Math questions = )

Test Preparation SAT Preparation
1
  1. A grocery customer spent a total of 9.60 for ground beef and coffee. the coffe cost2 times as much per poundas the ground beef and the customer bought 3 times as many pounds of ground beef as pounds of coffee.How much in dollars did the customer spend on coffe?

2)when the area of a certain circle is divided by pi the resullt is the square of an integer. which of the following could be the diameter of the circle?
A)12
B)11
C)9
D)7
E)5

3)The product of a and b is equal to x and the sum of a and b is equal to y.if x and y are positive numbers. what is 1/a +1/b in terms of x and y?
A) x/y
B)y/x
C)xy
D)1/x+1/y
E)1/x+y
ps: i solved it but am not sure of the way!

4)the first three terms of a sequence are given above
the nth term of the sequence is 1/(n)(n+1) which is equal to 1/n-1/n+1. what is the sum of the first 50 terms of this sequence ?
A)1
B)50/51
C)49/50
D)24/50
E)1/(50)(51)

5)p(0,2) and r (3,2)
p and r are endpoints of one of the diagonals of a square.which of the following are the coordinates of one of the other vertices of the square?
A)(1,1.5)
B)(1,3.5)
C)(1.5,1.5)
D)(1.5,2.5)
E)(1.5,3.5)

2
  1. Let n = number of lbs of coffee and p = price per lb of coffee. Then he spent np on coffee, and (3n)(p/2) = 1.5np on beef since he bought 3x as much beef, but beef costs half as much per lb. Then np + 1.5np = 9.60, 2.5np = 9.60, or np = 3.84.
  2. Area = pi*r^2 where r is any positive integer. The diameter is therefore 2r, which is even, so the answer is A.
  3. 1/a + 1/b = (a+b)/ab = y/x, B.
  4. Assuming you meant nth term is 1/(n(n+1)), note that the nth term is equal to 1/n - 1/(n+1). If we sum from n=1 to n=50, we obtain a telescoping sum, where the sum reduces to 1/1 - 1/51 = 50/51, B.
  5. Diagonal has length 3 and is parallel to the x-axis. If you draw it out, you should see that the x-coordinate of the other two points is 1.5, and the y-coordinates are 2 + 1.5 and 2 - 1.5. Therefore E, (1.5, 3.5) is a point on the square.
3

For the first one, you could also state that for each 3 dollars spent on beef … 2 dollars are spent on coffee. That makes the ratio of expenses for coffee 2/5 of the total. Multiply 9.60 by 2/5.

4

didnt get 1 and 4 :confused: :frowning:

5

@CrazinessISlife for 4. try some small cases. What is 1/(12) + 1/(23)? How about 1/(12) + 1/(23) + 1/(34) or 1/(12) + 1/(23) + 1/(34) + 1/(4*5)?

Rewriting 1/(n(n+1)) as 1/n - 1/(n+1) makes it much easier to solve, since the series telescopes.
See https://en.wikipedia.org/wiki/Telescoping_series

6

For 4, check the terms given in the problem. Don’t they add up to 3/4? From there, you can speculate that the sum of the 50 terms will follow the same pattern. Hence 50/51.

Actually, there is no speculation … if you follow the rules shown by MITer.

7

I actually find the telescope series hard xdddd i understood it by 1/(n)(n+1)…thankssss alottttttttttttttttttttttt :slight_smile:

8

@xiggi‌ in number 1
why did u say each 3 dollars spent on beef 2 dollars are spent on the coffee??
isnt the coffe costs two times the beef?

9

@CrazinessISlife but you also bought 3x as much ground beef.

10

@MITer94‌ but for every 3x of beef is 1 coffee
for the cost 2 beef for 1 coffee how 3 dollars of beef for 2 dollars of coffee

11

@CrazinessISlife assume ground beef costs $1/lb; then coffee must cost $2/lb. Also assume you bought 1 lb coffee; then you must’ve bought 3 lb of ground beef. Then you spend $3 on ground beef and $2 on coffee.

12

@MITer94‌ oh yeah i feel stupid :smiley: thankssssssssssssssssss