divelab/Sys2Bench huggingface dataset:
Question: Machine A produces pencils at a constant rate of 9000 pencils per hour, and machine B produces pencils at a constant rate of 7000 pencils per hour. If the two machines to gather must produce 100,000 pencils and if each machine can operate for at most 8 hours, what is the least amount of time V, in hours, that machine B must operate?
Options:
A)4
B)4 2/3
C)5 1/3
D)6
E)6 1/4
Rationale: Machine A produces pencils at a constant rate of 9,000 pencils per hour, and machine B produces pencils at a constant rate of 7,000 pencils per hour. If the two machines together must produce 100,000 pencils and if each machine can operate for at most 8 hours, what is the least amount of time V, in hours, that machine B must operate?
a) 4
b) 4 and 2/3
c) 5 and 1/3
d) 6
e) 6 and 1/4
To minimize the time that machine B must operate we must maximize the time machine A can operate, so make it operate 8 hours. In 8 hours machine A will produce 8*9,000=72,000 pencils, so 100,000-72,000=28,000 pencils are left to produce, which can be produced by machine B in 28,000/7,000=4 hours.
Answer: A.
Answer: A
Question: In how many ways a committee consisting of 5 men and 6 women can be formed from 8 men and 10 women?
Options:
A)12540
B)11450
C)11760
D)13250
E)12450
Rationale: Required number of ways = 8C5*10C5 = 8C3*10C4 = 11760
Answer is C
Answer: C
Question: In a survey of university students, 64 had taken mathematics course, 94 had taken computer science course, 58 had taken physics course, 28 had taken mathematics and physics, 26 had taken mathematics and computer science, 22 had taken computer science and physics course, and 14 had taken all the three courses. Find how many had taken mathematics course only.
Options:
A)64
B)14
C)12
D)14
E)24
Rationale: Let us represent the given data in a Venn diagram. Let M, C, P represent sets of students who had taken mathematics, computer science and physics respectively.
M=64
M and C and P=14
M and C not P=26-14=12
M and P not C=28-14=14
M only = 64-12-14-14=24
ANSWER E 24
Answer: E
Question: A woman spends 15% of her income in house rent, 15% of the rest on his children’s education, 10% of the rest miscellaneous causes and 15% in medical expenses. If she now posses Rs. 5548 then her income is?
Options:
A)10058
B)10068
C)10078
D)10088
E)10038
Rationale: X * (85/100) * (85/100) * (90/100) * (85/100)= 5548
X * 0.85 * 0.85 * 0.9 * 0.85 = 5548
X = 5548/0.5527
X = 10038
ANSWER:E
Answer: E
Question: 66.2 is what percent of 1000?
Options:
A)6.62
B)66.2
C)662
D)0.662
E)0.0662
Rationale: We assume that 1000 is 100%
assume 'x' is value we looking for
here,
1000 = 100% and
x% = 66.2
therefore,
100/x = 1000/66.2
100/x = 15.105
x = 6.62
A
Answer: A
Question: If b/c = 1.25, then c is what percent of b?
Options:
A)0.008
B)0.08
C)0.8
D)8
E)80
Rationale: You are given , b/c =1.25 ---> c < b but only 'just'. This eliminates A-C as you are asked % and as such these values will be further reduced by 1/100, making them even smaller.
Also, as c iscloseto 'b', eliminate D and mark E as the correct answer.
Alternatively, 1.25 = 5/4 ---> b/c=5/4 --> c = 4/5 (b) = 0.8b ---> c = 80% of b. E is the correct answer.
Answer: E
Question: If the reciprocals of two consecutive positive integers are added together, what is the sum in terms of the greater integer m?
Options:
A)(2m-2)/(m^2- m)
B)(2m-1)/(m^2- m)
C)(2m-1)/(m^4- m)
D)(3m-1)/(m^2- m)
E)(2m-1)
Rationale: Let two consecutive positive integers be m and m-1 (Greater integer is m)
So,
(1/m) + [1/(m-1)]
= (2m-1)/m(m-1)
=(2m-1)/(m^2- m)
Answer : B
Answer: B
Question: (998-1)(998-2)(998-3)........(998-n)=....... when n>1000
Options:
A)4
B)3
C)2
D)1
E)0
Rationale: The term (998-998) makes the whole expression = 0.
ANSWER:E
Answer: E
Question: How many numbers from 10 to 50 are exactly divisible by 3?
Options:
A)13
B)14
C)15
D)17
E)19
Rationale: 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45,48.
