Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 08 Feb 2016, 17:31

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Plz help to solve this ps

Author Message
TAGS:
Manager
Joined: 13 Aug 2009
Posts: 151
WE 1: 4 years in IT
Followers: 1

Kudos [?]: 125 [0], given: 7

Plz help to solve this ps [#permalink]  09 Dec 2009, 00:07
1
This post was
BOOKMARKED
00:00

Difficulty:

(N/A)

Question Stats:

50% (01:33) correct 50% (01:47) wrong based on 2 sessions
tricky ps

If equation encloses a certain region on the coordinate plane, what is the area of this region?

|x|/|2|+|y|/|2| =5

20
50
100
200
400

How many odd three-digit integers greater than 800 are there such that all their digits are different?

40
56
72
81
104

If a circle is inscribed in a square, then the area outside the circle is what percent of the total area of the square (approximately)?

14%
18%
22%
28%
30%
VP
Joined: 05 Mar 2008
Posts: 1473
Followers: 11

Kudos [?]: 236 [0], given: 31

Re: Plz help to solve this ps [#permalink]  09 Dec 2009, 06:01
raghavs wrote:
tricky ps

If equation encloses a certain region on the coordinate plane, what is the area of this region?

|x|/|2|+|y|/|2| =5

20
50
100
200
400

if x = 0 y = 10
if y = 0 x = 10
if x = 0 y= -10
if y = 0 x = -10

four triangles with base 10, height 10 area = 50
50*4 = 200
Senior Manager
Joined: 30 Aug 2009
Posts: 286
Location: India
Concentration: General Management
Followers: 3

Kudos [?]: 131 [0], given: 5

Re: Plz help to solve this ps [#permalink]  09 Dec 2009, 06:11
raghavs wrote:
tricky ps

If a circle is inscribed in a square, then the area outside the circle is what percent of the total area of the square (approximately)?

14%
18%
22%
28%
30%

let side of square be 2a then radius of circle will be a. Area of square = 4a^2 and Area of Circle = πa^2

So area outside circle is 4a^2 - πa^2

% of area outside = (4a^2 - πa^2)/a^2 *100 = 22% approx.
Manager
Joined: 13 Aug 2009
Posts: 151
WE 1: 4 years in IT
Followers: 1

Kudos [?]: 125 [0], given: 7

Re: Plz help to solve this ps [#permalink]  10 Dec 2009, 03:12
Thanks Lagomez and Kp1811 for the solution.
Intern
Joined: 08 Nov 2009
Posts: 47
Followers: 0

Kudos [?]: 33 [0], given: 0

Re: Plz help to solve this ps [#permalink]  11 Dec 2009, 18:56
2)

The first digit can only be 8 or 9.

If it is 8, the second digit can assume 9 values, 5 of which are odd and 4 of which are even. The third digit must be odd, hence it can assume 5 values at the most. If the second digit is even, we can pick any of these 5 values, hence we have 4(#of suitable even second digits)*5(#number of suitable odd third digits)=20. If the second digit is odd, the third has still to be odd, but it cannot assume the same value as the second, hence we have 5(#of suitable odd second digits)*4(# of suitable odd third digits)=20. The total in the 800-899 range is 40.

If the first digit is 9, the second digit can assume 4 even values and 5 odd values. If the second digit is even, the third digit can be any odd digit but 9, hence we have 5(# of suitable even second digits)*4(# of suitable odd third digits)=20. If the second digit is odd, the third digit cannot be 9 or equal to the second digit, and it still has to be odd, hence 4(# of suitable odd second digits)*3(# of suitable odd third digits)=12. The total in the 900-999 range is 32.

The total number of odd numbers with different digits above 800 is then 72.
Manager
Joined: 12 Oct 2008
Posts: 58
Followers: 1

Kudos [?]: 1 [0], given: 3

Re: Plz help to solve this ps [#permalink]  12 Dec 2009, 04:07
Verbal Forum Moderator
Joined: 02 Aug 2009
Posts: 2025
Followers: 77

Kudos [?]: 930 [0], given: 37

Re: Plz help to solve this ps [#permalink]  12 Dec 2009, 05:26
Expert's post
ans for 1) 200...
take 4 cases where both x n y are +,both -, and two cases where each are opposite to each other...
ull get a square with sides given by <(0,10)(10,0)> ,<(0,-10)(10,0)> , <(0,10)(-10,0)> and <(0,-10)(10,0)>...
the diag of sq will be 10+10=20...so each side is 10(2)^1/2....
2)
kp1811 wrote:
raghavs wrote:
tricky ps

If a circle is inscribed in a square, then the area outside the circle is what percent of the total area of the square (approximately)?

14%
18%
22%
28%
30%

let side of square be 2a then radius of circle will be a. Area of square = 4a^2 and Area of Circle = πa^2

So area outside circle is 4a^2 - πa^2

% of area outside = (4a^2 - πa^2)/a^2 *100 = 22% approx.

shud be 18%... as mentioned above but while dividing it has to be 4a^2 and not a^2
3) 72....
_________________

BACK IN CLUB AFTER A GAP OF 6 YEARS

http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372

Intern
Joined: 22 Dec 2009
Posts: 40
Followers: 0

Kudos [?]: 34 [0], given: 13

Re: Plz help to solve this ps [#permalink]  10 Jan 2010, 19:55
chetan2u wrote:
ans for 1) 200...
take 4 cases where both x n y are +,both -, and two cases where each are opposite to each other...
ull get a square with sides given by <(0,10)(10,0)> ,<(0,-10)(10,0)> , <(0,10)(-10,0)> and <(0,-10)(10,0)>...
the diag of sq will be 10+10=20...so each side is 10(2)^1/2....
2)
kp1811 wrote:
raghavs wrote:
tricky ps

If a circle is inscribed in a square, then the area outside the circle is what percent of the total area of the square (approximately)?

