = (36528.13 - 26000) = Rs.10528.13
Answer:E
Answer: E
Question: In 1970 there were 8,902 women stockbrokers in the United States. By 1978 the number had increased to 24,947. Approximately what was the percent increase?
Options:
A) 45%
B) 125%
C) 145%
D) 150%
E) 180%
Rationale: The percent increase is (24947-8902)/8902=16045/8902=1.80
So the approximate answer is E
Answer: E
Question: Find the invalid no.from the following series 13, 17, 22, 26, 31, 38
Options:
A)13
B)38
C)40
D)37
E)25
Rationale: The differences between two successive terms from the beginning are 4, 5, 4, 5, 4, 5. So, 38 is wrong.
Answer : B
Answer: B
Question: A man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
Options:
A)45
B)60
C)75
D)80
E)90
Rationale: Let number of notes of each denomination be x.
Then x + 5x + 10x = 480
16x = 480
x = 30.
Hence, total number of notes = 3x = 90.
answer :E
Answer: E
Question: In some quantity of ghee, 60% is pure ghee and 40% is vanaspati. If 10kg of pure ghee is added, then the strength of vanaspati ghee becomes 20%. The original quantity was?
Options:
A)10
B)15
C)20
D)18
E)22
Rationale: Let the original quantity be x
then, vanaspati ghee in xkg = 40x/100 kg= 2x/5kg
(2x/5)/(x+10) = 20/100
2x/(5x+50) = 1/5
x = 10
Answer is A
Answer: A
Question: What will come in place of the x in the following Number series? 25, 100, x, 1600, 6400
Options:
A)2345
B)3579
C)6400
D)6799
E)8646
Rationale: (C)
25 x 4 = 100, 100 x 4 = 400, 400 x 4 = 1600, 1600 x 4 = 6400.
Answer: C
Question: If 6x = 8y = 10z, then what is a possible sum of positive integers x, y, and z?
Options:
A)52
B)58
C)84
D)94
E)168
Rationale: 6x = 8y = 10z
3x = 4y = 5z
3(4*5) = 4(3*5) = 5(3*4)
Addition = 20+15+12 = 47
Answer would be multiple of 47 which is 94
Answer :D
Answer: D
Question: 2^(24) + 2^(25) + 2^(26) + ... + 2^(43) + 2^(44) =
Options:
A)2^24(2^(21)-1)
B)2^24(2^(20)-1)
C)2^24(2^(23)-1)
D)2^21(2^(20)-1)
E)2^21(2^(21)-1)
Rationale: 2^(24) + 2^(25) + 2^(26) + ... + 2^(43) + 2^(44) =
2^(24)*(1+2+4+...+2^(20)) =
2^(24)*(2^(21) - 1)
The answer is A.
Answer: A
Question: David pays the simple interest on an amount he borrowed from his boss, if interest rate is halved, then simple interest is multiplied by
Options:
A)2
B)1
C)1/4
D)1/2
E)4
Rationale: Formula for SI = (P*T*R)/100
SI = Simple Interest
P = Principle Amount
T = Time
R = Interest Rate
Say r=2 => SI1 = 2*SI
when r=1; SI2 = SI
SI2 = 1/2*SI1.
Answer : D
Answer: D
Question: Three people have $30, $72, and $98, respectively. If they pool their money then redistribute it among them, what is the maximum value for the median amount of money?
Options:
A)$72
B)$85
C)$98
D)$100
E)$202
Rationale: Solution -
Total money distributed is $200. In order to maximize median, one person has to accept $0 and remaining two people share $100 each. Hence median is $100.
ANS D
Answer: D
Question: If the length of a rectangle is halved and its breadth is tripled, what is the percentage change in its area?
Options:
A)40%
B)30%
C)50%
D)70%
E)65%
Rationale: C
50%
Length is halved.
i.e., length is decreased by 50%
Breadth is tripled
i.e., breadth is increased by 200%
Change in area
=(−50+200−(50×200/100))%=50%
i.e., area is increased by 50%
Answer: C
Question: What is value of ((2^5)*(9^2))/((8^2)*(3^5))=?