13 Numbers.
10/3 = 3 and 50/3 = 16 ==> 16 - 3 = 13. Therefore 13 digits.
A)
Answer: A
Question: A garage has a bin that is used by an "add stuff" worker and a "throw away" worker. Working alone, the "add stuff" worker can fill the bin in 5 hours. Working alone, the "throw away" worker can empty the bin in 15 hours. If it is desired that the bin should be filled, from empty, exactly 6 hours after the "add stuff" worker begins his shift at 9:30am, then at what time should the "throw away" worker begin his own shift?
Options:
A)10:00am
B)10:45am
C)12:00pm
D)12:30pm
E)1:30pm
Rationale: In 6 hours the "add stuff" worker can fill the bin equal to 6*1/5 = 6/5 of the bin. So, 1/5 more than necessary, which should be compensated by the "Throw away" worker. To get rid of 1/5 of the inventory the "throw away"worker needs 15/5 = 3 hours.
Therefore, the "throw away" worker should begin his shift at 9:30am + 6 hours - 3 hours = 12:30pm.
Answer: D.
Answer: D
Question: The ratio of flour to water to sugar in a recipe is 7:2:1. The ratio in a new recipe calls for a doubling of the ratio of flour to water from the original recipe and a halving of the ratio of flour to sugar. If the new recipe calls for 2 cups of water, how much sugar is required?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: The ratio of flour to water is 14:2.
The ratio of flour to sugar is 3.5:1=14:4.
The new ratio of flour to water to sugar is 14:2:4
If we need 2 cups of water, then we need 4 cups of sugar.
The answer is C.
Answer: C
Question: All the faces of a cube are painted with blue colour. Then it is cut into 125 small equal cubes.
How many small cubes will be formed having only one face coloured ?
Options:
A)54
B)8
C)16
D)24
E)34
Rationale: no.of small cubes will have only one face painted=(X-2)2*6
Here x=side of the small cube=5
therfore(X-2)2*6=54
ANSWER:A
Answer: A
Question: A and B entered into a partnership investing Rs.25000 and Rs.30000 respectively. After 4 months C also joined the business with an investment of Rs.35000. What is the share of C in an annual profit of Rs.47000?
Options:
A)14009
B)14409
C)14006
D)14000
E)14001
Rationale: 25*12: 30*12: 35*8
15:18:14
14/47 * 47000 = 14000
Answer: D
Answer: D
Question: A cab driver 5days income was $400, $250, $650, $400 , $500. Then his average income is?
Options:
A)$400
B)$420
C)$440
D)$460
E)$480
Rationale: avg = sum of observations/number of observations
avg income=(400+250+650+400+500)/5 = 440
Answer is C
Answer: C
Question: A train 50 m long is running with a speed of 68 kmph. In what time will it pass a man who is running at 8 kmph in the same direction in which the train is going?
Options:
A)3 sec.
B)7 sec.
C)9 sec.
D)11 sec.
E)None
Rationale: Solution
Speed of the train relative to man	=( 68 - 8 )
= 60 Kmph
= 60 x 5 / 18
=50/3 m/sec.
Time taken by it to cover 50 m at (50 /3)m/sec	= (112 - 50)kmph
= (50 x 3/50)sec
= 3 sec.
Answer A
Answer: A
Question: 15th august 2010 was which day of the week?
Options:
A)Thursday
B)Friday
C)Wednesday
D)Sunday
E)Monday
Rationale: ANSWER: Sunday
Explanation:
15th August 2010 can be written as 2009 + days from 1st January 2010 to 15th August 2010.
=> Total number of odd days in 400 years = 0
Hence, total number of odd days in 2000 years = 0 (as 2000 is a perfect multiple of 400)
Odd in days in the period 2001-2009:
7 normal years + 2 leap yeas
=> (7*1) + (2*2) = 11
=> Odd days will be 11- (7*1) = 4
Days from January 1 to August 15 in 2010: 31+28+31+30+31+30+31+15
= 227 days.
= 32 weeks and 3 days, this gives additional 3 odd days.
=> Total odd days= 3+4=7
=> 7 odd days=1 week= 0 odd days
=> 0 odd days= Sunday
Thus, 15th August 2010 was a Sunday.
Answer: D
Answer: D
Question: A man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current ?
Options:
A)2.5 kmph
B)6.5 kmph
C)1.5 kmph
D)8.5 kmph
E)1.7 kmph
Rationale: Explanation:
72 --- 9
? ---- 1
=> Down Stream = 8
45 ---- 9
? ---- 1
=> Up Stream = 5
Speed od current S = ?
