Cracking The SAT Premium

shown   is      of  the area    of  a   full    circle. The area    of  the figure  can be  calculated  as  

(16π)   =   0.375(16π)  =   6π  »   18.8    »   19. The correct answer  is  19.

35. 
    

    6 The two triangles share three angles; thus they are similar. AC is twice the length of BC
    because it is bisected by BD. This relationship is constant between the two similar
    triangles. Therefore, BD is half of AE: 12 ÷ 2 = 6.

    
    


36. 
    

    20 First, determine the grams of protein in the bar. If the bar contains 32% of the daily

    
    

recommended  serving     of  protein,    and     the     daily   recommended     serving     of  protein     is  50

grams,  then    the bar contains    0.32    ×   50  =   16  grams   of  protein.    Next,   determine   the grams   of

fat in  the bar by  using   the percent change  equation:   percent change  =       ×   100.    The

percent change  is  700,    and the original    is  the grams   of  fat (because    percent more    means   the

original    is  the smaller number),    which   means   700 =       ×   100.    Divide  both    sides   by

100:    7   =    .  Multiply    both    sides   by  x   to  get 7x  =   16  –   x.  Add x   to  both    sides   to  get 8x  =

16. Divide both sides by 8 and you find x = 2. That is the number of grams of fat in the bar.

To  find    the daily   recommended serving of  fat,    translate   English to  math.   2   is  10% of  the

daily   recommended serving,    so  if  the daily   recommended serving is  y,  2   =   0.10y.  Divide

both    sides   by  0.10,   and you find    that    the daily   recommended serving of  fat is  20.

37. 
    

    1 First, you need to determine the content of Set R. If Set R consists of all the one-digit prime
    numbers, then R = {2, 3, 5, 7}. The sum of the elements of Set S would therefore be 2 + 3 +
    5 + 7 + x = 30. Combine like terms: 17 + x = 30. Subtract 17 from both sides, and you find
    x = 13. Plug x = 13 into the equation and solve: (13)^2 – 11(13) – 25 = 1.

    
    


38. 
    

    8 The additional positive integer x cannot equal 2, 3, 5, or 7 (otherwise there would be a

    
    

mode).  Next,   determine   what    the median  could   be  for various ranges  of  x.  If  x   is  less    than    2,

then    the set would   be, in  consecutive order,  {x, 2,  3,  5,  7}, making  the median  3.  Try this

set.    If  the median  equals  the mean,   then    the sum of  the elements    divided by  5   (the    number  of

elements)   must    equal   3:      =   3.  Multiply    both    sides   by  5   and combine like

terms:  x   +   17  =   15. Subtract    17  from    both    sides,  and you find    x   =   −2. However,    x   must    be  a