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# If there is a least integer that satisfies the inequality 9/x ≥ 2 what

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Senior Manager
Joined: 04 Sep 2017
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If there is a least integer that satisfies the inequality 9/x ≥ 2 what  [#permalink]

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21 Sep 2019, 04:55
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56% (01:03) correct 44% (01:08) wrong based on 407 sessions

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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.

PS41471.01
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Re: If there is a least integer that satisfies the inequality 9/x ≥ 2 what  [#permalink]

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21 Sep 2019, 10:29
1
Is the question correct? 9/2 greater than or equal to 2?
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Re: If there is a least integer that satisfies the inequality 9/x ≥ 2 what  [#permalink]

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28 Sep 2019, 08:10
1
gmatt1476 wrote:
If there is a least integer that satisfies the inequality 9/2 ≥ 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.

PS41471.01

Hi Bunuel bb gmatt1476

The question above needs to be modified. The inequality is 9/x ≥ 2.

Thanks!
Math Expert
Joined: 02 Sep 2009
Posts: 60778
Re: If there is a least integer that satisfies the inequality 9/x ≥ 2 what  [#permalink]

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28 Sep 2019, 08:12
swatjazz wrote:
gmatt1476 wrote:
If there is a least integer that satisfies the inequality 9/2 ≥ 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.

PS41471.01

Hi Bunuel bb gmatt1476

The question above needs to be modified. The inequality is 9/x ≥ 2.

Thanks!

Done. Thank you for noticing!
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Re: If there is a least integer that satisfies the inequality 9/x ≥ 2 what  [#permalink]

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29 Sep 2019, 22:32
1
The question asks for the least value that satisfies the inequality 9/x > 2

The quickest method is to test the answers

A. 9/0 = 0 but 0 is <2 not greater than 2...Incorrect
B. 9/1 = 9 9>2 this works.
C 9/4 =2.25 although 2.25 is greater than 2, 4 is not the least value for x that would make the inequality work

For this reason B is correct.
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Re: If there is a least integer that satisfies the inequality 9/x ≥ 2 what  [#permalink]

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13 Oct 2019, 01:32
dcummins wrote:
The question asks for the least value that satisfies the inequality 9/x > 2

The quickest method is to test the answers

A. 9/0 = 0 but 0 is <2 not greater than 2...Incorrect
B. 9/1 = 9 9>2 this works.
C 9/4 =2.25 although 2.25 is greater than 2, 4 is not the least value for x that would make the inequality work

For this reason B is correct.

IMHO, regarding option A, we can just say that the denominator cannot be 0 at all! So there's actually no need to do any kind of calculation.
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If there is a least integer that satisfies the inequality 9/x ≥ 2 what  [#permalink]

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26 Oct 2019, 18:04
gmatt1476 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.

PS41471.01

option A :- 9 / 0 = undefined So option A is discarded.

Option B :- Put x = 1 and check .
9 / 1 >= 2 ...So option B satisfies the inequality.

Please give me KUDOs if you liked my explanation.
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Joined: 25 Feb 2019
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Re: If there is a least integer that satisfies the inequality 9/x ≥ 2 what  [#permalink]

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03 Nov 2019, 20:14
Guys is there a way to solve this using algebra and not by plugging in?

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Re: If there is a least integer that satisfies the inequality 9/x ≥ 2 what  [#permalink]

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07 Nov 2019, 03:04
porwal1

9/x >= 2, this inequality tells us that x can't be negative or 0, because in either case inequality is violated (Example : 9/(-ve number) is negative, 9/0 is undefined)
now solving the inequality gives us :
x<= 9/2
x<= 4.5
So the possible integer values are {1,2,3,4}, of which the minimum is 1 (answer)
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Re: If there is a least integer that satisfies the inequality 9/x ≥ 2 what  [#permalink]

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09 Nov 2019, 02:57
Bunuel integer x is not specified to be either positive or negative.

Hence if x was negative the expression would become $$x>=9/2$$ --> least integer 4.

