Of the following, which is the greatest?

Question

A.  \frac{7}{9} 
B.  \frac{5}{7} 
C.  (\frac{7}{9})^2 
D.  (\frac{5}{7})^3 
E.  (\frac{7}{9})^3

gchandana · Answer

Official Explanation

Usernamevisible · Answer

You need to know fraction 
1/9 is 0.1111
and 
1/7 = 0.1428

Now 7/9 = 0.77 and 5/9 = (14*5=70) = ~0.7

Thus 7/9 is greater

Now for B,C and D
in fraction squaring and cubing always result into lower number

Thus A

Usernamevisible · Answer

Detailed solution -

Question:
A. 7/9
B. 5/7
C. (7/9)^2
D. (5/7)^3
E. (7/9)^3
----------

GMAT Fast Pattern
For any positive fraction less than 1:
0 < x < 1
Raising it to a power makes it smaller.
For example:
(7/9)^3 < (7/9)^2 < 7/9
and
(5/7)^3 < 5/7
So immediately eliminate:
• C < A
• E < C < A
• D < B
Now only compare A vs B.
------------------------

Compare 7/9 and 5/7
Cross multiply:
7 × 7 = 49
9 × 5 = 45
Since:
49 > 45
we have:
7/9 > 5/7
Therefore:
7/9 > 5/7 > (5/7)^3
and
7/9 > (7/9)^2 > (7/9)^3
So the greatest number is:
7/9
Answer: A
---------

GMAT Takeaway
Whenever all choices are positive fractions:
• If 0 < x < 1, then x > x2 > x3
• If x > 1, then x < x2 < x3
This lets you eliminate most exponent choices without calculating anything.

Of the following, which is the greatest?

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Of the following, which is the greatest?

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