If x > 0 and two sides of a certain triangle have lengths and respectively, which of the following could be the length of the third side of the triangle?

Indicate all possible lengths.

The answers are A, C, and E. Remember, for this MAQ, you must choose all 3 correct answers (no more, no less, no B, and no D!) in order to get full credit.

Video explanation:

Let us know if you have any trouble understanding the explanations. If you’d like to read up on this new question type, I’d recommend the posts on the category page for MAQ!

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I have one doubt. As per me, the answer will be only A and C .

Because for case E, Let’s say if i take x=1, in this case E will come 19 and other two sides will become 3 and 7 . Now in this case , sum of two sides is not greater than third side.

Hence, in my opinion E cannot be the answer of this

The wording of the question is a little tricky– because it says, “which of the following could be the length of the third side of the triangle?”, if the answer (for any value of x) can output a length that fits the requirements, then it is one of the correct answers.

So you are correct, in that if x=1, Answer E=19 and 4<19<10 is definitely not true. However, if x=10, Answer E=37, and 13<37<55 is true.

If you try this with Answer C (when x=1 or x=10), you'll see that C, too, is only true for certain values-- and the crucial part to remember is that even if it is only true for ONE value, it is still a correct answer.

Apologies for the obvious question in advance!
How can the test taker figure out that the length of the 2nd side is 2x+1 when it isn’t specified in the question? Does this relate to the property of triangles?

Actually, it was my fault: the formatting was a little wonky for the typed questions, and the 2x+1 part wasn’t displaying correctly. The problem in text should now look just the way it does in the explanation, with the given formulas specified for each side. Sorry for the confusion!

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Hi Guys , pls send all the practise questions and the questions that you have taken in your new gre tests. pls …thank you.

Thanks Margarette for the Explanation!!

I have one doubt. As per me, the answer will be only A and C .

Because for case E, Let’s say if i take x=1, in this case E will come 19 and other two sides will become 3 and 7 . Now in this case , sum of two sides is not greater than third side.

Hence, in my opinion E cannot be the answer of this

see the question is all possible answers.even i thought the same .the answer C is valid for higher value of x.

Hi, Sachin

The wording of the question is a little tricky– because it says, “which of the following could be the length of the third side of the triangle?”, if the answer (for any value of x) can output a length that fits the requirements, then it is one of the correct answers.

So you are correct, in that if x=1, Answer E=19 and 4<19<10 is definitely not true. However, if x=10, Answer E=37, and 13<37<55 is true.

If you try this with Answer C (when x=1 or x=10), you'll see that C, too, is only true for certain values-- and the crucial part to remember is that even if it is only true for ONE value, it is still a correct answer.

Hope that helps! 🙂

Hi Margarette,

Apologies for the obvious question in advance!

How can the test taker figure out that the length of the 2nd side is 2x+1 when it isn’t specified in the question? Does this relate to the property of triangles?

Thanks for your response.

Hi, Nicola– no problem!

Actually, it was my fault: the formatting was a little wonky for the typed questions, and the 2x+1 part wasn’t displaying correctly. The problem in text should now look just the way it does in the explanation, with the given formulas specified for each side. Sorry for the confusion!

Sure, thanks for clarifying!