Problem
If
y
is 45 percent of
x
and
z
is 25 percent of
x
, what is
y
+
z
in terms of
x
?
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|
GRE: Problem Solving Question #1 |
|
Question:
| If |
a |
and |
b |
are integers, |
b |
< |
30, |
and the ratio of |
a |
to | b |
is |
7:5, |
what |
| is the maximum possible value of |
a? |
Choices:
| Since the ratio tells us that |
|
a |
|
|
 |
|
|
b |
|
|
= |
|
7 |
|
|
|
|
|
5 |
|
|
, we know that |
a |
= |
|
7 |
|
|
|
|
|
5 |
|
|
b. |
So the |
| greatest possible value of a will occur when we have the greatest |
| possible value of |
b. |
We know that |
b |
is a multiple of |
5 |
(since the |
| ratio of |
7:5 |
cannot be reduced) and that |
b |
must be less than |
30. |
| The greatest multiple of |
5 |
that is less than |
30 |
is |
25. |
So the |
| greatest possible value of |
b |
is |
25. |
| Now |
a |
= |
|
7 |
|
|
|
|
|
5 |
|
|
b |
and we now know that the greatest possible value |
| of |
a |
will occur when |
b |
= |
25. |
So the greatest possible value of |
a |
is |
|
7 |
|
|
|
|
|
5 |
|
|
( |
25 |
) |
= |
7 |
( |
5 |
) |
= |
35. |
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|
