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Difficulty:
65%
(hard)
Question Stats:
55% (01:52) correct
45%
(02:05)
wrong
based on 189
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Which of the following statements must be true?
1) If x/y is a fraction and y has 17 as one of its prime factors then the resulting decimal will be terminating
2) If x/y is a fraction where 2 and 5 are the only two prime factors of y then the resulting decimal will be terminating.
3) If x/y is a fraction such that y=(10^n -1) for n≥1 then the repeating decimals in the result would just be the digits of the numerator.
4) If the interest is accounted annually then for the first compounded interest would be equal to the simple interest.
A) 2,3
B) 2,3,4
C) 1,2,3
D) 2,4
E) 1,3
1) If x/y is a fraction and y has 17 as one of its prime factors then the resulting decimal will be terminating
2) If x/y is a fraction where 2 and 5 are the only two prime factors of y then the resulting decimal will be terminating.
3) If x/y is a fraction such that y=(10^n -1) for n≥1 then the repeating decimals in the result would just be the digits of the numerator.
4) If the interest is accounted annually then for the first compounded interest would be equal to the simple interest.
A) 2,3
B) 2,3,4
C) 1,2,3
D) 2,4
E) 1,3
16 Aug 2016, 20:22
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A terminating decimal is such that the denominator only has powers of 2 and/or 5. Statement 1 is never true and statement 2 is always true.
Statement 3: Let's try some examples:
1/9 = 0.11111.....
23/99 = 0.2323232323.....
61/999 = 0.061061061061061.....
Statement 3 is always true.
Statement 4: I think first year is implied by the word "first".
Let's take principal = 100 and interest rate = 20%
Compound interest after 1 year = 100*(1+1/5) - 100 = 20
Simple interest after 1 year = (100*20*1)/100 = 20
Let's take principal = 300 and interest rate = 50%
Compound interest after 1 year = 300*(1+1/2) - 300 = 150
Simple interest after 1 year = (300*50*1)/100 = 150
Statement 4 is always true.
Answer (B).
Statement 3: Let's try some examples:
1/9 = 0.11111.....
23/99 = 0.2323232323.....
61/999 = 0.061061061061061.....
Statement 3 is always true.
Statement 4: I think first year is implied by the word "first".
Let's take principal = 100 and interest rate = 20%
Compound interest after 1 year = 100*(1+1/5) - 100 = 20
Simple interest after 1 year = (100*20*1)/100 = 20
Let's take principal = 300 and interest rate = 50%
Compound interest after 1 year = 300*(1+1/2) - 300 = 150
Simple interest after 1 year = (300*50*1)/100 = 150
Statement 4 is always true.
Answer (B).
15 Sep 2016, 20:40
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In statement 3 what if n is not an integer? for example n=1.5, then statement 3 is false. therefore answer choice D is correct.
