CHAPTER 6 / WHAT THE SAT MATH IS REALLYTESTING 239
Concept Review I
- To map means to represent the general problem
situation and goal, either mentally or on paper. - Because the choices tell you the range of values to
consider, as well as the form of the numbers (in-
tegers, fractions, etc.) and format (factored, deci-
mal, etc.). - Oddmeans an integer not divisible by 2and is
sometimes confused with negativebecause of the
“negative” tone of both words. - Evenmeans an integer divisible by 2and is some-
times confused with positivebecause of the “posi-
tive” tone of both words. - Perimetermeans distance around a figureand is
sometimes confused with area,which is the num-
ber of square units that fit inside a figure.
6. Integersare whole numbers and negative whole
numbersand are sometimes confused with count-
ing numbers, which are thepositiveintegers: 1, 2,
3, 4,...
7. Let nbe the smaller of the two numbers. Then the
next odd number is n+2, so an equation that says
that the sum of two consecutive odd numbers is
28 is n+n+ 2 =28.
8. Let estand for Ellen’s current age and mstand for
Maria’s current age. An equation that says that
Ellen is twice as old as Maria is e= 2 m.
9. Let jstand for Jennifer’s age now and bstand for
Brian’s age now. Last year, Jennifer was j−1 years
old, so an equation that says that last year Jennifer
was twice as old as Brian is now is j− 1 = 2 b.
SAT Practice 1
- 8 If the product of a set of integers is 0, then one of
the numbers must be 0. To maximize the value of any
one of them, let 0 be the smallest of the integers.
If they are consecutive evenintegers, they must
be 0, 2, 4, 6, and 8. If your answer was 4, then you
overlooked the fact that the numbers are even. - 48 Your first tool in mapping a geometry prob-
lem is a good diagram. This one has no diagram,
so you must draw your own. Draw a rectangle,
labeling its width wand its length l:
3. E Let cbe the number of dollars Carlos had to
start and dbe the number of dollars David had to
start. The question asks for the value of c+d.If Carlos
begins with twice as much money as David, then
c= 2 d.After Carlos gives $12 to David, he has c− 12
dollars, and David has d+12 dollars. If Carlos still
has $10 more than David, then c− 12 =(d+12) +10.
Simplify: c− 12 =d+ 22
Add 12: c=d+ 34
Substitute c= 2 d: 2 d=d+ 34
Subtract d: d= 34
Plug back in: c=2(34) = 68
So c+d= 34 + 68 =102.
4. C To “map” this problem, you must know that
distance =speed ×time. You must find the num-
ber of miles from Corinne’s home to work, so call
that d.If she travels from home to work at an
average speed of 50 miles per hour, then it must
take her d/50 hours, or 60 ×d/50 = 6 d/5 minutes. If
she returns home at 60 miles per hour, it must
take her d/60 hours, or 60 ×d/60 =dminutes. If it
takes her 10 more minutes to get to work than it
takes her to get home, then:
Simplify:Multiply by 5: d= 50d
5= 10
6 d
d
5−= 10
Since the perimeter of the rectangle is 28 inches,
you can set up an equation: 2w+ 2 l=28. Divide
both sides of the equation by 2 to get w+l=14.
Since the area is x,you can set up the equation lw=x.
If xis even, then land wcan’t both be odd. (Can
you see how we know that?) You should be able
to see that the possible values for wand lare 2
and 12, 4 and 10, and 6 and 8. (Check them
and see.) This means that xcan have values of
2 × 12 =24, 4 × 10 =40, or 6 × 8 =48. The greatest
of these, of course, is 48.Answer Key I:Mapping Problems
w