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# a couple from the gmat prep I took today

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Current Student
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a couple from the gmat prep I took today [#permalink]

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07 Nov 2009, 10:06
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Question Stats:

75% (00:33) correct 25% (01:55) wrong based on 20 sessions

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Attachment:

semicircle.png [ 13.18 KiB | Viewed 3811 times ]

Attachment:

99.png [ 18.52 KiB | Viewed 3817 times ]

I'm really interested in an explanation to the semicircle one,
I still can't figure out (I'm terrible at geometry).
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Senior Manager
Joined: 18 Aug 2009
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Re: a couple from the gmat prep I took today [#permalink]

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07 Nov 2009, 10:22
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saruba wrote:
Attachment:
semicircle.png

Triangle POQ is a right angle triangle. So $$PQ^2 = PO^2 + OQ^2$$
$$(s+\sqrt{3})^2 + (t-1)^2 = ((-\sqrt{3}-0)^2 + (1-0)^2) + ((s-0)^2 + (t-0)^2)$$
$$s^2+2s\sqrt{3}+3+t^2+1-2t = 4+s^2+t^2$$
$$t=s\sqrt{3}$$

We also know that $$PO = OQ$$
so $$s^2+t^2 = 4$$
$$s^2+3s^2 = 4$$
$$s=1$$

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Senior Manager
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Re: a couple from the gmat prep I took today [#permalink]

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07 Nov 2009, 10:28
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saruba wrote:
Attachment:
99.png
.

Old number of employees = $$x$$
Old avg salary = $$s$$
So Old total salary = $$s*x$$

New number of employees = $$0.9*x$$
New avg salary = $$1.1*s$$
So New total salary = $$1.1*s*0.9*x = 0.99*s*x$$

$$% = (0.99*s*x/s*x)*100 = 99%$$

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Manager
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Re: a couple from the gmat prep I took today [#permalink]

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08 Nov 2009, 00:05
Picking numbers method could reduce the time taken to answer Ques 2.. took me about 80 secs.

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Re: a couple from the gmat prep I took today [#permalink]

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08 Nov 2009, 00:49
abhi758 wrote:
Picking numbers method could reduce the time taken to answer Ques 2.. took me about 80 secs.

well, took me less than 25 seconds...

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Re: a couple from the gmat prep I took today [#permalink]

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08 Nov 2009, 02:27
for the second question, the only trick is in making sense of the convoluted language in the question stem.
took me a minute to make sense of all the decrease... 10%, before and after july 1..... jumble.

After that, the actual calculation takes very little time regardless of the method used (algebra / number substitution).

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Senior Manager
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Re: a couple from the gmat prep I took today [#permalink]

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08 Nov 2009, 06:01
The semicircle one was really dodgy. hgp2k, nice solution and with abhi758, amazed @ ur speeds great going!
saruba, if you don't mind my asking, how much was the quant score for this prep test? wondering if it is a 750 level Q

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Re: a couple from the gmat prep I took today [#permalink]

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08 Nov 2009, 07:54
The semicircle problem;

If we draw a perpendicular line through the point P to x axis at point A (-sqrt[3], 0), we have POA as 30-60-90 Triangle, where PA=2; PA =1; AO=sqrt[3]

Similarly we draw a perpendicular line through the point Q to x axis at point B; we have QOB as 60-30-90 Triangle , where OB =1; QB=sqrt[3]; OQ=2 (Since POQ is right angle triangle)

We have “s” =OB= 1

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Re: a couple from the gmat prep I took today [#permalink]

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08 Nov 2009, 18:28
Here is another solution for Question 1.

OP and OQ are perpendicular. Two lines are perpendicular, then the product of the slopes = -1.

Slope of OP = 1/sqrt(3) (Diff in Y coordinates / diff in X coordinates)
Slope of OQ = t/-s

Product of the slopes = t/(-s*sqrt(3)) = -1 ==> t = s*sqrt(3)

Since it is given that the fig is a semi circle, OP = OQ. Applying diff between two points forumula, we have

4 = s^2 + t^2.

Substitute t = s*sqrt(3) and we get 4s^2 = 4 ==> s^2 = 1 ==> s = +/- 1. Among the option that we have, s = 1. (Ans B)

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Re: a couple from the gmat prep I took today [#permalink]

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12 May 2011, 05:51
Solution for 2:

Let P = 100

1.1 * S/100 = S1/90

S1/S * 100 = 1.1 * 90/100 * 100 = 99

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Re: a couple from the gmat prep I took today [#permalink]

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19 May 2011, 11:05
Solving for the semi-circle problem.
I used trignometry to solve the problem. We know that x^2+y^2= 3+1=4, therefore the radii OP is 2.

This radii OP is the hypotenuse for the right triangle formed by height 1 and sqrt3. solving for the exterior angle i.e. POX.
Using sine theta formula:
Sine theta = opp/hyp = 1/2. Therefore the angle is 30. once you know this angle is 30, then the angle QOX on the other side is 60.

Now the radii OQ is 2.
Cos 60 = s/2
s = 1, since cos 60 is 1/2
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Re: a couple from the gmat prep I took today [#permalink]

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19 May 2011, 12:04
Attachment:

99.png [ 18.52 KiB | Viewed 2828 times ]

Employees before July 1st: $$100$$
Total salary before july 1st: $$T_b$$
Average before July 1st: $$\frac{T_b}{100}$$

Employees after July 1st: $$90$$
Total salary after july 1st: $$T_a$$
Average after July 1st: $$\frac{T_a}{90}$$

$$\frac{T_a}{90} = 1.1*\frac{T_b}{100}$$

$$\frac{T_a}{T_b} = 1.1*\frac{90}{100} = \frac{9.9}{10} = \frac{99}{100} = 0.99 = 99%$$

Ans: "B""
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Re: a couple from the gmat prep I took today   [#permalink] 19 May 2011, 12:04
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