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

 It is currently 18 Sep 2018, 23:01

### 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

# In the above figure, if QRTV is a square, and the length of PV, VT and

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 49241
In the above figure, if QRTV is a square, and the length of PV, VT and  [#permalink]

### Show Tags

27 Sep 2017, 04:49
00:00

Difficulty:

25% (medium)

Question Stats:

100% (00:41) correct 0% (00:00) wrong based on 25 sessions

### HideShow timer Statistics

In the above figure, if QRTV is a square, and the length of PV, VT and TS are each 3, what is the value of x + y?

(A) 135
(B) 125
(C) 120
(D) 115
(E) 105

Attachment:

2017-09-27_1107_002.png [ 5.53 KiB | Viewed 598 times ]

_________________
Retired Moderator
Joined: 28 May 2014
Posts: 528
GMAT 1: 730 Q49 V41
Re: In the above figure, if QRTV is a square, and the length of PV, VT and  [#permalink]

### Show Tags

27 Sep 2017, 07:08
QRTV is a square. Hence, RT = VT.

Again it is provided that:
PV = VT = TS;
So, TS = RT;

For △ RTS, <RTS = 90, and TS = RT; Hence, y = 45;

So, x + y = 90 + 45 = 135
Ans: A.
_________________
Senior SC Moderator
Joined: 22 May 2016
Posts: 1973
In the above figure, if QRTV is a square, and the length of PV, VT and  [#permalink]

### Show Tags

27 Sep 2017, 17:17
Bunuel wrote:

In the above figure, if QRTV is a square, and the length of PV, VT and TS are each 3, what is the value of x + y?

(A) 135
(B) 125
(C) 120
(D) 115
(E) 105

Attachment:
2017-09-27_1107_002.png

x + y = 90 + 45 = 135

∠x = vertex of square QRTV
∠x = 90

∠ y = 45 - y is a 45° angle of ∆ RST

∆ RST is an isosceles right triangle

90° angle, adjacent to the square, is at T

∆ RST has legs of equal length
Both legs = 3
One leg, TS, is given as 3
Leg RT = side of square = 3 (square side VT = 3, all sides are equal)

Isosceles right triangles have angle measures of 90-45-45
∠y = 45

x + y = 90 + 45 = 135

_________________

In the depths of winter, I finally learned
that within me there lay an invincible summer.

In the above figure, if QRTV is a square, and the length of PV, VT and &nbs [#permalink] 27 Sep 2017, 17:17
Display posts from previous: Sort by

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.