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How many subsets does the set {2, 5, 7, 11, 13, 17, 19, 23} have?

Correct Answer: 256

Explanation:

The number of subsets of a set with n elements is given by 2^n.
The given set has 8 elements.
Number of subsets = 2^8 = 256
[x^2=x*x]

Question: 2

Sam borrowed $5000 from Ben at 4% rate of compound interest. He had to pay him back $408 as interest. How much interest would he have had to pay to Ben, had he borrowed twice the sum that he did for the same time period?

Correct Answer: $816

Explanation:

Ben applied compound interest.
When P, r and t are the principal, rate and time, then the compound interest CI, is given by
CI = P[(1+r/100)^t-1]
408 = 5000[(1+4/100)^t-1]
408/5000+1=(104/100)^t
5408/5000=(104/100)^t
10816/10000 = (104/100)^t
t = 2 years
If the sum were twice, it would be $5000*2 = $10000
CI = 10000[(1+4/100)^2-1]
= 10000[(104/100)^2-1]
= 10000(816/10000) = 816
The interest would be $816.

Question: 3

Children of a school have to stand in different rows holding flags such that each row has children holding flags of the same colour. There are 25 children holding red flags, 35 holding green flags and 100 holding blue flags. What is the least number of rows that should be formed for the arrangement such that all the rows have the same number of children?

Correct Answer: 32

Explanation:

Maximum number of children per row = HCF of 25, 35 and 100
= 5
Each row can contain 5 children, at the most.
Number of rows = 25/5 + 35/5 + 100/5
= 5 + 7 + 20 = 32 rows.
The least number of rows is 32.

Question: 4

Akram appeared for 15 different tests in a year. His average for the first session of five tests was 72, for the second session of six tests it was 60 and for the third session of 4 tests it was 120. What was his average score for the complete year?

Correct Answer: 80

Explanation:

Total = Average*number of observations
The sum of his scores = 5*72 + 6*60 + 4*120
= 360+360+480 = 1200
Average for the complete year = Sum/Number of observations
= 1200/15 = 80
This average score for the complete year was 80

Question: 5

The mixture contains 5 parts of substance A for every 2 parts of substance B. Substance A consists of 5 parts of sugar, 2 of salt and 4 of other ingredients. Substance B consists of 3 parts of sugar, 2 parts of salt and 3 parts of other ingredients. How many parts of sugar does the mixture contain for every 248 parts of salt?

Correct Answer: 532

Explanation:

Substance A contains 5 parts of sugar, 2 of salt and 4 of other ingredients.
Divide substance A into 11 parts.
1 part of substance A contains 5/11 parts of sugar, 2/11 parts of salt and 4/11 parts of other ingredients.
5 parts of substance A contain (5*5/11= ) 25/11 parts of sugar, (5*2/11= ) 10/11 parts of salt and (5*4/11=) 20/11 parts of other ingredients.

Substance B contains 3 parts of sugar, 2 of salt and 3 of other ingredients.
Divide substance B into 8 parts.
1 part of substance B contains 3/8 parts of sugar, 2/8 parts of salt and 3/8 parts of other ingredients.
2 parts of substance B contain (2*3/8=) 6/8 parts of sugar, (2*2/8=) 4/8 parts of salt and (2*3/8=) 6/8 parts of other ingredients.

Total sugar in the mixture = 25/11+6/8
= (25*8+6*11)/(11*8)
= 266/88
Total salt in the mixture = 10/11+4/8
= (10*8+4*11)/(11*8)
= (80+44)/88
= 124/88

248/(124/88) = 2*88 = 176
266/88*176 = 266*2 = 532
The mixture contains 532 parts of sugar for every 248 parts of salt in it.

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