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Two sides of a triangle have lengths 4 and 10. If the third side

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by BTGModeratorVI » Sat May 16, 2020 7:33 am

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B

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E

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Two sides of a triangle have lengths 4 and 10. If the third side has a length of integer x, how many possible values are there for x ?

A. 4
B. 5
C. 6
D. 7
E. 8

Answer: D
Source: Manhattan prep
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Re: Two sides of a triangle have lengths 4 and 10. If the third side

by Brent@GMATPrepNow » Sat May 16, 2020 9:16 am
BTGModeratorVI wrote: ↑
Sat May 16, 2020 7:33 am
 Two sides of a triangle have lengths 4 and 10. If the third side has a length of integer x, how many possible values are there for x ?

A. 4
B. 5
C. 6
D. 7
E. 8

Answer: D
Source: Manhattan prep
IMPORTANT RULE: If two sides of a triangle have lengths A and B, then |A-B| < third side < A+B

So, for this question, we get: |10 - 4| < third side < 10 + 4
Simplify: 6 < x < 14

Since x is an INTEGER, x can be 7, 8, 9, 10, 11, 12 or 13 (7 possible values)

Answer: D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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