prachi18oct wrote:Does the decimal expression of the fraction y/4 have more than 2 distinct non-zero digits?
(1) y is a digit greater than 3
(2) y is an odd prime number
Let's examine some values of y:
y = 1: we get 1/4 = 0.25, which has 2 distinct non-zero digits (2 and 5)
y = 2: we get 2/4 = 0.5, which has 1 distinct non-zero digit (5)
y = 3: we get 3/4 = 0.75, which has 2 distinct non-zero digits (7 and 5)
y = 4: we get 4/4 = 1, which has 1 distinct non-zero digit (1)
y = 5: we get 5/4 = 1.25, which has
3 distinct non-zero digits (1, 2 and 5)
y = 6: we get 6/4 = 1.5, which has 2 distinct non-zero digits (1 and 5)
y = 7: we get 7/4 = 1.75, which has
3 distinct non-zero digits (1, 7 and 5)
y = 8: we get 8/4 = 2, which has 1 distinct non-zero digit (2)
y = 9: we get 9/4 = 2.25, which has 2 distinct non-zero digits (2 and 5)
.
.
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y = 23: we get 23/4 = 5.75, which has 2 distinct non-zero digits (5 and 7)
Okay, onto the question:
Target question: Does the decimal expression of the fraction y/4 have more than 2 distinct non-zero digits?
Statement 1: y is a digit greater than 3
Hmmmmmmmm. I think you mean that y is an INTEGER greater than 3. I'll assume that this is the case.
This statement doesn't
FEEL sufficient, so I'm going to TEST some values.
There are several values of y that satisfy statement 1. Here are two:
Case a: y = 4, in which case
the decimal expression of the fraction y/4 does NOT have more than 2 distinct non-zero digits
Case b: y = 5, in which case
the decimal expression of the fraction y/4 DOES have more than 2 distinct non-zero digits
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: https://www.gmatprepnow.com/articles/dat ... lug-values
Statement 2: y is an odd prime number
There are several values of y that satisfy statement 2. Here are two:
Case a: y = 3, in which case
the decimal expression of the fraction y/4 does NOT have more than 2 distinct non-zero digits
Case b: y = 5, in which case
the decimal expression of the fraction y/4 DOES have more than 2 distinct non-zero digits
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
If we assume that statement 1 is supposed to say that y is an INTEGER greater than 3, then the answer is
E
Consider these 2 conflicting cases:
Case a: y = 23, in which case
the decimal expression of the fraction y/4 does NOT have more than 2 distinct non-zero digits
Case b: y = 5, in which case
the decimal expression of the fraction y/4 DOES have more than 2 distinct non-zero digits
Since we cannot answer the
target question with certainty, the combined statements are NOT SUFFICIENT
Answer =
E
Cheers,
Brent
have edited my original post now.
