Data Sufficiency

Experts can you please help me figure this one out.


In the former Soviet Union, rubles came in denominations of 1, 3, 5, 10, 25, 50, and 100. Boris and Natasha are at the bank to change an enormous pile of 50 and 100 ruble notes, but the teller is out of 10s and is forced to give them their change in nothing but 1, 3, 5, and 25 ruble notes. Did the teller give Boris and Natasha the correct change?

(1) The teller gave Boris and Natasha 2013 notes.

(2) The teller did not give Boris and Natasha any 3 ruble notes.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked

Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient

EACH statement ALONE is sufficient to answer the question asked

Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed

OA : A

Source : Veritas prep free question Bank

manik11 wrote:In the former Soviet Union, rubles came in denominations of 1, 3, 5, 10, 25, 50, and 100. Boris and Natasha are at the bank to change an enormous pile of 50 and 100 ruble notes, but the teller is out of 10s and is forced to give them their change in nothing but 1, 3, 5, and 25 ruble notes. Did the teller give Boris and Natasha the correct change?

(1) The teller gave Boris and Natasha 2013 notes.

(2) The teller did not give Boris and Natasha any 3 ruble notes.

Let x = the total number of 50 ruble notes and y = the total number of 100 ruble notes.
Total amount brought in by Boris and Natasha = 50x + 100y = 50(x + 2y) = multiple of 50.

Statement 1:The teller gave Boris and Natasha 2013 notes.
Let:
a = the number of 1 ruble notes.
b = the number of 3 ruble notes.
c = the number of 5 ruble notes.
d = the number of 25 ruble notes.
Thus:
a + b + c + d = 2013.

If the correct change is given for the total amount brought in by Boris and Natasha, then a + 3b + 5c + 25d = multiple of 50.
Adding together a + 3b + 5c + 25d = multiple of 50 and a + b + c + d = 2013, we get:
(a + 3b + 5c + 25d) + (a + b + c + d) = (multiple of 50) + 2013
2a + 4b + 6c + 26d = even + odd
even + even + even + even = odd
even = odd.
Doesn't work.
Thus, it is not possible that the correct change is given.
SUFFICIENT.

Statement 2: The teller did not give Boris and Natasha any 3 ruble notes.
Let x=1 and y=1, implying that the total amount = 50(1) + 100(1) = 150.
If the teller gives Boris and Natasha three 50 ruble notes -- for a total of 150 rubles -- then the correct change is given.
If the teller gives Boris and Natasha two 50 ruble notes -- for a total of 100 rubles -- then the correct change is NOT given.
INSUFFICIENT.

The correct answer is A.

Thanks a lot Mitch. I got stuck after the initial a+b+c+d=2013
Never saw this approach coming

GMATGuruNY wrote: (a + 3b + 5c + 25d) + (a + b + c + d) = (multiple of 50) + 2013
2a + 4b + 6c + 26d = even + odd
even + even + even + even = odd
even = odd.
Doesn't work.
Thus, it is not possible that the correct change is given.
SUFFICIENT.