GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 22 Oct 2018, 22:21

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Is the perimeter of a certain triangle less than 24 inches?

Author Message
TAGS:

### Hide Tags

Manager
Joined: 28 Jun 2018
Posts: 142
Location: India
Concentration: Finance, Marketing
GMAT 1: 650 Q49 V30
GPA: 4
Is the perimeter of a certain triangle less than 24 inches?  [#permalink]

### Show Tags

22 Sep 2018, 09:07
1
00:00

Difficulty:

45% (medium)

Question Stats:

55% (00:53) correct 45% (01:02) wrong based on 33 sessions

### HideShow timer Statistics

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.

_________________

What to do if you are new to GMAT:
https://gmatclub.com/forum/what-to-do-if-you-are-new-272708.html#p2108758

Give me kudos if you like it , it's totally harmless

GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 392
Re: Is the perimeter of a certain triangle less than 24 inches?  [#permalink]

### Show Tags

22 Sep 2018, 16:16
GMATbuster92 wrote:
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.

$$0 < a \le b \le c\,\,\,\,\left[ {{\rm{inches}}} \right]\,\,\,\,\,\,\,\,\,\,\left( * \right)$$

$$a + b + c\,\,\mathop < \limits^? \,\,24$$

$$\left( 1 \right)\,\,\,a = 8{1 \over 4}\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,a + b + c\,\,\, \ge \,\,\,3 \cdot \left( {8{1 \over 4}} \right)\,\,\,\, > \,\,\,24\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left\langle {{\rm{NO}}} \right\rangle$$

$$\left( 2 \right)\,\,\,\left\{ \matrix{ a = b = x \hfill \cr c = x + 1 \hfill \cr \,\left( {\Delta \,\,{\rm{existence}}} \right)\,\,\,x + 1 < 2x\,\,\,\, \Leftrightarrow \,\,\,\,x > 1\,\,\,\left( {**} \right) \hfill \cr} \right.\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\,\left( {a,b,c} \right) = \left( {2,2,3} \right)\,\,\,\,\,\mathop \Rightarrow \limits^{\left( {**} \right)} \,\,\,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \hfill \cr \,{\rm{Take}}\,\,\,\left( {a,b,c} \right) = \left( {8,8,9} \right)\,\,\,\,\,\mathop \Rightarrow \limits^{\left( {**} \right)} \,\,\,\,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \hfill \cr} \right.\,\,\,\,\,\,$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________

Fabio Skilnik :: https://www.GMATH.net (Math for the GMAT)
Course release PROMO : finish our test drive till 31/Oct with (at least) 60 correct answers out of 92 (12-questions Mock included) to gain a 60% discount!

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2069
Re: Is the perimeter of a certain triangle less than 24 inches?  [#permalink]

### Show Tags

23 Sep 2018, 03:12

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.

_________________

Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Re: Is the perimeter of a certain triangle less than 24 inches? &nbs [#permalink] 23 Sep 2018, 03:12
Display posts from previous: Sort by