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If n is an integer between 30 and 50 inclusive, what is the

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by Max@Math Revolution » Sun Nov 18, 2018 11:27 pm

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[Math Revolution GMAT math practice question]

If n is an integer between 30 and 50 inclusive, what is the value of n?

1) When n is divided by 8, the remainder is 7
2) When n is divided by 16, the remainder is 7
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by Brent@GMATPrepNow » Mon Nov 19, 2018 6:48 am
Max@Math Revolution wrote:If n is an integer between 30 and 50 inclusive, what is the value of n?

1) When n is divided by 8, the remainder is 7
2) When n is divided by 16, the remainder is 7
Target question: What is the value of n?

Given: n is an integer between 30 and 50 inclusive

Statement 1: When n is divided by 8, the remainder is 7
------ASIDE--------------------------------------
When it comes to remainders, we have a nice rule that says:
If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.
For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.
----------------------------------------------------
Based on statement 1, the possible values of n are: 7, 15, 23, 31, 39, 47, 55, . . . etc
Since n is an integer between 30 and 50 inclusive, we can see that n COULD equal 31, 39, or 47
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: When n is divided by 16, the remainder is 7
The possible values of n are: 7, 23, 39, 55, 71, . . . etc
Since n is an integer between 30 and 50 inclusive, we can see that n MUST equal 39
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by fskilnik@GMATH » Mon Nov 19, 2018 10:42 am
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

If n is an integer between 30 and 50 inclusive, what is the value of n?

1) When n is divided by 8, the remainder is 7
2) When n is divided by 16, the remainder is 7
$$30\,\,\, \le \,\,\,n\,\,{\mathop{\rm int}} \,\,\, \le \,\,\,50\,\,\,\,\left( * \right)$$
$$? = n$$

$$\left( 1 \right)\,\,n = 8Q + 7\,\,,\,\,Q\,\,{\mathop{\rm int}} \,\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,Q = 3\,\,\,\, \Rightarrow \,\,\,\,\,? = 31\,\, \hfill \cr
\,{\rm{Take}}\,\,Q = 4\,\,\,\, \Rightarrow \,\,\,\,\,? = 39\,\, \hfill \cr} \right.\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{INSUFF}}.$$

$$\left( 2 \right)\,\,n = 16K + 7,\,\,K\,\,{\mathop{\rm int}} \,\,\,\,\,\mathop \Rightarrow \limits^{\left( {**} \right)} \,\,\,\,\,K = 2\,\,\,\,\,\, \Rightarrow \,\,\,\,? = 39\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}{\rm{.}}$$
$$\left( {**} \right)\,\,\,39 - 16 < 30\,\,\,{\rm{and}}\,\,\,39 + 16 > 50\,\,,\,\,\,{\rm{impossible}}\,\,{\rm{by}}\,\,\left( * \right)$$


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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Portuguese-speakers :: https://www.gmath.com.br
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by Max@Math Revolution » Wed Nov 21, 2018 2:24 am
=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 1 variable (n) and 0 equations, D is most likely to be the answer. So, we should consider each condition on its own first.

Condition 1)
We can express n = 8k+7 for some integer k.
If k = 3, then n = 31.
If k = 4, then n = 39.
Since we don't have a unique solution, condition 1) is not sufficient.

Condition 2)
We can express n = 16m+7 for some integer m.
If m = 2, then n = 39.
If m = 1, then n = 23 and n < 30.
If m = 3, then n = 55 and n > 50.
Thus n = 39 is the unique solution and condition 2) is sufficient.

Therefore, B is the answer.
Answer: B

If the original condition includes "1 variable", or "2 variables and 1 equation", or "3 variables and 2 equations" etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
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