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GMATbuster92
Joined: 28 Jun 2018
Last visit: 20 Jul 2019
Posts: 147
Given Kudos: 32
Location: India
Concentration: Finance, Marketing
Schools: CUHK '21 (II)
GMAT 1: 650 Q49 V30
GPA: 4
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22 Sep 2018, 09:07
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
58% (01:21) correct
42%
(01:28)
wrong
based on 227
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Is the perimeter of a certain triangle less than 24 inches?
(1) The shortest side of the triangle is \(8\frac{1}{4}\) inches.
(2) The triangle is isosceles and the longest side is 1 inch longer than each of the other sides.
(1) The shortest side of the triangle is \(8\frac{1}{4}\) inches.
(2) The triangle is isosceles and the longest side is 1 inch longer than each of the other sides.
22 Sep 2018, 16:16
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GMATbuster92
\(0 < a \le b \le c\,\,\,\,\left[ {{\rm{inches}}} \right]\,\,\,\,\,\,\,\,\,\,\left( * \right)\)
\(a + b + c\,\,\mathop < \limits^? \,\,24\)
\(\left( 1 \right)\,\,\,a = 8{1 \over 4}\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,a + b + c\,\,\, \ge \,\,\,3 \cdot \left( {8{1 \over 4}} \right)\,\,\,\, > \,\,\,24\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left\langle {{\rm{NO}}} \right\rangle\)
\(\left( 2 \right)\,\,\,\left\{ \matrix{\\
a = b = x \hfill \cr \\
c = x + 1 \hfill \cr \\
\,\left( {\Delta \,\,{\rm{existence}}} \right)\,\,\,x + 1 < 2x\,\,\,\, \Leftrightarrow \,\,\,\,x > 1\,\,\,\left( {**} \right) \hfill \cr} \right.\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left\{ \matrix{\\
\,{\rm{Take}}\,\,\,\left( {a,b,c} \right) = \left( {2,2,3} \right)\,\,\,\,\,\mathop \Rightarrow \limits^{\left( {**} \right)} \,\,\,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \hfill \cr \\
\,{\rm{Take}}\,\,\,\left( {a,b,c} \right) = \left( {8,8,9} \right)\,\,\,\,\,\mathop \Rightarrow \limits^{\left( {**} \right)} \,\,\,\,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \hfill \cr} \right.\,\,\,\,\,\,\)
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
23 Sep 2018, 03:12
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Solution
To find:
- • Whether the perimeter of a certain triangle less than 24 inches or not
Analysing Statement 1
As per the information given in statement 1, the shortest side of the triangle is 8.25 inches
- • So, the other two sides are greater than 8.25 inches.
• Hence, the perimeter can be 8.25 + (>8.25) + (>8.25) inches = greater than 24.75 inches
As we can conclude that perimeter is greater than 24 inches, statement 1 is sufficient.
Analysing Statement 2
As per the information given in statement 2, the triangle is isosceles, and the longest side is 1 inch longer than each of the other sides.
- • From this statement, we can’t find the exact length of the sides, and hence, can’t find the perimeter.
Therefore, statement 2 is not sufficient.
Hence, the correct answer is option A.
Answer: A
