If x, y, and z are the lengths of the three sides of a triangle, is y > 4?
(1) z = x + 4
(2) x = 3 and z = 7
Source: Official Guide
Answer: D
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
If x, y, and z are the lengths of the three sides
This topic has expert replies
-
BTGModeratorVI
- Legendary Member
- Posts: 1223
- Joined: Sat Feb 15, 2020 2:23 pm
- Followed by:1 members
GMAT/MBA Expert
-
Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
IMPORTANT RULE: If two sides of a triangle have lengths A and B, then . . .BTGModeratorVI wrote: ↑Sat Feb 15, 2020 2:51 pmIf x, y, and z are the lengths of the three sides of a triangle, is y > 4?
(1) z = x + 4
(2) x = 3 and z = 7
Source: Official Guide
Answer: D
DIFFERENCE between A and B < length of third side < SUM of A and B
Given: x, y, and z are the lengths of the three sides of a triangle
Target question: Is y > 4?
Statement 1: z = x + 4
This means that x and x+4 are the lengths of two sides of the triangle.
When we apply the rule above, we can see that: (x + 4) - x < length of third side (aka y) < (x + 4) + x
Simplify: 4 < y < 2x + 4
At this point we can see that the answer to the target question is YES, y IS greater than 4
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: x = 3 and z = 7
When we apply the rule above, we can see that:7 - 3 < length of third side (aka y) < 7 + 3
Simplify: 4 < y < 10
The answer to the target question is YES, y IS greater than 4
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer: D
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
-
deloitte247
- Legendary Member
- Posts: 2214
- Joined: Fri Mar 02, 2018 2:22 pm
- Followed by:5 members
Is y > 4?
For any given triangle, the triangle inequality theorem states that the sum of the lengths of any two sides is greater than the length of the third side.
Statement 1: z = x + 4
Length of traingle:
x = x
y = y
z = z
Following the inequality theorem => x+y > z where z = x + 4
Therefore, x + y > x + 4 (subtract x from both sides)
y > 4
Statement 1 is SUFFICIENT
Statement 2: x=3 and z=7
Following the inequality theorem => x+y > 2 where x=3, and z=7
Therefore, 3+y>7
y > 7-3
y > 4
Statement 2 is SUFFICIENT.
Since each statement alone is SUFFICIENT, then, the correct answer is option D.
For any given triangle, the triangle inequality theorem states that the sum of the lengths of any two sides is greater than the length of the third side.
Statement 1: z = x + 4
Length of traingle:
x = x
y = y
z = z
Following the inequality theorem => x+y > z where z = x + 4
Therefore, x + y > x + 4 (subtract x from both sides)
y > 4
Statement 1 is SUFFICIENT
Statement 2: x=3 and z=7
Following the inequality theorem => x+y > 2 where x=3, and z=7
Therefore, 3+y>7
y > 7-3
y > 4
Statement 2 is SUFFICIENT.
Since each statement alone is SUFFICIENT, then, the correct answer is option D.
