In triangle XYZ, whatis the length of YZ?

IMO: D

taking only A, not sufficient because only one side is known
taking only B , insufficient since only one side is known

combining both together , sufficiant because it forms a triplet and the third side = 4

From S1:knowing length of one side is not sufficient to determine length of others in a triangle unless it is of a particular type.
From S2:Sam explanation.Insuffficient.
Combining the two we could have the third side as 3,4,5,6,7(sum of two sides in a triangle always greater than third) but no single length can be known.
Ans.E

Statement 1: From length XY = 3, we cannot determine the length of YZ; Not Sufficient.
Statement 2: From lenth XZ = 5, we cannot determine the length of YZ; Not Sufficient.

Combining both statements, we still cannot definitely find a value for YZ as the length of YZ could be any integer from 3 to 7. Do not assume that YZ will be 4, as nowhere has it been stated that the triangle is a right angled triangle.

Ans is (E).

Rule: length of 3rd side must be greater than the difference of the other 2 sides and less than the sum of the other two sides; hence, the length of the third side is 5-3 < yz < 5+3. Given that there are multiple values in this range, the answer would therefore be E.

IMPORTANT RULE: If two sides of a triangle have lengths A and B, then . . .
DIFFERENCE between A and B < length of third side < SUM of A and B

Target question: What is the length of YZ?

We can see that each statement alone provides information about only ONE side of the triangle, so we can jump straight to...

Statements 1 and 2 combined
Statement 1 tells us that one side has length 3
Statement 2 tells us that one side has length 5
According to the above rule, we can say: 5 - 3 < length of side YZ < 5 + 3
In other words: 2 < length of side YZ < 8
This means there are infinitely many answers to the target question
For example, the length of side YZ COULD be 4 or 7 or 5.3 or 3.001 or ...
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

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In triangle XYZ, whatis the length of YZ?


(1) The length of XY is 3.

Clearly insufficient.

(2) The length of XZ is 5.

Clearly insufficient.

(1&2) We know the length of two sides are 3 and 5. The third side needs to be greater than the difference of the other two sides and less than the sum of those two sides.

Thus:

2 < YZ < 8

There are many values that satisfy this equation. INSUFFICIENT.

Answer is E.

Solution:

We need to determine the length of side YZ of triangle XYZ.

Statement One Alone:

Knowing only the length of one side of a triangle does not allow us to determine the length of another side of the triangle, especially since we don’t know what type of triangle XYZ is. Statement one alone is not sufficient.

Statement Two Alone:

Like statement one, knowing only the length of one side of a triangle does not allow us to determine the length of another side of the triangle, especially since we don’t know what type of triangle XYZ is. Statement two alone is not sufficient.

Statements One and Two Together:

Knowing the lengths of two sides of a triangle does not allow us to determine the length of the remaining side of the triangle. Since XY = 3 and XZ = 5, YZ could be 3, 4 or 7, as long as it’s less than the sum of the lengths of XY and XZ and more than the positive difference of the lengths of XY and XZ. Both statements together are not sufficient.

Answer: E

ScottTargetTestPrep
Thank you for this helpful explanation. To confirm, we cannot assume that this triangle is a 3-4-5 triangle because we do not know if it is a right triangle, correct?

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