Options:
A)1/6
B)1/3
C)2/3
D)1/4
E)4
Rationale: =>((2^5)*((3^2)^2)/((2^3)^2)*(3^5))
=>((2^5)*(3^4))/((2^6)*(3^5))
=>1/(2*3)
=>1/6
Option A is answer
Answer: A
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
Options:
A)120 metres
B)180 metres
C)324 metres
D)150 metres
E)175 metres
Rationale: Explanation:
Speed= 60 x	5/18	m/sec	= 50/3	m/sec.
Length of the train = (Speed x Time).
Length of the train = 50/3	x 9	m = 150 m.
ANSWER IS D
Answer: D
Question: A can do a piece of work in 4 hours; B and C together can do it in 3 hours, which A and C together can do it in 2 hours. How long will B alone take to do it?
Options:
A)1/19
B)1/11
C)1/12
D)1/17
E)1/14
Rationale: A's 1 hour work = 1/4;
(B + C)'s 1 hour work = 1/3;
(A + C)'s 1 hour work = 1/2
(A + B + C)'s 1 hour work = (1/4 + 1/3) = 7/12
B's 1 hour work = (7/12 + 1/2) = 1/12
B alone will take 12 hours to do the work.
Answer: C
Answer: C
Question: Three 6 faced dice are thrown together. The probability that all the three show the same number on them is ?
Options:
A)1/37
B)1/36
C)1/31
D)1/33
E)1/32
Rationale: It all 3 numbers have to be same basically we want triplets. 111, 222, 333, 444, 555 and 666. Those are six in number. Further the three dice can fall in 6 * 6 * 6 = 216 ways.
Hence the probability is 6/216 = 1/36.Answer: B
Answer: B
Question: There are three different hoses used to fill a pool: hose U, hose V, and hose W. Hose x can fill the pool in a days, hose y in b days, and hose z in c days, where a > b > c. When all three hoses are used together to fill a pool, it takes d days to fill the pool. Which of the following must be true?
I. d<c
II. d>b
III. c/3<d<a/3
Options:
A)I
B)III
C)I and II only
D)II & III
E)II
Rationale: Name T = full pool
U fills a pool in a days ==> 1 day U fills: T/a
V fills a pool in b days ==> 1 day V fills: T/b
W fills a pool in c days ==> 1 day W fills: T/c
1 day (U+V+W) together fill: T(1/a + 1/b + 1/c)
d days (U+V+W) together fill: T
==> d = T1 / T(1/a+1/b+1/c) = abc/(ab+bc+ca)
==>d = abc/(ab+bc+ca)
d cannot be greater than c ; d is greater than b ; d is greater than c/3 but not less than a/3
E
Answer: E
Question: A man’s speed with the current is 14 km/hr and the speed of the current is 2.5 km/hr. the man’s speed against the current is :
Options:
A)9 km/hr
B)8.5 km/hr
C)10 km/hr
D)12.5 km/hr
E)None of these
Rationale: Solution
Man's rate in still water = (14-2.5) km/hr = 11.5 km/hr.
Man's rate against the current = (11.5-2.5) km/hr = 9 km/hr Answer A
Answer: A
Question: Two motor cycles A & B are started from one point at 4 Kmph & 6 Kmph; After 45 min B starts returning, at what time they will meet ?
Options:
A)54 mins
B)55 mins
C)56 mins
D)57 mins
E)58 mins
Rationale: Distance covered by A in 45 mins= 3 kms.
Distance covered by B in 45 mins= 4.5 kms.
Distance between and B after 45 mins= 1.5 kms.
Relative speed when B is returning = 4+6=10 kmph
Distance between A and B is covered in 1.5/10 = 0.15 hrs = 9 mins
so they will meet again after 54 mins from starting time.
ANSWER:A
Answer: A
Question: Set A consists of all the prime numbers between 2 and 13. What is the range of set A?
Options:
A)12
B)13
C)16.6
D)17
E)8
Rationale: The range of a set of data is the difference between the highest and lowest values in the set
In this set,
Highest number = 11
Lowest number = 3
Range = Highest - Lowest = 11 - 3 = 8
Option E
Answer: E
Question: How many shots of 1cm radius can be prepared from a sphere of 6cm radius?