S = (8 - 5)/2 = 1.5 kmph.
Answer: C
Answer: C
Question: How many different arrangements of A, B, C, D, and E are possible where A is not adjacent to B ?
Options:
A)72
B)48
C)32
D)30
E)1
Rationale: So you have A,B,C,D,E
five possible ways to arrange it = 5! = 120
AB cannot be adjacents
(AB),C,D,E = 4! = 24 x 2(because it can be (AB) or (BA) ) = 48
120 -48- = 72 possible ways
A
Answer: A
Question: Bottle R contains 350 capsules and costs $6.25. Bottle T contains 130 capsules and costs $2.99. What is the difference between the cost per capsule for bottle R and the cost per capsule for bottle T?
Options:
A) $0.25
B) $0.12
C) $0.0052
D) $0.003
E) $0.002
Rationale: Cost per capsule in R is 6.25/350=0.0178
Cost per capsule in T is 2.99/130=0.023
The difference is 0.0052
The answer is C
Answer: C
Question: 45 litres of mixture is created by mixing Liquid A and Liquid B in the ratio 3:2. How much more Liquid B must be added to make the ratio 9:11?
Options:
A)9 Litres
B)10 Litres
C)12 Litres
D)15 Litres
E)16 Litres
Rationale: In current ratio A = (3/5) * 45 = 27
B is 18
Suppose "b" amount of b is added
new ratio = 27/(b+18) = 9/11
=> b+18 = 33
=> b = 15
So, answer will be D
Answer: D
Question: When 3 fair coins are tossed together, what is the probability of getting 2 tails?
Options:
A)1/2
B)1/3
C)1/4
D)3/4
E)2/3
Rationale: We can get 2 tails in 3C2 ways.
We can get 3 tails in exactly one way.
Also, there are a total out 8 possible outcomes.
Thus, the required probability = (3 + 1)/8 = 1/2
ANSWER:A
Answer: A
Question: A certain galaxy is known to comprise approximately 4 x 10^12 stars. Of every 50 million of these stars, one is larger in mass than our sun. Approximately how many stars in this galaxy are larger than the sun?
Options:
A)800
B)1,250
C)80,000
D)12,000
E)80,000
Rationale: Total no. of stars on galaxy = 4 * 10^12
Of every 50 million stars, 1 is larger than sun.
1 million = 10^6 therofore, 50 million = 50 * 10^6
total no. of stars larger than sun = 4 * 10^12 / 50 * 10^6
=40 * 10^4 /5
= 80000
therefore answer is C
Answer: C
Question: How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length?
Options:
A)12.5
B)12.1
C)12.9
D)12.7
E)12.2
Rationale: Speed = 72 * 5/18 = 20 m/sec
Total distance covered = 110 + 132 = 242 m.
Required time = 242/20 = 12.1 sec.
Answer: B
Answer: B
Question: Apple Infotech has 4 Senior Managing Directors and 5 Managing Directors. Each investment banking deal requires the guidance of two managing directors, at least one of which must be a Senior Managing Director. How many possible investment banking deals can Apple Infotech possibly provide guidance for?
Options:
A) 16
B) 20
C) 26
D) 54
E) 64
Rationale: P(at least 1 S D) = P(Total) - P(0 Senior Director)
=9C2 - 5C2
= 26
Answer: C
Question: Rebecca's annual income is $15, and Jimmy's annual income is $18. By how much must Rebecca's annual income increase so that it constitutes 50% of Rebecca and Jimmy's combined income?
Options:
A)7
B)8
C)9
D)3
E)10
Rationale: total rebecca = x+15; total = x+20+18
x+15/x+33 = 50/100 therefore x =3
D
Answer: D
Question: In a ratio which is equal to 4:6, if the antecedent is 50, then the consequent is?
Options:
A)75
B)85
C)64
D)51
E)45
Rationale: We have 4/6 = 50/x
4x = 50*6
x = 75
consequent = 75
Answer is A
Answer: A
Question: In what ratio must tea at Rs.60 per Kg be mixed with tea at Rs.70 per Kg so that the mixture must be worth Rs.67.5 per Kg?
Options:
A)3 : 1
B)3 : 2
C)4 : 3
D)1 : 3
E)None
Rationale: Required ratio = 250 : 750 = 1 : 3
Answer D
Answer: D
Question: Which of the following represents 1<x<9?
