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# If 7/5, 8/5 and p are sides of a triangle and p is a prime number, wha

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Math Expert
Joined: 02 Sep 2009
Posts: 49275
If 7/5, 8/5 and p are sides of a triangle and p is a prime number, wha  [#permalink]

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02 Sep 2018, 22:07
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25% (medium)

Question Stats:

70% (00:25) correct 30% (00:20) wrong based on 30 sessions

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If 7/5, 8/5 and p are sides of a triangle and p is a prime number, what is p?

A. 2
B. 3
C. 5
D. 7
E. 11

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Math Expert
Joined: 02 Aug 2009
Posts: 6796
Re: If 7/5, 8/5 and p are sides of a triangle and p is a prime number, wha  [#permalink]

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02 Sep 2018, 23:05
Bunuel wrote:
If 7/5, 8/5 and p are sides of a triangle and p is a prime number, what is p?

A. 2
B. 3
C. 5
D. 7
E. 11

Use The triangle inequality rule : the length of a side of a triangle is less than the sum of the lengths of the other two sides and greater than the difference of the lengths of the other two sides.

the length of a side of a triangle is less than the sum of the lengths of the other two sides
so $$p<\frac{7}{5}+\frac{8}{5}.........p<\frac{15}{5}........p<3$$
Only possibility is 2

A
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Re: If 7/5, 8/5 and p are sides of a triangle and p is a prime number, wha  [#permalink]

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03 Sep 2018, 08:43
Bunuel wrote:
If 7/5, 8/5 and p are sides of a triangle and p is a prime number, what is p?

A. 2
B. 3
C. 5
D. 7
E. 11

$$\frac{8}{5} - \frac{7}{5} < p < \frac{8}{5} + \frac{7}{5}$$

Or, $$\frac{1}{5} < p < 3$$

Among the given options only (A) 2 fits in, hence answer must be (A)
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Re: If 7/5, 8/5 and p are sides of a triangle and p is a prime number, wha  [#permalink]

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11 Sep 2018, 17:11
Bunuel wrote:
If 7/5, 8/5 and p are sides of a triangle and p is a prime number, what is p?

A. 2
B. 3
C. 5
D. 7
E. 11

7/5 = 1 2/5 = 1.4

8/5 = 1 3/5 = 1.6

These first two sides of the triangle sum to 3. Since the sum of any 2 sides of a triangle must be greater than the third, p must be 2.

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Re: If 7/5, 8/5 and p are sides of a triangle and p is a prime number, wha &nbs [#permalink] 11 Sep 2018, 17:11
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