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If there is a least integer that satisfies the inequality

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by [email protected] » Wed Dec 11, 2019 9:00 pm
Hi All,

We're given the inequality 9/X ≥ 2. We're asked for the LEAST integer that satisfies the inequality. While this question is relatively straight-forward, it's written in such a way that you might lose track of what you're ultimately solving for. To reiterate, we want the SMALLEST INTEGER that "fits" the inequality.

We need 9/X to be greater than or equal to 2, so we need X to be POSITIVE. We are NOT asked to make 9/X as small as possible.

Thus, the smallest positive integer that 'fits' the inequality is 1.

Final Answer: B

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by Brent@GMATPrepNow » Thu Dec 12, 2019 6:15 am
BTGmoderatorDC wrote:If there is a least integer that satisfies the inequality 9/x ≥ 2, what is that least integer?

A. 0
B. 1
C. 4
D. 5
E. There is not a least integer that satisfies the inequality.
If 9/x is greater than 2, we know that x is POSITIVE

Since x is POSITIVE, we can eliminate answer choice A.
At this point, we can test values, starting with the smallest possible value.

B) 1
If x = 1, our inequality becomes 9/1 ≥ 2, which is TRUE
Done!

Answer: B

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by Scott@TargetTestPrep » Fri Dec 13, 2019 1:08 pm
BTGmoderatorDC wrote:If there is a least integer that satisfies the inequality 9/x ≥ 2, what is that least integer?

A. 0
B. 1
C. 4
D. 5
E. There is not a least integer that satisfies the inequality.


OA B

Source: Official Guide
We see that x can't be 0 or negative (otherwise, 9/x will be undefined or negative, respectively). So x must be positive, and if x = 1, we have 9/x = 9/1 = 9 ≥ 2.

Answer: B

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by deloitte247 » Thu Dec 19, 2019 10:55 pm
$$Given\ that\ \frac{9}{x}\ge2$$
We are looking for the smallest number that will divide 9 and its result will be greater than or equal to 2.
For this reason, 9/x must not be negative, and x cannot be a negative integer because it will make 9/x be less than 2
Also, variable x cannot be 0 because 9/0 is an undefined mathematical expression.
$$Therefore,\ \frac{9}{x}\ge2$$
$$9\ge2x$$
$$2x\le9$$
$$x\le\frac{9}{2}$$
$$x\le4.5$$
With all the information provided, and data obtained from the question,
$$1\le x\le4.5$$
x = any number between 1 and 4.5, and the least integer = 1.

Answer = option B


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