Options:
A)33
B)88
C)216
D)288
E)299
Rationale: 4/3 Ï€ * 6 * 6 * 6 = 4/3 Ï€ * 1 * 1 * 1 * x
x = 216
Answer: C
Answer: C
Question: The numbers of pizza slices that are sold in Joey's Pizza are only in quantities of 3 and 5 slices per customer. How many slices cannot be bought?
Options:
A)19.
B)38.
C)33.
D)22.
E)21.
Rationale: Let X pizzas of 3 slices and Y pizzas of 5 slices.
3X + 5Y.
Lets check options wise.
A. 19 => 3(3) + 5(2)
B. 38 => 3(6) + 5(4)
C. 33 => 3(1) + 5(6)
D. 22 => 3(4) + 4(2)
E. 21 = we can't write anything with 3 and 5 series..Lets try 3(5) + 5(1) = 20 , 3(4) + 4(2) = 22 , nothing works out.
Answer: correct option is E
Answer: E
Question: a=2, b=3, c=6 Find the value of c/(a+b)-(a+b)/c
Options:
A)8/30
B)9/30
C)10/30
D)11/30
E)12/30
Rationale: c/(a+b)-(a+b)/c
= (c/(a+b))-((a+b)/c)
= (6/(2+3))-((2+3)/6)
= (6/5)-(5/6)
= 11/30
ANSWER:D
Answer: D
Question: Lamp A flashes every 6 seconds, Lamp B flashes every 8 seconds, Lamp C flashes every 10 seconds. At a certain instant of time all three lamps flash simultaneously. During the period of 10 minutes after that how many times will exactly two lamps flash? (Please include any flash of exactly two lights which occurs at the 10 minute mark.)
Options:
A)41
B)42
C)43
D)44
E)45
Rationale: 10 minutes is 600 seconds.
Lamp A and Lamp B will flash together every 24 seconds.
600/24=25.
In the time period, Lamp A and Lamp B will flash together 25 times.
Lamp A and Lamp C will flash together every 30 seconds.
600/30=20.
In the time period, Lamp A and Lamp C will flash together 20 times.
Lamp B and Lamp C will flash together every 40 seconds.
600/40=15.
In the time period, Lamp B and Lamp C will flash together 15 times.
All three lights will flash together every 2*2*2*3*5=120 seconds.
600/120=5.
We have counted these triple flashes three times, so we need to subtract three times the number of times that all three lights flash together.
The number of times that exactly two lights flash together is 25+20+15-15=45 times.
The answer is E.
Answer: E
Question: At the recent downhill mountain bike race 4 entrants entered a challenging slalom event. Prem came first. The entrant wearing no 2 wore red. whereas kian did not wear yellow. the loser wore blue and rahul wore no 1.Sanjay beat rahul and the person who came second wore no 3.te entrant in yellow beat the entrant in green. Only one of the entrant s wore the same number and the final position. Determine who finished 3rd, the no and the color they wore?
Options:
A)Rahul 1 green
B)rahul 2 red
C)Kiran 4 blue
D)Kiran 7 blue
E)none of these
Rationale: the names are prem, sanjay, rahul, kian
colors are red,yellow,green,blue
since prem came 1st and sanjay beat rahul so, given that sanjay came 2nd, wore no 3, yellow color
and rahul wore no 1, green color, came 3rd
hence,
name position wore t-shirt no color
prem 1 2 red
sanjay 2 3 yellow
rahul 3 1 green
kian 4 (1,2,3) blue
ANSWER:A
Answer: A
Question: Find the area of a parallelogram with base 32 cm and height 18 cm?
Options:
A)576 cm2
B)384 cm2
C)672 cm2
D)267 cm2
E)286 cm2
Rationale: Area of a parallelogram
= base * height
= 32 * 18
= 576 cm2
Answer: A
Answer: A
Question: Souju's age is 115% of what it was 10 years ago, but 83 1/3% of what it will be after 10 years. What is her present age?
Options:
A)56 years
B)72 years
C)56 years
D)66 years
E)76 years
Rationale: Let the age before 10 years =x. Then,
115x/100=x+10
⇒115x=100x+1000
⇒x=1000/15=66
Present age =x+10=66+10=76
ANSWER:E
Answer: E
Question: On the first of the year, James invested x dollars at Proudstar bank in an account that yields 0.5% in interest every quarter year. At the end of the year, during which he made no additional deposits or withdrawals, he had y dollars in the account. If James had invested the same amount in an account which pays interest on a yearly basis, what must the interest rate be for James to have y dollars at the end of the year?
