decimals

[prachi18oct]

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

[DavidG@VeritasPrep]

Does the decimal expression of the fraction have more than 2 distinct non-zero digits?

(1) y is a digit greater than 3
(2) y is an odd prime number

I think we're missing something here...

[prachi18oct]

Does the decimal expression of the fraction have more than 2 distinct non-zero digits?

(1) y is a digit greater than 3
(2) y is an odd prime number

I think we're missing something here...

Hi David,

This is the complete question I have.

[rumi21]

Hello Prachi,

I also think the question is incomplete. As observed from the statements it is mentioning the facts about 'y'. But as observed in the question there is nothing mentioned about 'y'.

[nikhilgmat31]

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

Statement 1

y =4,5,6,7,8,9
4/4 = 1
5/4 = 1.25
6/4 = 1.5
7/4 = 1.75
8/4 = 2
9/4 = 2.25

NOT SUFFICIENT

statement 2

y is odd number - 1,3,5,7,9

y/4 = leads to decimals as .25,.75,.25,.75 so SUFFICIENT.

Answer is B.

[prachi18oct]

Sorry guys! My bad have edited my original post now.

[Brent@GMATPrepNow]

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)
.
.
.
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

[nikhilgmat31]

Brent, Question says decimal expression of fraction.

Doesn't it mean digits after decimal point. ?

[Brent@GMATPrepNow]

Brent, Question says decimal expression of fraction.

Doesn't it mean digits after decimal point. ?

No. The decimal expression basically means the equivalent version of the fraction written as a non-fraction.

So, the decimal expression of 11/8 = 1.375

Cheers,
Brent

[nikhilgmat31]

Thanks Brent for explanation.

[Max@Math Revolution]

In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem.

Remember equal number of variables and equations ensures a solution.

In original condition, we have 1 variable (y) then we need 1 equation. (1) is 1 equation (sufficient) and (2) is 1 equation. D is likely to be the answer.
In (1), if y=0, y/4=4/4=1 (No). if y=5, y/4=5/4=1.25 (Yes), Not sufficient.
In (2), if y=3, y/4=3/4=0.75 (No). if y=5, Yes. Not sufficient.
In (1) and (2), if y is odd prime greater than 3, y/4=1.25, 1.75, 2.75 Like this, always yes so sufficient. C is the answer.

In general, if we have 1 variable in original condition, probability of answer D is 60%. But in this case, C is the answer.

Why C? If you know our own innovative logics to find the answer, you don't need to solve the problem.
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[Max@Math Revolution]

We have 1 variable (y) in the original condition, so we need 1 equation to solve for this variable.
Condition 1 gives us an equation, and condition 2 gives us another equation, so the chances are high that D is the answer.

In condition 1), if y=4, then y/4=4/4=1 (no), and if y=5, then y/4=5/4=1.25 (yes)
Since we have "no" and "yes" appearing at the same time, this condition alone is not sufficient

In condition 2), if y=3, then y/4=3/4=0.75 (no), and if y=5, then (yes)
Again, we have "no" and "yes" appearing at the same time, so this condition alone is not sufficient

If we take the conditions together, 1) & 2), if y is an odd prime greater than 3, then y/4=1.25, 1,75, 2.75.., and we can answer "yes" always.
The two conditions together are sufficient and the answer becomes C

In general, if the original condition has 1 variable, about 60% of the time the answer will be D. This is a special case where the answer is C.

[nikhilgmat31]

We have 1 variable (y) in the original condition, so we need 1 equation to solve for this variable.
Condition 1 gives us an equation, and condition 2 gives us another equation, so the chances are high that D is the answer.

In condition 1), if y=4, then y/4=4/4=1 (no), and if y=5, then y/4=5/4=1.25 (yes)
Since we have "no" and "yes" appearing at the same time, this condition alone is not sufficient

In condition 2), if y=3, then y/4=3/4=0.75 (no), and if y=5, then (yes)
Again, we have "no" and "yes" appearing at the same time, so this condition alone is not sufficient

If we take the conditions together, 1) & 2), if y is an odd prime greater than 3, then y/4=1.25, 1,75, 2.75.., and we can answer "yes" always.
The two conditions together are sufficient and the answer becomes C

In general, if the original condition has 1 variable, about 60% of the time the answer will be D. This is a special case where the answer is C.

But Consider case of 23 which satisfies statement1 & 2.

23/4 = 5.75 Here number of distinct digits are 5 & 7. so only 2

where as in 5/4 = 1.25 Here number of distinct digits are 1,2 & 5 . so 3

Answer is E

[Max@Math Revolution]

In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem.
Remember equal number of variables and equations ensures a solution.



In original condition, we have 1 variable (y) then we need 1 equation. (1) is 1 equation (sufficient) and (2) is 1 equation. D is likely to be the answer.

In (1), if y=0, y/4=4/4=1 (No). if y=5, y/4=5/4=1.25 (Yes), Not sufficient.

In (2), if y=3, y/4=3/4=0.75 (No). if y=5, Yes. Not sufficient.

In (1) and (2), if y is odd prime greater than 3, y/4=1.25, 1.75, 2.75 Like this, always yes so sufficient. C is the answer.


In general, if we have 1 variable in original condition, probability of answer D is 60%. But in this case, C is the answer.



If you know our own innovative logics to find the answer, you don't need to actually solve the problem.


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