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Is a + b > 0 ? 1. 7a - b > 0 2. b - 6a > 0 Thanks.

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Is a + b > 0 ? 1. 7a - b > 0 2. b - 6a > 0 Thanks. [#permalink] New post 30 Oct 2009, 11:59
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Is a + b > 0 ?

1. 7a - b > 0
2. b - 6a > 0

Thanks.

New Addition: These are PS questions but because I am not able to post a new topic, I am adding these questions to my existing post (DS Forum).

Please help me with the questions below. I am able to solve these but looking for faster way to do so. Can anybody please explain tricks for these questions? Thanks.


1) a couple decides to have 4 children. If they succeed in having 4 children and each child is equally likely to be a boy or a girl, what is the probability that they will have exactly 2 girls and 2 boys?

a. 3/8
b. 1/4
c. 3/16
d. 1/8
e. 1/16

2) A square wooden plaque has a square brass inlay in the center, leaving a wooden strip of uniform width around the brass square. If the ratio of the brass area to the wooden area is 25 to 39, whick of the following could be, in inches, the width of the wooden strip?

I. 1
II 3
III 4

I only
II only
I and II only
I and III only
I, II, and III


3) An ice-cream sundae consists of two ice-cream scoops, one flaver per scoop, and one topping. How many different types of sundaes can be prepared if four ice-cream flavors and two toppings are available?

a. 12
b. 14
c. 16
d. 18
e. 20

Thanks.

Last edited by swatirpr on 17 Nov 2009, 05:25, edited 1 time in total.
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1 KUDOS received
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Re: Is a+b > 0 ? [#permalink] New post 30 Oct 2009, 18:17
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C

(A) and (B) by themselves does not gives enough info (use substitution)

Combining them together
6a<b<7a

Case 1 a is positive.
Above equation can be satisfied for b lying between 6a and 7a. So b is also positive.

Case 2 a is negative.
We cannot find b lying between 6a and 7a (a=1 -6<??<-7)

So only Case 1 remains, using which we can say a+b>0. Sufficient
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a couple decides to have 4 children; types of Sundaes? [#permalink] New post 17 Nov 2009, 05:29
New Addition: These are PS questions but because I am not able to post a new topic, I am adding these questions to my existing post (DS Forum).

Please help me with the questions below. I am able to solve these but looking for faster way to do so. Can anybody please explain tricks for these questions? Thanks.


1) a couple decides to have 4 children. If they succeed in having 4 children and each child is equally likely to be a boy or a girl, what is the probability that they will have exactly 2 girls and 2 boys?

a. 3/8
b. 1/4
c. 3/16
d. 1/8
e. 1/16

2) A square wooden plaque has a square brass inlay in the center, leaving a wooden strip of uniform width around the brass square. If the ratio of the brass area to the wooden area is 25 to 39, whick of the following could be, in inches, the width of the wooden strip?

I. 1
II 3
III 4

I only
II only
I and II only
I and III only
I, II, and III


3) An ice-cream sundae consists of two ice-cream scoops, one flaver per scoop, and one topping. How many different types of sundaes can be prepared if four ice-cream flavors and two toppings are available?

a. 12
b. 14
c. 16
d. 18
e. 20

Thanks.
1 KUDOS received
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Re: a couple decides to have 4 children; types of Sundaes? [#permalink] New post 17 Nov 2009, 05:56
1
This post received
KUDOS
swatirpr wrote:
New Addition: These are PS questions but because I am not able to post a new topic, I am adding these questions to my existing post (DS Forum).

Please help me with the questions below. I am able to solve these but looking for faster way to do so. Can anybody please explain tricks for these questions? Thanks.


1) a couple decides to have 4 children. If they succeed in having 4 children and each child is equally likely to be a boy or a girl, what is the probability that they will have exactly 2 girls and 2 boys?

a. 3/8
b. 1/4
c. 3/16
d. 1/8
e. 1/16

2) A square wooden plaque has a square brass inlay in the center, leaving a wooden strip of uniform width around the brass square. If the ratio of the brass area to the wooden area is 25 to 39, whick of the following could be, in inches, the width of the wooden strip?

I. 1
II 3
III 4

I only
II only
I and II only
I and III only
I, II, and III


3) An ice-cream sundae consists of two ice-cream scoops, one flaver per scoop, and one topping. How many different types of sundaes can be prepared if four ice-cream flavors and two toppings are available?

a. 12
b. 14
c. 16
d. 18
e. 20

Thanks.


(1) I got 3/8
Listed the favorable ways BBGG, BGBG, BGGB (x2=6) and total ways 2x2x2x2=16
probablity = 3/8

don't know why 2nd is stuck... skipping to goto 3rd
getting 20 there
case 1: same 2 flavor with different topping... possibilities 4x2=8
case 2: different 2 flavors (4x3)/2=6 [divide by 2 'coz it is the same combination with the flavors reversed]
...with different topping 6x2=12
Total 8+12=20
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Re: Is a+b > 0 ?; a couple decides to have 4 children; Sundaes? [#permalink] New post 17 Nov 2009, 06:15
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and 2nd is E it seems :)
ratio-problem-64346.html
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Re: Is a+b > 0 ?; a couple decides to have 4 children; Sundaes? [#permalink] New post 17 Nov 2009, 08:38
Thanks gmattokyo. I appreciate your quick reply.

Quote:
(1) I got 3/8
Listed the favorable ways BBGG, BGBG, BGGB (x2=6) and total ways 2x2x2x2=16 Can you please explain how you calculated total ways here.
probability = 3/8


You got all the answers right.

Thanks again.

[Reveal] Spoiler:
1. A
2. E
3. E
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Re: Is a+b > 0 ?; a couple decides to have 4 children; Sundaes? [#permalink] New post 17 Nov 2009, 09:42
1) Probability of boy = Probability of girl = 1/2

Therefore, Probability of 2 boys and 2 girls = (1/2)*(1/2)*(1/2)*(1/2)*[4!/(2!*2!)]

That is number of ways of selecting 4 objects in which two are similar.

= 3/8

3) (4C2)*(2C1) + (4C1)*(2C1) = 12 + 8 = 20
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Re: Is a+b > 0 ?; a couple decides to have 4 children; Sundaes? [#permalink] New post 17 Nov 2009, 17:42
swatirpr wrote:
Thanks gmattokyo. I appreciate your quick reply.

Quote:
(1) I got 3/8
Listed the favorable ways BBGG, BGBG, BGGB (x2=6) and total ways 2x2x2x2=16 Can you please explain how you calculated total ways here.
probability = 3/8


You got all the answers right.

Thanks again.

[Reveal] Spoiler:
1. A
2. E
3. E

glad if it helped :)
Total ways- for first kid, it can be either B or G so two possibilities, similarly for 2nd, 3rd and 4th... 2x2x2x2
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Re: Is a+b > 0 ?; a couple decides to have 4 children; Sundaes? [#permalink] New post 17 Nov 2009, 19:34
Quote:
(1) I got 3/8
Listed the favorable ways BBGG, BGBG, BGGB (x2=6) and total ways 2x2x2x2=16 Can you please explain how you calculated total ways here.
probability = 3/8


glad if it helped :)
Total ways- for first kid, it can be either B or G so two possibilities, similarly for 2nd, 3rd and 4th... 2x2x2x2


:-D Got it, thanks again.
Re: Is a+b > 0 ?; a couple decides to have 4 children; Sundaes?   [#permalink] 17 Nov 2009, 19:34
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