Options:
A)2.04%
B)4.12%
C)5%
D)8.25%
E)10%
Rationale: Per quarter, interest = 0.5% So for a year, interest = 2% Due to quarter cumulation, effective yield (YTM) would be slight higher than 2% Answer = 2.04% =ANSWER:A
Answer: A
Question: A set consists of 15 numbers, all are even or multiple of 5. If 8 numbers are even and 10 numbers are multiple of 5, how many numbers is multiple of 10?
Options:
A) 0
B) 1
C) 2
D) 3
E) 5
Rationale: {Total} = {Even} + {Multiple of 5} - {Both} + {Nether}.
Since{Neither}=0(allare even or multiple of 5) then:
15 = 8 + 10 - {Both} + 0;
{Both}=3(so 1 number is both even AND multiple of 5, so it must be a multiple of 10).
Answer: D.
Answer: D
Question: A shopkeeper purchased 70 kg of potatoes for Rs. 420 and sold the whole lot at the rate of Rs. 6.20 per kg. What will be his gain percent?
Options:
A)8 1/7 %
B)2 1/3 %
C)3 1/3 %
D)8 1/8 %
E)8 1/9 %
Rationale: C.P. of 1 kg = 420/70 = Rs. 6
S.P. of 1 kg = Rs. 6.20
Gain % = 0.20/6 * 100 = 10/3
= 3 1/3 %
Answer:C
Answer: C
Question: What should be the least number to be added to the 51234 number to make it divisible by 9?
Options:
A)12
B)17
C)18
D)77
E)26
Rationale: Explanation:
The least number to be added to the numbers to make them divisible by 9 is equal to the difference of the least multiple of 9 greater than the sum of the digits and sum of the digits.
Sum of digits = 15.
Nearest multiple of 9 greater than sum of digits = 18.
Hence 3 has to be added.
Answer: C
Answer: C
Question: A set of numbers has the property that for any number t in the set,t+2 is in the set. If -2 is in the set, which of the following must also be in the set? I. -3 II. 1 III. 4
Options:
A)II only
B)I,III only
C)III only
D)II,III only
E)I only
Rationale: question is asking for must be there elements.
According to the question if t is there t+2 must be there.
if -2 is the starting element the sequence is as follows.
S ={-2,0,2,4,6....}
if -2 is not the starting element the sequence is as follows
S = {...-4,-2,0,2,4,6...}
By observing the above two sequences we can say that 4 must be there in set S.
Answer : C
Answer: C
Question: After allowing a discount of 15% on the marked price, the selling price is Rs. 6800 for an article. If it was sold at marked price, there would have been a profit of 60%. The cost price of the article is?
Options:
A)Rs.2989
B)Rs.5029
C)Rs.5000
D)Rs.5197
E)Rs.5029
Rationale: Given SP = Rs. 6800
Marked price = [SP(100)]/(100 - d%) = (6800 * 100)/(100 - 15)
= Rs. 8000
If SP = Rs. 8000, profit
60%
CP = [SP(100)]/(100 + 60)
= (8000 * 100)/160
= Rs.5000
Answer: C
Answer: C
Question: Tanks A and B are each in the shape of a right circular cylinder. The interior of tank A has a height of 10 meters and a circumference of 8 meters, and the interior of tank B has a height of 8 meters and a circumference of 10 meters. The capacity of tank A is what percent of the capacity of tank B?
Options:
A)90%
B)50%
C)60%
D)70%
E)80%
Rationale: circumference of A = 2(pie)r = 8 so r = 4/pie
volume = pie(4/pie)^2*10 = 160/pie
circumference of B = 2(pie)r = 10 so r = 5/pie
volume = pie(5/pie)^2*8 = 200/pie
so ratio of capacities = 160/200 = 0.8
so capacity of A will be 80% of the capacity of B
ANSWER:E
Answer: E
Question: If x, y, and z are positive integers, and 2x = 5y = 7z, then the least possible value of x + y + z is
Options:
A)15
B)28
C)37
D)42
E)59
Rationale: Take LCM of 2,5 and 7 = 70
Now 2x = 70 => x =35
5y = 70 => y = 14
7z = 70 => z =10
35+14+10 = 59.
