MGMAT solution:
Rephrase this question by solving the inequality for x:
is x > 1/16 + 5/8 ?
is x > 11/16 ?
(1) INSUFFICIENT: Translate this statement into math.
4x < 3
x < 3/4
x < 12/16
Some potential x values that are less than 12/16 are greater than 11/16 (x = 11.5/16 = 23/32, for example), but others are less than 11/16 (x = 0, for example). Therefore, it is uncertain whether x > 11/16.
(2) INSUFFICIENT: Translate this statement into math
(1/3)(2) < x
2/3 < x
or x > 2/3
First, how do 2/3 and 11/16 compare? Which one is bigger?
Compare the two fractions by cross-multiplying, giving 3 × 11 = 33 for the left-hand fraction and 2 × 16 = 32 for the right-hand fraction. Because 33 is bigger than 32, 11/16 is bigger than 2/3.
Draw a number line and place both 11/16 and 2/3 on that number line. If x > 2/3, there are some values between 2/3 and 11/16 (that is, some values of x are less than 11/16). There are also some values greater than 11/16. Therefore, it is uncertain whether x > 11/16.
(1) AND (2) INSUFFICIENT: Combining the information from the two statements gives a range for x:
2/3 < x < 12/16
Place these values on a number line: 2/3, 11/16, 12/16. Also draw in the range of possible values for x. This range still allows for values of x that are less than 11/16 and for values of x that are greater than 11/16. It is still uncertain whether x > 11/16.
The correct answer is E.