Magoosh
\(w, x\) and \(y\) are positive integers such that \(w \leq x \leq y\). If the average (arithmetic mean) of \(w, x\) and \(y\) is \(20\), is \(w > 15\)?
1) \(y = 28\)
2) One of the three numbers is \(17\)
OA C
\(w, x\) and \(y\) are positive integers such that
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First, infer everything we can from the given information:
\(w, x\) and \(y\) are positive integers such that \(w \leq x \leq y\)
the average (arithmetic mean) of \(w, x\) and \(y\) is \(20\)
Infer --> the sum of w, x, and y is 60.
Question: is \(w > 15\)?
Since we know that the sum is 60 and w is the smallest value, w would equal 15 if \(x + y = 45\). Thus, w > 15 if \(x + y < 45\).
Rephrased question: is x + y < 45 ?
1) y = 28
This doesn't tell us whether x + y < 45.
But to be sure that it's insufficient, it's best to test cases:
Case 1:
w = 12, x = 20, y = 28
is \(w > 15\)? --> No.
Case 2:
w = 16, x = 16, y = 28
is \(w > 15\)? --> Yes.
Since we can get a "yes" or a "no" answer while keeping the statement true, this is insufficient.
2) One of the three numbers is 17.
Again, this doesn't tell us whether x + y < 45. But to be sure that it's insufficient, we'll test cases again:
Case 1:
w = 17, x = 20, y = 23
is \(w > 15\)? --> Yes.
Case 2:
w = 10, x = 17, y = 33
is \(w > 15\)? --> No.
Since we can get a "yes" or a "no" answer while keeping the statement true, this is insufficient.
(1) & (2) Together: y = 28 and one value = 17.
Since 28 + 17 = 45, then the 3rd value must be 15. And since w is the lowest value, w must equal 15. This is sufficient to answer the question: w is definitively not greater than 15.
The answer is C.
\(w, x\) and \(y\) are positive integers such that \(w \leq x \leq y\)
the average (arithmetic mean) of \(w, x\) and \(y\) is \(20\)
Infer --> the sum of w, x, and y is 60.
Question: is \(w > 15\)?
Since we know that the sum is 60 and w is the smallest value, w would equal 15 if \(x + y = 45\). Thus, w > 15 if \(x + y < 45\).
Rephrased question: is x + y < 45 ?
1) y = 28
This doesn't tell us whether x + y < 45.
But to be sure that it's insufficient, it's best to test cases:
Case 1:
w = 12, x = 20, y = 28
is \(w > 15\)? --> No.
Case 2:
w = 16, x = 16, y = 28
is \(w > 15\)? --> Yes.
Since we can get a "yes" or a "no" answer while keeping the statement true, this is insufficient.
2) One of the three numbers is 17.
Again, this doesn't tell us whether x + y < 45. But to be sure that it's insufficient, we'll test cases again:
Case 1:
w = 17, x = 20, y = 23
is \(w > 15\)? --> Yes.
Case 2:
w = 10, x = 17, y = 33
is \(w > 15\)? --> No.
Since we can get a "yes" or a "no" answer while keeping the statement true, this is insufficient.
(1) & (2) Together: y = 28 and one value = 17.
Since 28 + 17 = 45, then the 3rd value must be 15. And since w is the lowest value, w must equal 15. This is sufficient to answer the question: w is definitively not greater than 15.
The answer is C.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education