Hundreds and hundredth

[neeti2711]

Is the tens digit of p equal to 6?

(1) p/10000 has a thousandths digit of 6.
(2) 0.1p has a hundreds digit of 6

(A) Statement (1) ALONE is sufficient, but statement (2) is not sufficient.
(B) Statement (2) ALONE is sufficient, but statement (1) is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.

[DavidG@VeritasPrep]

Is the tens digit of p equal to 6?

(1) p/10000 has a thousandths digit of 6.
(2) 0.1p has a hundreds digit of 6

(A) Statement (1) ALONE is sufficient, but statement (2) is not sufficient.
(B) Statement (2) ALONE is sufficient, but statement (1) is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.

If the thousandths digit is 6, we know we're looking at the following x.xx6xx (the first digit to the right of the decimal is the tenths digit. The second is the hundredths. The third is the thousandths.)

Statement 1: Say p/10000 = 0.006. p = .006 *10000 = 60. The tens digit is 6.
Say p/10000 = .116. p = 1160. The tens digit is 6. Notice that no matter what we pick, that 6 is going to slide into the tens digit. So this statement alone is sufficient to answer the question

Statement 2: Case 1: .1p = 600; p = 6000 and the tens digit is 0.
Case 2: .1p = 625; p = 6250 and the tens digit is 5. Because we do not get a unique value, statement 2 alone is not sufficient to answer the question.

The answer is A

[DavidG@VeritasPrep]

(Worth noting: it is much easier to select a number for p/10,000 or .1p and then solve for p than it is to attempt to mentally select a p that will satisfy the conditions.)

[Jay@ManhattanReview]

Is the tens digit of p equal to 6?

(1) p/10000 has a thousandths digit of 6.
(2) 0.1p has a hundreds digit of 6

(A) Statement (1) ALONE is sufficient, but statement (2) is not sufficient.
(B) Statement (2) ALONE is sufficient, but statement (1) is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.

We have to see whether the tens digit of p is equal to 6.

S1: p/10000 has a thousandths digit of 6.

Let us assume a number for p/10000 such that its thousandths digit is 6.

Say p/10000 = abc.xy6z

=> p = abc.xy6z * 10000

=> p = abcxy6z

We see that the tens digit is '6.'

The answer is YES. Sufficient.

S2: 0.1p has a hundreds digit of 6.

Say 0.1p = a6bc.xyz

=> p/10 = a6bc.xyz

=> p = a6bcx.yz

We see that the hundreds digit is 'b'; if 'b = 6', the answer is YES; however b is other than '6,' the answer is NO. No unique answer. Insufficient.

The correct answer: A

Hope this helps!

Relevant book: Manhattan Review GMAT Data Sufficiency Guide

-Jay
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[Scott@TargetTestPrep]

Is the tens digit of p equal to 6?

(1) p/10000 has a thousandths digit of 6.
(2) 0.1p has a hundreds digit of 6

We can let our number be ABCD, in which A is the thousands digit, B is the hundreds digit, C is the tens digit, and D is the units digit. We need to determine the value of C.

Statement One Alone:

p/10000 has a thousandths digit of 6.

ABCD/10,000 = 0.ABCD, and since 0.ABCD has a thousandths digit of 6, C = 6. Statement one alone is sufficient to answer the question.

Statement Two Alone:

0.1p has a hundreds digit of 6

0.1 x ABCD = ABC.D, and ABC.D has a hundreds digit of 6. Thus, A = 6. However, since we do not have a value for C, statement two alone is not sufficient.

Answer: A