Which of the following statements must be true?

Question

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

Donnie84 · Answer

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).

cheeerio · Answer

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.

KarishmaB · Answer

We know that when the denominator is a multiple of 2 and/or 5, we get a terminating decimal. For more on this, check: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2013/12 ... -the-gmat/ So stmnt 2 is true but stmt 1 is not. We know that in case of annual compounding, amount after first year is same as amount after first year in case of simple interest. For more on this, check: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/03 ... imple-one/ Stmnt 3 is not clear. First of all, it doesn't say that x/y is a proper fraction. So in a case such as 12/9 = 1.3333... you don't get just the digits of the numerator. The intent of the question was perhaps that n is a positive integer but it hasn't been mentioned either. So stmnt 3 isn't necessarily true. Answer (D) What is the source of this question?

Kinshook · Answer

Asked: 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: NO
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. : YES
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. : YES
4) If the interest is accounted annually then for the first compounded interest would be equal to the simple interest. : YES

A) 2,3
B) 2,3,4
C) 1,2,3
D) 2,4
E) 1,3

IMO B

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Which of the following statements must be true?

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