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The symbols $, # , and @ each represent a different positive

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The symbols $, # , and @ each represent a different positive

by ithamarsorek » Thu Mar 10, 2011 3:25 pm
Question: Didn't the question stem indicated that each represents a DIFFERENT positive digit?
does this mean that each has a different digit from the other and that digit is positive? or that each have any positive digit? Please clarify... This just sounds odd.

The symbols $, # , and @ each represent a different positive digit. If $-# = @, what is the value of # ?

(1) The value of $ is 8.

(2) # = 7@
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by tomada » Thu Mar 10, 2011 3:40 pm
IMO the answer is B.

The only information we can glean from Statement (1) is that # <> 9, since this would result in @ = -1, which is not allowed. This is INSUFFICIENT

Statement (2) can be re-written as $ - 7@ = @
Thus, $ = 8@.

There is only one possible value of @ such that @ and $ are each a different positive digit, and that value for @ = 1.
Thus, @ = 1 and $ = 8. Then, # = 7.

Statement (2) is SUFFICIENT
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by ithamarsorek » Thu Mar 10, 2011 3:45 pm
Didn't the question stem indicated that each represents a DIFFERENT positive digit? That what through me off.
Does this mean that each has a different digit from the other and that digit is positive? or that each have any positive digit? Please clarify... This just sounds odd
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by Night reader » Thu Mar 10, 2011 4:36 pm
received pm to comment.

$, #, @ {single digit numbers, +ve} > 0, $-#=@, find ONE value of # ?

statement (1) $ =8. By using this information we can deduct that 8-#=@ and # can have more than ONE values, e.g. 8-3=5, #=3 OR 8-2=6, #=2 Not Sufficient;
statement (2) # = 7@. By using this we might have other than @=1, #=7, $=8 values IF the digits were equal to 0, BUT the digits are positive. Sufficient

answer B

p.s. to solve this kind of questions more efficiently one would benefit from substituting all symbols $, #, @ with a,b,c - one example. Otherwise a confusion may arise during the algebraic translations.
ithamarsorek wrote:Question: Didn't the question stem indicated that each represents a DIFFERENT positive digit?
does this mean that each has a different digit from the other and that digit is positive? or that each have any positive digit? Please clarify... This just sounds odd.

The symbols $, # , and @ each represent a different positive digit. If $-# = @, what is the value of # ?

(1) The value of $ is 8.

(2) # = 7@
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