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# Which of the following describes the possible range of values of y?

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Math Expert
Joined: 02 Sep 2009
Posts: 50627
Which of the following describes the possible range of values of y?  [#permalink]

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12 Jul 2018, 00:12
00:00

Difficulty:

15% (low)

Question Stats:

78% (00:52) correct 22% (01:22) wrong based on 49 sessions

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Which of the following describes the possible range of values of y?

A. $$9 < y < 11$$

B. $$5 < y < 11$$

C. $$9 < y < 15$$

D. $$5 < y < 15$$

E. $$10 < y < 20$$

Attachment:

triangle (1).jpg [ 7.65 KiB | Viewed 551 times ]

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Which of the following describes the possible range of values of y?  [#permalink]

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Updated on: 12 Jul 2018, 00:33
1
+1 for E.

11 - 5 < y-4 < 11 + 5 (Property of triangle)
6 < y - 4 < 16
6+4 < y-4+4 < 16+4 (adding 4)
10 < y < 20

Hence, E.
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Originally posted by sudarshan22 on 12 Jul 2018, 00:19.
Last edited by sudarshan22 on 12 Jul 2018, 00:33, edited 1 time in total.
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Re: Which of the following describes the possible range of values of y?  [#permalink]

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12 Jul 2018, 00:25
Bunuel wrote:

Which of the following describes the possible range of values of y?

A. $$9 < y < 11$$

B. $$5 < y < 11$$

C. $$9 < y < 15$$

D. $$5 < y < 15$$

E. $$10 < y < 20$$

Attachment:
triangle (1).jpg

$$y-4+5>11$$
$$y>10$$

$$y-4<5+11$$
$$y<20$$

$$10<y<20$$

Property used - No side of a triangle can be greater than the sum of other 2 sides.

Hence E
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Which of the following describes the possible range of values of y?  [#permalink]

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12 Jul 2018, 06:25
Bunuel wrote:

Which of the following describes the possible range of values of y?

A. $$9 < y < 11$$

B. $$5 < y < 11$$

C. $$9 < y < 15$$

D. $$5 < y < 15$$

E. $$10 < y < 20$$

Attachment:
triangle (1).jpg

Note:[color= The sum of the any 2 legs will be greater than the 3rd leg. [/color]. This question is designed solely based on this concept.

Given,

legs = 11 , 5 , ( y - 4)

CASE 1:

(y- 4 ) + 5 > 11

y> 10

CASE 2:

y-4 < 11+ 5

y < 20.

Combining both cases :

10 < y < 20.

Thus option E is the best answer.
Which of the following describes the possible range of values of y? &nbs [#permalink] 12 Jul 2018, 06:25
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