14%
18%
22%
28%
30%

let side of square be 2a then radius of circle will be a. Area of square = 4a^2 and Area of Circle = πa^2

So area outside circle is 4a^2 - πa^2

% of area outside = (4a^2 - πa^2)/a^2 *100 = 22% approx.

shud be 18%... as mentioned above but while dividing it has to be 4a^2 and not a^2
3) 72....

Hi.. plz help me with this calculation..

% of area outside = (4a^2 - πa^2)/4a^2 *100 = 18% , how do you calculate this to get 18%
Manager
Joined: 27 Apr 2008
Posts: 190
Followers: 1

Kudos [?]: 54 [0], given: 1

Re: Plz help to solve this ps [#permalink]  10 Jan 2010, 22:01
Question c)
----------

Let d represent the length of the square's side. Therefore, the radius of the circle is d/2.

Area of square = $$d^2$$
Area of circle = (pi)$$(d/2)^2$$ = pi*(d^2)/4

The area of of the square less the inscribed circle is:
$$d^2$$ - pi*(d^2)/4
= $$\frac{d^2*(4-pi)}{4}$$

As a percentage of the square's area, we get

= $$\frac{d^2*(4-pi)}{4}$$ * 1/d^2

Simplifying, we get $$\frac{4-pi}{4}$$
= 1-pi/4
= 1-(22/7)/4
= 1-11/14
= 3/14

Since 3/14 > 3/15, and 3/15 is 20%, we get 22% as the answer.
Verbal Forum Moderator
Joined: 02 Aug 2009
Posts: 2025
Followers: 77

Kudos [?]: 930 [0], given: 37

Re: Plz help to solve this ps [#permalink]  11 Jan 2010, 05:16
Expert's post
gmatJP wrote:

Hi.. plz help me with this calculation..

% of area outside = (4a^2 - πa^2)/4a^2 *100 = 18% , how do you calculate this to get 18%

(4a^2 - πa^2)/4a^2 *100 =a^2(4-pi)/4a^2*100=(4-22/7)/4*100=(6/7)*100/4=600/28=22%..
and sorry i meant 22% when i wrote 18%
_________________

BACK IN CLUB AFTER A GAP OF 6 YEARS

http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372

Manager
Joined: 27 Aug 2009
Posts: 144
Followers: 2

Kudos [?]: 18 [0], given: 1

Re: Plz help to solve this ps [#permalink]  12 Jan 2010, 16:09
for Q1, why can't we take the coordinates to be(+-8,+-2) and why only integers?
Math Expert
Joined: 02 Sep 2009
Posts: 31286
Followers: 5348

Kudos [?]: 62189 [0], given: 9444

Re: Plz help to solve this ps [#permalink]  12 Jan 2010, 17:34
Expert's post
$$|\frac{x}{2}| + |\frac{y}{2}| = 5$$

After solving you'll get equation of four lines:

$$y<0$$ and $$x<0$$ --> $$y=-10-x$$
$$y>0$$ and $$x<0$$ --> $$y=10+x$$
$$y>0$$ and $$x>0$$ --> $$y=10-x$$
$$y<0$$ and $$x>0$$ --> $$y=x-10$$

If you draw these four lines (line segments) you'll see that the figure (square) which is bounded by them is turned by 90 degrees and has a center at the origin.

Diagonal of this square would be 20, so the $$Area=\frac{20*20}{2}=200$$. Or the $$Side= \sqrt{200}$$, $$Area=\sqrt{200}^2=200$$.

Hope it's clear.
_________________
Intern
Joined: 22 Dec 2009
Posts: 40
Followers: 0

Kudos [?]: 34 [0], given: 13

Re: Plz help to solve this ps [#permalink]  30 Apr 2010, 00:59
Bunuel wrote:
$$|\frac{x}{2}| + |\frac{y}{2}| = 5$$

After solving you'll get equation of four lines:

$$y<0$$ and $$x<0$$ --> $$y=-10-x$$
$$y>0$$ and $$x<0$$ --> $$y=10+x$$
$$y>0$$ and $$x>0$$ --> $$y=10-x$$
$$y<0$$ and $$x>0$$ --> $$y=x-10$$

If you draw these four lines (line segments) you'll see that the figure (square) which is bounded by them is turned by 90 degrees and has a center at the origin.

Diagonal of this square would be 20, so the $$Area=\frac{20*20}{2}=200$$. Or the $$Side= \sqrt{200}$$, $$Area=\sqrt{200}^2=200$$.

Hope it's clear.

I still dont understand how area becomes 200..
First, the question says certain region then how do you know its square or rectangle and not triangle..
Second, if each side of the length of square is 10 then area should be 100 no?

Re: Plz help to solve this ps   [#permalink] 30 Apr 2010, 00:59
Similar topics Replies Last post
Similar
Topics:
2 Need help in corretly solving this PS question... 4 11 Sep 2011, 19:22
2 Need Help solving 600-700 level PS 1 15 Oct 2010, 09:20
2 PS ALGEBRA TRANSLATION PROBLEM- Need help solving 7 05 Oct 2010, 12:10
Plz help me solve this problem 3 10 Jan 2010, 20:10
OG, PS 124? Help Me Plz!! 6 27 Aug 2008, 01:46
Display posts from previous: Sort by