Is x – 1/16 greater than 5/8?

Find the least common denominator to make fraction comparison easier.

Question: is \(x-\frac{1}{16}>\frac{5}{8}\)? --> is \(\frac{11}{16}=\frac{33}{48}<x\)?

(1) Four times the value of x is less than three --> \(4x<3\) --> \(x<\frac{3}{4}=\frac{36}{48}\). Not sufficient.

(2) One third of two is less than the value of x --> \(\frac{2}{3}=\frac{32}{48}<x\). Not sufficient.

(1)+(2) \(\frac{32}{48}<x<\frac{36}{48}\). Not sufficient.

Answer: E.
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This problem can be tackled algebraically. The trick is make sure you work neatly and stop to reflect before deciding sufficiency.

X-1/16 > 5/8?
Or x>11/16?

Goal: Prove (yes/no) that x is in fact greater than 11/16 (or, conversely, that it is equal to or less than 11/16).

Statement 1: 4x<3 or x<3/4. Use the cross multiplication method to compare fractions (3*16 and 4*11). 48>44, so then 3/4 is greater than 11/16. But we know that x is less than 3/4 so it could be less than 11/16 or more than 11/16 because we do not know the relationship between x and 11/16. So this answer is not sufficient because YES or NO is possible.

Statement 2: For this one, we are told that 2/3<x. We can quickly realize that 2/3<11/16. But once again, we cannot state if x is greater than or less than 11/16 because x > 2/3, so it could be between 2/3 and 11/16 or it could be greater than 11/16. Not sufficient.

Combined: Here we know that 2/3 < x < 3/4, but since 11/16 falls in this range, we cannot state whether 11/16 is greater than x definitively.

Can someone tell me why it is wrong to say :
(x−1)/16 > 5/8 so 8(x-1) > 5 ( 16) and the question then be : is x > 11 ?

It's x – 1/16 NOT (x – 1)/16. So, It's \(x – \frac{1}{16}\) NOT \(\frac{x – 1}{16}\).
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Question stem is asking whether x>0.6875?

(1) tells us that x<0.75 so its not sufficient since it could be 0.62 or 0.72 (or any number within that range)

(2) tells us that x> 0.66 which means x could be 0.67 or 0.77 (any number within that range) so its not sufficient either

(C) together it tells us that 0.66<x<0.75 which means x could either be 0.67 or 0.72 (any number within the range)

Therefore answer is (E)

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.

I like your approach
General question how much time did it take divide