Option E.
Answer: E
Question: What is the least number of squares tiles required to pave the floor of a room 2 m 42 cm long and 1 m 76 cm broad?
Options:
A)88
B)82
C)84
D)44
E)54
Rationale: Length of largest tile = H.C.F. of 242 cm and 176 cm = 22 cm.
Area of each tile = (22 x 22) cm2.
Required number of tiles =242 x 176/(22^2)= 88.
ANSWER:A
Answer: A
Question: A money lender finds that due to a fall in the annual rate of interest from 8% to 7 ¾ % his yearly income diminishes by Rs.61.50. his capital is
Options:
A)22378
B)3778
C)24600
D)27888
E)12771
Rationale: Explanation:
Capital = Rs.x , then
x = 24600
Answer: C) Rs.24600
Answer: C
Question: A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. How far is the place?
Options:
A)2.89
B)2.88
C)2.82
D)2.84
E)2.83
Rationale: M = 6
S = 1.2
DS = 6 + 1.2 = 7.2
US = 6 - 1.2 = 4.8
x/7.2 + x/4.8 = 1
x = 2.88
Answer:B
Answer: B
Question: A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is?
Options:
A)272
B)111
C)822
D)150
E)379
Rationale: Let the length of the train be x meters and its speed be y m/sec.
They, x / y = 15 => y = x/15
x + 100 / 25 = x / 15
x = 150 m.
Answer:D
Answer: D
Question: Indu gave Bindu Rs.2500 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest?
Options:
A)1
B)2
C)7
D)4
E)9
Rationale: 2500 = D(100/4)2
D = 4
Answer:D
Answer: D
Question: x = y - (1/y), where x and y are both > 0. If the value of y is doubled in the equation above, the value of x will
Options:
A)decrease
B)stay the same
C)increase four fold
D)just more than double
E)increase to more than five times
Rationale: Alternate approach
Plug in some values of y > 0
Let y = 10
So, x = y - (1/y)
Or, x = 10 - (1/10) = 9.9
Let y = 20
So, x = y - (1/y)
Or, x = 20 - (1/20) =>19.95
So, x increases from 9.9 to 19.95
Hence the number increases 2 times, thus the correct answer will be (D)
Answer: D
Question: A tourist purchased a total of $3,500 worth of traveler’s checks in $10 and $50 denominations, During the trip the tourist cashed 7 checks and then lost all of the rest. If the number of $10 checks cashed was one more or one less than the number of $50 checks cashed, what is the minimum possible value of the checks that were lost?
Options:
A)$1,430
B)$2,310
C)$2,290
D)$3,270
E)$4,150
Rationale: Let the number of $10 checks cashed beT
Let the number of $50 checks cashed beF
7 checks cashed;
T+F=7
Now; T can be F+1 OR T can be F-1
Let's check both conditions;
T=F+1
T+F=7
F+1+F=7
2F=6
F=3
T=4
Value cashed = 3*50+4*10=150+40=$190
Let's check the other condition as well;
T=F-1
T+F=7
F-1+F=7
2F=8
F=4
T=3
Value cashed = 4*50+3*10=200+30=$230
The more money he cashes, the less loss he incurs. Thus, we must consider the latter case.
Value cashed = $230
Value lost = 3000-230 = $3270
Ans:D
Answer: D
Question: Dany bought a total of 20 game cards some of which cost $0.25 each and some of which cost $0.15 each. If Dany spent $4.2 to buy these cards, how many cards of each type did he buy?