Options:
A)|x|<3
B)|x+5|<4
C)|x-1|<9
D)|-5+x|<4
E)|3+x|<5
Rationale: |x| is the distance of x from the origin on the number line.
|x - 5| is the distance of x from the point 5 on the number line.
|x + 3| is the distance of x from the point -3 on the number line. (That's because x + 3 = x - (-3))
So, we want to write 1<x<9 as a distance statement.
Step #1: find the middle of that region. The midpoint is at 5. So, this is about distance from 5 ---> |x - 5|
Step #2: how far can we get from 5? Well, up to almost 9, or down to almost 1 -- that is, almost 4. Thus:
distance from 5 < 4
|x - 5| < 4
ANSWER:D
Answer: D
Question: Find the simple interest on Rs.500 for 9 months at 6 paisa per month?
Options:
A)288
B)270
C)999
D)278
E)121
Rationale: I = (500*9*6)/100 = 270
Answer:B
Answer: B
Question: An old priest fell on a bottom of the well of a church.
The well is 20 inches deep.
At day time, the old priest climbs 5-inches but when at dark he slip back 4 inches.
In how many days priest will come out of the well ?
Options:
A)16-days
B)14-days
C)11-days
D)19-days
E)10-days
Rationale: A
16-days
In 15-days, he will climb 15-inch and when he climbs 5 inch more, he will be out of the well :-)
Answer: A
Question: Find the odd one out:
125, 106, 84, 76, 65, 58, 53
Options:
A)33
B)84
C)26
D)18
E)222
Rationale: Explanation:
This sequence represents a series in which from the reverse order a prime number is added:
53+5=58
58+7=65
65+11=76
76+13=89
89+17=106
106+19=125
Hence 84 is the answer.
ANSWER: B
Answer: B
Question: If Josh, Doug, and Brad have a total of $72 between them, and Josh has three times as much money as Brad but only three-fourths as much as Doug, how much money does Brad have?
Options:
A)$8
B)$9
C)$27
D)$32
E)$36
Rationale: Josh+Doug+Brad = 72 ; Joush = 3 brad, Josh =3/4 doug
Josh+1/3 Josh+ 4/3 Josh = 72 (substituted the given values)
Josh = 27. 27= 3/4 doug => doug =36
Josh+Doug+Brad = 72
27 + 36 + Brad = 72
Brad = 9
Answer is B.
Answer: B
Question: In a particular year, the month of january had exactly 4 thursdays, and 4 sundays. On which day of the week did january 1st occur in the year.
Options:
A)33
B)Monday
C)299
D)299
E)277
Rationale: Ans: If a month has 31 days, and it starts with sunday, Then Sundays, Mondays, tuesdays are 5 for that month. If this month starts with monday, then mondays, tuesdays, and wednesdays are 5 and remaining days are 4 each. so this month start with Monday.
Answer:B
Answer: B
Question: If the square root of p^2 is an integer greater than 1, which of the following must be true?
I. p^2 has an odd number of positive factors
II. p^2 can be expressed as the product of an even number of positive prime factors
III. p has an even number of positive factors
Options:
A)I
B)II
C)III
D)I and II
E)II and III
Rationale: It is given that p2−−√p2>1 and is an integer..
Also p2−−√p2=p
so p^2 is a perfect square and p is an integer>1..
lets see three statements:-
I. p^2 has an odd number of positive factors-- TRUE
A perfect square has an Odd number of perfect square ..
WHY? Because all factors will have a different integer as a pair except p..
p*p=p^2.. so that will be just one factor
II. p^2 can be expressed as the product of an even number of positive prime factors
again TRUE
25 =5*5 ; 49= 7*7 ; 36 = 2*2*3*3
III. p has an even number of positive factors..
Since it uses 'HAS', if we find one which does not follow the statement is not true..
we already know that A perfect square has an Odd number of perfect square ..
so if p is a perfect square itself ans is No
ONLY I and II are true
ANSWER:D
Answer: D
Question: Which of the below fractions has the highest value?
Options:
A)A)23/77
B)B)23/78
C)C)23/84
D)D)23/87
E)E)23/40
Rationale: 23/40.
Now, all options have the same numerator 23. If numerator is same, the fraction with the highest value will be the one with the lowest denominator.
Answer (E).
Answer: E
Question: A discount electronics store normally sells all merchandise at a discount of 10 percent to 30 percent off the suggested retail price. If, during a special sale, an additional 25 percent were to be deducted from the discount price, what would be the lowest possible price of an item costing $260 before any discount?
