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# In the rectangular coordinate system, are the points (r,s)

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In the rectangular coordinate system, are the points (r,s) [#permalink]  07 Apr 2006, 04:09
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In the rectangular coordinate system, are the points (r,s) and (u,v) equidistant from the origin?

1 . r + s = 1
1. u = 1 -r and v = 1 - s.

I believe the answer is C, since by combining statement I and II we get s = U and V = R.

141

On Jane's credit card account, the average daily balance for a 30-day billing cycle is the average (arithmetic mean) of the daily balances at the end of each of the 30 days. At the beginning of a certain 30 day billing cycle, Jane's credit card account had a balance of 600. Jane made a payment of 300 on the account during the billing cycle. If no other amounts were added to or subtracted from the account during the billing cycle, what was the average daily balance on Jane's account for the billing cycle?

a. Jane's payment was credited on the 21st day of the billing cycle.
b. The average daily balance through the 25th day of the billing cycle was 540

This one is trick !!

not sure
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140.

Distance to origin from pt (a,b) is square root of (a^2 + b^2). So to answer this we need to evaluate if r^2 + s^2 is equal to u^2 + v^2

1) Insufficient info. Doesn't tell us anything about u and v
2) u^2 + v^2 = (1-r)^2 + (1-s)^2 = 1 -2r + r^2 + 1 -2s + s^2 = 2 - 2(r+s) + r^2 + s^2
By itself this is insufficient to answer the question.

Substituting r+s = 1 from 1) into the above we are left with r^2+s^2.
So it is C (both together are sufficient)

141.

Let's say Jane makes a payment of \$300 on day 'x'. To get the average we need
( (x * 600) + ( (30 - x) * 300) ) / 30

1) Sufficient. Tells us that x is 21. So the answer is either A or D
2) Sufficient. Tells us that ( (x * 600) + ( (25 - x) * 300) ) / 25 is equal to 540. So we can solve for x to get the day she made the payment and plug it back into the original equation to get the average.

So answer is D (each is sufficient)
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1) Insufficient
2) Insufficient

Since if you plug r=1, s=1 (r,s) are sqrt(2) away
(u,v) are the origin

plug in r=2, s = -1 (r,s) are sqrt(5) away
(u,v) are sqrt(5) away

So take 1) and 2) together, you can find if they are equidistant from the origin

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