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There is a certain triangle with sides 7, 10, and X . If it is known that X is an integer, how many different values are there of X ? (A) 8 (B) 10 (C) 13 (D) 14 (E) 16 Source: GMAT Club Tests - hardest GMAT questions Didn't get the explanation.
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Let me try answering this, I am not too sure:
As per the Logic any side of a triangle cannot be more than sum of two side and cannot be less than the difference of two sides.
Hence as per the logic: 10-7<X<10+7 i.e. 3<X<17
Hence X can have at the most 13 possible values. The answer is c.
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Mankhu8, that is correct. That rule is known as the Triangle Inequality Rule. I can't post URLs yet, but search for triangle third side rule on Google and you'll get a link to a SparkNotes SAT page with all useful triangle rules.
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It's also important to not become careless and simply subtract 3 from 17. That would give us the wrong answer. INCORRECT: 17 - 3 = 14 CORRECT: Since 3 < x < 17, we list all the possible integers between these two extremes: 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, and 16. There are 13 possibilities.
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bandit wrote: There is a certain triangle with sides 7, 10, and X . If it is known that X is an integer, how many different values are there of X ? (A) 8 (B) 10 (C) 13 (D) 14 (E) 16 Source: GMAT Club Tests - hardest GMAT questions Didn't get the explanation. Remember the third side rule: perimeter-of-triangle-abc-87112.html#p654725traingle-sides-85784.html#p643924
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GT
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C.
Any side of a triangle cannot be greater than the sum of other two sides and cannot be less than the difference of two sides. As soon as this condition is broken, the only way to draw the triangle is by making it a straight line.
Hence boundaries for X < 10 + 7 = LT17 (max) and 10 - 7 = GT3 (min)
17 - 3 - 1 = 13
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Senior Manager
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Rule: Any side in a triangle must be smaller than the sum of the other sides, and greater than the difference of the other sides.
By considering above rule : 3<x<17. Different values are: 4,5,6,7,8,9,10,11,12,13,14,15,16. There are 13 different values.Answer is C
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the ans will be 13. sol as explained by Gmatters in above post.
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Answer is C - 13 As :: 3 < X < 17 ,
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silasaaa2 wrote: A 
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x is btwn (10-7) and (10+7) so 3<x<17
Ans C
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Manager
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Good question testing the famous triangle concept
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Manager
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The sum of any two sides of a triangle must be greater than the third side.
Answer is 3< x < 17
Since answer must be integers, they are 4-16 which equals 13.
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Manager
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This cannot be the hardest one for sure... 
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close