Options:
A) $136.50
B) $145.60
C) $163.80
D) $182.00
E) $210.00
Rationale: Since the question is essentially just about multiplication, you can do the various mathstepsin a variety of ways (depending on whichever method you find easiest).
We're told that the first discount is 10% to 30%, inclusive. We're told that the next discount is 25% off of the DISCOUNTED price....
We're told to MAXIMIZE the discount (thus, 30% off the original price and then 20% off of the discounted price). Thatmathcan be written in a number of different ways (fractions, decimals, etc.):
30% off = (1 - .3) = (1 - 30/100) = (.7) and the same can be done with the 20% additional discount...
The final price of an item that originally cost $260 would be.....
($260)(.7)(.75) =
($260)(.525)=136.5
Final Answer:
A
Answer: A
Question: he ratio between the sale price and the cost price of an article is 4:7. What is the ratio between the profit and the cost price of that article?
Options:
A)2:6
B)3:7
C)3:8
D)2:1
E)8:3
Rationale: Let C.P. = Rs. 7x and S.P. = Rs. 4x.
Then, Gain = Rs. 3x
Required ratio = 3x : 7x = 3:7.
Answer:B
Answer: B
Question: In year Y imported machine tools accounted for 25 percent of total machine-tools sales in the United States, and Japanese imports accounted for 40 percent of the sales of imported machine tools. If the total sales of machine tools imported from Japan that year was x billion dollars, then the total sales of all machine tools in the United States was how many billion dollars?
Options:
A)9x/80
B)13x/20
C)80/9x
D)10x
E)80x/9
Rationale: Sales of imported tools = 25% of the total sales = 0.25*{total} = {total}/4;
Sales of Japanese tools = 40% of the sales of imported tools = 0.40*{total}/4 = 2/5*{total}/4 = 2*{total}/20.
Since the sales of of Japanese tools was x, then 2*{total}/20 = x --> {total} = 10x.
Answer: D.
Answer: D
Question: The average of first ten prime numbers which are odd is?
Options:
A)15.7
B)15.0
C)15.2
D)15.8
E)15.1
Rationale: Sum of first 10 prime no. which are odd = 158
Average = 158/10 = 15.8
Answer: D
Answer: D
Question: If 1 kilometer is approximately 0.6 mile, which of the following best approximates the number of kilometers in 7 miles?
Options:
A)22/5
B)20/5
C)15/5
D)21/5
E)16/4
Rationale: 1 km is approxmately equal to 0.6 miles
So 7 km = 7*0.6 = 4.2 miles . Multiple & divide by 10
i.e 4.2*10/10 = 42/10 = 21/5
Answer : D
Answer: D
Question: A person’s age is 125% of what it was one decade ago, but 83(1/3)% of what it will be after one decade. What is his current age? [1 decade = 10 years]
Options:
A)50 years
B)60 years
C)30 years
D)70 years
E)80 years
Rationale: A
50 years
Let, current age is A years.
Then, 125% of (A – 10) = A
and, 83(1/3)% of (A + 10) = A
Therefore 125% of (A-10) = 83(1/3)% of (A+10)
or, (5/4) (A – 10) =(5/6)(A+10)
or, (5/4)A -(5/6)A = (50/6)+(50/4)
or, (5A/12)= (250/12) or,
A=50 years.
Answer: A
Question: A student took five papers in an examination, where the full marks were the same for each paper. His marks in these papers were in the proportion of 6 : 7 : 8 : 9 : 10. In all papers together, the candidate obtained 60% of the total marks. Then the number of papers in which he got more than 61% marks is
Options:
A)6
B)5
C)4
D)3
E)2
Rationale: Here we can assume that one subject is of 100 marks so total there are 5 subjects => 100*5 = 500.
Now according to the question he secured 60 % of those which is 60%of 500 = 300 marks in total.
The ratio between the marks is given as 6 : 7 : 8 : 9 : 10 , so now we can distribute 300 marks according to the ratio.
Total ratio = 40
For 6 : (300/40)*6 = 45
Similarly , we will get for others as 52.5 , 60 , 62.5 , 75.
Hence , there are 2 subject where he secured more that 50 %.
The answer is 2.
E
Answer: E
Question: If n = 14p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n ?
Options:
A) Two
B) Three
C) Four
D) Six
E) Eight
Rationale: If n = 14p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n ?
(A) Two
(B) Three
(C) Four
(D) Six
(E) Eight
Since we cannot have two correct answers just pick a prime greater than 2, and see how many different positiveevendivisors will 14p have.
p = 3 --> 14p = 42--> 42 has 4 even divisors: 2, 6, 14, 42 .
