Cracking The SAT Premium

spent   on  biofuels    in  2017    by  multiplying 0.34    by  the total   of  $254    million:    0.34    ×   254 =

$86.36  million.    Because 57  million new dollars will    be  spent   on  alternative energy, the

new total   will    be  254 +   57  =   $311    million.    Divide  $86.36  million by  $311    million to  get

the new proportion:     =   0.28,   which   is  (C).

23. 
    

    D In quadrant II, the x-coordinate is negative, and the y-coordinate is positive. Therefore,
    eliminate (C). Whenever the question includes variables and the answer choices are
    numbers, think Plugging In the Answers. Of the remaining choices, (B) is easiest to work
    with. In (B), the x-value is –4 and the y-value is 2. Plug these values into the second
    equation to get –4 = –2 + 2. Since this is not a true statement, eliminate (B). Try the values
    in (A) in the second equation to get 3 = –(–3 + 2. This is also not true, so the correct
    answer is (D).

    
    


24. 
    

    B Right away, (A) can be eliminated, since point C has a negative y-coordinate. Given any

    
    

two points, the slope   of  the line    can be  determined  using   the equation     .  Use this

formula to  find    the value   of  b   by  setting the slope   of  AB  equal   to  the slope   of  BC. Use points

(0, 3)  and (5b,    b)  in  the left    side    of  the equation    and points  (5b,    b)  and (10b,   –b) in  the right

side    of  the equation    to  get  .  Simplify    both    sides   of  the equation    to  get 

,   or   .  Cross-multiply  to  get 5(3 –   b)  =   10b.    Divide  both    sides   by

5   get 3   –   b   =   2b, then    3   =   3b, and finally b   =   1.  Plug    in  b   =1  for point   C   to  get [10(1), –   (1)],

or  (10,    –1).    Therefore,  the correct answer  is  (B).

25. A The formula for compound interest is A = P(1 + r)t, where P is the starting principle, r is

the rate    expressed   as  a   decimal,    and t   is  the number  of  times   the interest    is  compounded.

Melanie received    less    than    5%  interest,   so  you can eliminate(B)    because 1.05    =   1   +   0.05,

which   indicates   that    she was receiving   5%  interest.   You can also    eliminate   (C) because

over    the course  of  a   year    the interest    is  compounded  4   times,  not     of  a   time.   Because

Melanie invested    $1,100  at  what    she thought was 5%  compounded  4   times   (12 months  in  a

year     ÷   3   months  per     period),    she     expected    1,100(1     +   0.05)^4 =   $1,337.06   after   a   year.

Instead,    she has 1,337.06    –   50  =   $1,287.06   after   one year.   Because t   is  in  years   in  the