Options:
A)2
B)3
C)5
D)8
E)13
Rationale: Let X be the number of cards that cost $0.25 each and Y the number of cards that cost $0.15 each. The total number of cards is 20. Hence
X + Y = 20
If X is the number of cards at $0.25, then the X cards cost
0.25 X
If Y is the number of cards at $0.15, then the Y cards cost
0.15 Y
The total cost of the X cards and the the Y cards is known to be $4.2 and also given by
0.25 X + 0.15 Y = 4.2
We now need to solve the system of equations
X + Y = 20
0.25 X + 0.15 Y = 4.2
The first equation gives Y = 20 - X. Substitute y by 20 - x in the second equation and solve
0.25 X + 0.15 (20 - X) = 4.2
X(0.25 - 0.15) + 3 = 4.2
0.1 X = 1.2
X = 12 and Y = 20 - 12 = 8
correct answer D
Answer: D
Question: What is vasu salary if salary of vasu is more than rajan salary working in same company i)vasu salary is 100 more than rajan salary. ii)rajan found 2000 allowns which is 50 less than vasu. (iii)basic salry of rajan is 1000.
Options:
A)only i is required
B)i & ii is required
C)i& iii is required
D)i&ii&iii is required
E)none of these
Rationale: i and iii is enough
ANSWER:B
Answer: B
Question: The distance light travels in one year is approximately 5,850,000,000,000 miles. The distance light travels in 100 years is
Options:
A)A) 587 × 108 miles
B)B) 587 × 1010 miles
C)C) 587 × 10-10 miles
D)D) 585 × 1012 miles
E)E) 587 × 10-12 miles
Rationale: The distance of the light travels in 100 years is:
5,850,000,000,000 × 100 miles.
= 585,000,000,000,000 miles.
= 585 × 1012 miles.
The answer is (D)
Answer: D
Question: A box contains four nickel coins, of which two coins have heads on both their faces, one coin has tail on both its faces and the fourth coin is a normal one. A coin is picked at random and then tossed. If head is the outcome of the toss, then find the probability that the other face (hidden face) of the coin tossed is also a head.
Options:
A)3/5
B)2/5
C)4/5
D)1/5
E)3/4
Rationale: There are four ways (2 heads in one two-headed coin and 2 heads in the other two-headed coin)
How many ways can you get heads from this entire set of coins? There are five ways (four as identified above and one from the normal coin)
Therefore probability = (number of ways to get heads from a two-headed coin)/(number of ways to get heads from any coin)
= 4/5
C
Answer: C
Question: The owner of a furniture shop charges his customer 60% more than the cost price. If a customer paid Rs. 1000 for a computer table, then what was the cost price of the computer table?
Options:
A)750
B)650
C)625
D)115
E)400
Rationale: CP = SP * (100/(100 + profit%))
= 1000(100/160) = Rs. 625.
Answer: B
Answer: B
Question: If x is an integer and 3.134 × 10^x is less than 31,000 what is the greatest possible value for x?
Options:
A)7
B)6
C)5
D)4
E)3
Rationale: If x=4
3.134 × 10^4 = 31340 > 31000
So, x = 3
Answer : E
Answer: E
Question: For each hour of production, a certain factory requires 1 assembly line worker for every 25 units to be produced in that hour. The factory also requires 12 managers regardless of the number of units to be produced. Which of the following expressions represents the total number of assembly line workers and managers that this factory requires to produce 75N in one hour, where N is a positive integer?
Options:
A)12 + 50N
B)12 + 3N
C)62N
D)37N
E)25
Rationale: 25 units = 1 worker;
75N units = 75N/25 = 3N workers.
So, the answer is 3N workers plus 12 managers.
Answer: B.
Answer: B
Question: calculate the time required to become sum 2 times of itself at rate of 10%.
Options:
A)5year
B)15year
C)10year
D)8year
E)12year
Rationale: if sum become 2 time then simple interest equal to x.
x=x*10*t/100
t=100/10=10year
answer C
Answer: C
Question: find 3 consecutive odd integers, all less than 100, such that the sum of their squares forms a Unidigit (that is, all its digits are the same). Thus, for integer abc, a^2 + b^2 +c^2 equals a Unidigital.
Options:
A)39,43,45
B)43,45,47
C)45,47,49
D)41,43,45
E)41,43,47
Rationale: If numbers are x,x-2,x+2, then
x^2+(x+2)^2 =(x-2)^2 = x^2+2x^2+8 = 3x^2+8
Now 3x^2+8 should be unidigital.
checking different combinations , we get
x=43.
so numbers are 41,43,45
ANSWER:D
Answer: D