Answer: C.
Answer: C
Question: In a stack of boards at a lumber yard, the 20th board counting from the top of the stack is immediately below the 17th board counting from the bottom of the stack. How many boards are in the stack?
Options:
A)38
B)36
C)35
D)34
E)32
Rationale: Counting from the top, after the 20th board, there are 15 boards left to count.
The answer is C.
Answer: C
Question: A man is standing on a railway bridge which is 240 m long. He finds that a train crosses the bridge in 20 seconds but himself in 8 seconds. Find the length of the train and its speed.
Options:
A)10 m/sec
B)15 m/sec
C)18 m/sec
D)20 m/sec
E)25 m/sec
Rationale: If length of train is l and speed of train is s, then
l/s = 8
(l+240)/s = 20
(l+240)/l = 20/8 =5/2
2l+480 =5*l
3*l= 480
l=160 mtrs
s= l/8 = 160/8 = 20 m/sec
ANSWER:D
Answer: D
Question: For one toss of a certain coin, the probability that the outcome is heads is 0.3. If this coin is tossed 5 times, which of the following is the probability that the outcome will be heads at least 4 times?
Options:
A)(0.3)^5
B)2(0.3)^4
C)3(0.3)^4
D)4(0.3)^4(0.7) + (0.3)^5
E)5(0.3)^4(0.7) + (0.3)^5
Rationale: P(5 heads) = (0.3)^5
There are 5 ways to get 4 heads: HHHHT, HHHTH, HHTHH, HTHHH, THHHH
P(4 heads) = 5*(0.3)^4(0.7)
The answer is E.
Answer: E
Question: A train traveled the first d miles of its journey it an average speed of 50 miles per hour, the next d miles of its journey at an average speed of y miles per hour, and the final d miles of its journey at an average speed of 160 miles per hour. If the train’s average speed over the total distance was 96 miles per hour, what is the value of y?
Options:
A) 68
B) 84
C) 90
D) 120
E) 160
Rationale: Average speed=Total distance traveled /Total time taken
3d/d/50+d/y+d/160=96
Solving for d and y,
15y=11y+480
3y=480
y=160
Answer E
Answer: E
Question: If 75 percent of a girls answered the first question on a certain test correctly, 55 percent answered the second question on the test correctly, and 20 percent answered neither of the questions correctly, what percent answered both correctly?
Options:
A) 10%
B)(8) 20%
C) 30%
D) 40%
E) 50%
Rationale: {Total} = {First} + {Second} - {Both} + {Neither}
100% = 75% + 55% - {Both} + 20% --> {Both} = 50%.
Answer: E.
Answer: E
Question: A certain quantity is measured on two different scales, the T-scale and the S-scale, that are related linearly. Measurements on the T-scale of 6 and 24 correspond to measurements on the S-scale of 30 and 60, respectively. What measurement on the T-scale corresponds to a measurement of 100 on the S-scale?
Options:
A) 20
B) 36
C) 48
D) 60
E) 84
Rationale: First, we have to understand what linearly means. It's not a straight ratio (since 6:30 does NOT equal 24:60). We need to look at the increases in each measurement to see what the scalar actually is.
From 6 to 24 we have an increase of 18. From 30 to 60 we have an increase of 30. Therefore, the increase ratio is 18:30 or 3:5. In other words, for every 3 that T increases, S increases by 5.
We know that S is 100. To get from 60 to 100, we went up by 40, or 8 jumps of 5; therefore, T will go up by 8 jumps of 3.
24 + 8(3) = 24 + 24 = 48=C
Answer: C
Question: A, B and C can do a piece of work in 24, 30 and 40 days respectively. They start the work together but C leaves 4 days before the completion of the work. In how many days is the work done?
Options:
A)11 days
B)14 days
C)13 days
D)10 days
E)20 days
Rationale: x/24 + x/30 + x/40 = 1
x = 11 days
ANSWER A
Answer: A
Question: Set A {3,3,3,4,5,5,5} has a standard deviation of 1. What will the standard deviation be if every number in the set is multiplied by 8?
Options:
A)A)1
B)B)2
C)C)4
D)D)8
E)E)16
Rationale: Points to remember -
1. If oneAdd/Subtractthe same amont from every term in a set, SD doesn't change.
2. If oneMultiply/Divideevery term by the same number in a set, SD changes by same number.
Hence the answer to the above question is D
Answer: D