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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: 53060
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, 21:07
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Difficulty:

15% (low)

Question Stats:

77% (00:47) correct 23% (00:39) wrong based on 37 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: 7334
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, 22:05
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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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

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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, 07:43
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, 16:11
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   [#permalink] 11 Sep 2018, 16:11
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