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Quantitative Help!!

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Director
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Quantitative Help!! [#permalink] New post 18 Feb 2006, 19:08
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Another few questions that needs some answer. By the way thanks for you help in answering my first query .

1. If 3 and 8 are the lenghts of two sides of a triangular region, which of the following can be the length of the third side?

I. 5
II. 8
III. 11

(A) II only
(B) III only
(C) I and II only
(D) II and III only
(E) I, II and III

2. The size of a television screen is given as the length of the screen's diagonal. If the screen were flat, then the area of a square 21 - inch screen would be how many square inches greater than the area of a square 19- inch screen?

(A). 2
(B). 4
(C). 16
(D). 28
(E). 40


3. If x is an integer and Y = 3x + 2, whcih of the following CANNOT BE A DIVISOR of Y?

(A). 4
(B). 5
(C). 6
(D). 7
(E). 8

Question #1: if-3-and-8-are-the-lengths-of-two-sides-of-a-triangular-21008.html
Question #2: the-size-of-a-television-screen-is-given-as-the-length-of-135484.html
Question #3: if-x-is-an-integer-and-y-3x-2-which-of-the-following-110666.html

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Location: Milwaukee,WI
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 [#permalink] New post 18 Feb 2006, 19:36
Ans 1 : - A -- ie ( II only ) because the sum of 2 sides of traingle should always be greater than the third side and the difference of any two sides of circle should always be less than than the third side

Ans 2 :- E - 40

say for 21 inch tv lenght is L1 so L1 ^2 + L1 ^2 = 21 ^ 2 =441
so L1 ^2 = 441 /2 --- equation 1

say for 19 inch tv lenght is L2 so L2 ^2 + L2 ^2 = 19 ^ 2 =361
so L1 ^2 = 361 /2 --- equation 2

from above equation 1 - equation 2 = 80/2 = 40

Ans 3 : - C 3x+2 wil be divisible all the number except 6
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 [#permalink] New post 18 Feb 2006, 19:42
1.) The length of any one side of a triangle cannot be greater than or equal to the sum of the remaining two.

I - 3-5-8 triangle is impossible
II - 3-8-8 triangle is isoceles
III - 3-8-11 is impossible

(A) it is.

2.) Note that is a square screen.

Since the diagonals (hypotenuses) are 21" and 19", the remaing sides are (21 / sqrt(2)) and (19 / sqrt(2)), respectively. Pictorially, if the diagonal was 21 * sqrt(2), then the sides would be 21; so just divide through by sqrt(2).

Since we're looking for differences in area, we must find the areas of both screens.

21"
= (21 / sqrt(2)) ^ 2
= 21^2 / (sqrt(2) ^ 2)
= 441 / 2

19"
= (19 / sqrt(2)) ^ 2
= 19^2 / (sqrt(2) ^ 2)
= 361 / 2

= 441 - 361 / 2
= 80 / 2
= 40

(E)

Quicker way, in retrospect:
Compare 21" and 19" screen:
21^2 = 441
19^2 = 361

Since the 21" and 19" are diagonals, divide through by sqrt(2), squared for area, so effectively divide by 2.

441 - 361 = 80; 80/2 = 40.

3.) Intuitively, (C):
2, 5 (B), 8 (A, E), 11, 14 (D).

More logically, for y to be a multiple of 6, it must also be a multiple of 3. (That is, y = 3x, or even 3 * some integer * x). However, y is always equal to 3x + some integer that is not a multiple of 3. Hence, it is never divisble by 3 and transitively never divisible by 6.

Hope this helps!
Expert Post
Magoosh GMAT Instructor
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Re: Quantitative Help!! [#permalink] New post 25 Mar 2013, 11:13
Expert's post
alimad wrote:
Another few questions that needs some answer. By the way thanks for you help in answering my first query .
1. If 3 and 8 are the lengths of two sides of a triangular region, which of the following can be the length of the third side?

I. 5
II. 8
III. 11

(A) II only
(B) III only
(C) I and II only
(D) II and III only
(E) I, II and III

This is simply a question about the Triangle Inequality. Here's a GMAT blog that discusses these:
http://magoosh.com/gmat/2012/facts-abou ... -the-gmat/
All the possible lengths must be greater than 8-3 = 5 and less than 8 + 3 = 11, so (A) is the answer.
alimad wrote:
2. The size of a television screen is given as the length of the screen's diagonal. If the screen were flat, then the area of a square 21 - inch screen would be how many square inches greater than the area of a square 19- inch screen?
(A). 2
(B). 4
(C). 16
(D). 28
(E). 40

I don't like this question, only because real television screens are not square! Good GMAT questions are totally realistic in the data they cite in word problems.

Having said that, I'll solve this. This link discusses the 45-45-90 triangle (a.k.a. the Isosceles Right Triangle), which plays into this calculations.
http://magoosh.com/gmat/2012/the-gmats- ... triangles/
If 19 is the diagonal, then \frac{19}{sqrt(2)} is the length of the side, and the area is \frac{19^2}{2}. Without a calculator, I don't want to calculate that if I don't have to.
If 21 is the diagonal, then \frac{21}{sqrt(2)} is the length of the side, and I am going to write that as \frac{19+2}{sqrt(2)}, and when we square that we get
\frac{(19+2)^2}{2}=\frac{19^2 + 2*2*19 + 2^2}{2}
Subtract the first area, and we are left with
difference in area = \frac{2*2*19 + 4}{2} = 2*19 + 2 = 38 + 2 = 40
Answer = (E)

alimad wrote:
3. If x is an integer and Y = 3x + 2, which of the following CANNOT BE A DIVISOR of Y?
(A). 4
(B). 5
(C). 6
(D). 7
(E). 8

Here's a blog on factors that might be germane.
http://magoosh.com/gmat/2012/gmat-math-factors/
Well, we know 3x will be divisible by 3, and if we add 2, we know we create a number that never will be divisible by 3. If Y is not divisible by 3, then it's not divisible by 6.
Answer = C

Let me know if anyone reading this has any questions.

Mike :-)
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Magoosh Test Prep

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Re: Quantitative Help!! [#permalink] New post 26 Mar 2013, 01:29
Expert's post
alimad wrote:
Another few questions that needs some answer. By the way thanks for you help in answering my first query .

1. If 3 and 8 are the lenghts of two sides of a triangular region, which of the following can be the length of the third side?

I. 5
II. 8
III. 11

(A) II only
(B) III only
(C) I and II only
(D) II and III only
(E) I, II and III

2. The size of a television screen is given as the length of the screen's diagonal. If the screen were flat, then the area of a square 21 - inch screen would be how many square inches greater than the area of a square 19- inch screen?

(A). 2
(B). 4
(C). 16
(D). 28
(E). 40


3. If x is an integer and Y = 3x + 2, whcih of the following CANNOT BE A DIVISOR of Y?

(A). 4
(B). 5
(C). 6
(D). 7
(E). 8

Thanks again guys, you'll are great!!!


Question #1: if-3-and-8-are-the-lengths-of-two-sides-of-a-triangular-21008.html
Question #2: the-size-of-a-television-screen-is-given-as-the-length-of-135484.html
Question #3: if-x-is-an-integer-and-y-3x-2-which-of-the-following-110666.html
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Re: Quantitative Help!!   [#permalink] 26 Mar 2013, 01:29
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