However, if we consider x being positive, the expression gives x=1 as least integer.

I think the question stem shoud specify that x is positive.
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Posts: 60778
Re: If there is a least integer that satisfies the inequality 9/x ≥ 2 what  [#permalink]

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09 Nov 2019, 03:05
1
Camach700 wrote:
Bunuel integer x is not specified to be either positive or negative.

Hence if x was negative the expression would become $$x>=9/2$$ --> least integer 4.

However, if we consider x being positive, the expression gives x=1 as least integer.

I think the question stem shoud specify that x is positive.

This is an official questions so it must and is correct.

If 9/x ≥ 2, then x cannot be negative, because if x is negative, then 9/x = 9/negative = negative and cannot be more than a positive number.
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Re: If there is a least integer that satisfies the inequality 9/x ≥ 2 what  [#permalink]

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11 Dec 2019, 22:47
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.

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Re: If there is a least integer that satisfies the inequality 9/x ≥ 2 what  [#permalink]

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12 Dec 2019, 07:33
Top Contributor
gmatt1476 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.

PS41471.01

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!

Cheers,
Brent
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Re: If there is a least integer that satisfies the inequality 9/x ≥ 2 what  [#permalink]

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17 Dec 2019, 08:36
I'm curious to know why this question has been added to the GMAT Official Advanced Questions book! (Question No. 14) That book is meant to contain only hard questions lol. Or maybe according to the GMAT database a lot of people choose E?
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Re: If there is a least integer that satisfies the inequality 9/x ≥ 2 what  [#permalink]

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17 Dec 2019, 20:55
1
gmatt1476 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.

PS41471.01

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.

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If there is a least integer that satisfies the inequality 9/x ≥ 2 what  [#permalink]

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25 Dec 2019, 00:13
dcummins wrote:
The question asks for the least value that satisfies the inequality 9/x > 2

The quickest method is to test the answers

A. 9/0 = 0 but 0 is <2 not greater than 2...Incorrect
B. 9/1 = 9 9>2 this works.
C 9/4 =2.25 although 2.25 is greater than 2, 4 is not the least value for x that would make the inequality work

For this reason B is correct.

if the question asked for greatest integer then would 4 be the answer then ?
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Re: If there is a least integer that satisfies the inequality 9/x ≥ 2 what  [#permalink]

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25 Dec 2019, 18:22
1
Hi mockingjay,

YES - if the question was changed and we were asked for the largest integer-value of X, then the answer would be 4.

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Re: If there is a least integer that satisfies the inequality 9/x ≥ 2 what  [#permalink]

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25 Dec 2019, 19:20
1
Unbelievable, do you really think 9/0 undefined? It’s infinite and infinity is definitely greater than 2. If this is an official question, I question the test are we to understand that the test limits it’s understanding to algebra and so those of us who have a calculus background are at a disadvantage? Too bad. Bad question

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Re: If there is a least integer that satisfies the inequality 9/x ≥ 2 what  [#permalink]

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25 Dec 2019, 23:54
EMPOWERgmatRichC wrote:
Hi mockingjay,

YES - if the question was changed and we were asked for the largest integer-value of X, then the answer would be 4.

GMAT assassins aren't born, they're made,
Rich

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If there is a least integer that satisfies the inequality 9/x ≥ 2 what  [#permalink]

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27 Jan 2020, 22:37
Stonely wrote:
Unbelievable, do you really think 9/0 undefined? It’s infinite and infinity is definitely greater than 2. If this is an official question, I question the test are we to understand that the test limits it’s understanding to algebra and so those of us who have a calculus background are at a disadvantage? Too bad. Bad question

Posted from my mobile device

in the case of calculus, x tends to 0, not actually 0. This is why infinity is considered. calculus doesn't really talk about absolute value in the cases. X is so small that it is nearest to 0 (we don't know what is nearest to any number), so in that case, dividing the above number from 0.0000000000000000000000000000000000000000000000......1 will give so big a value that it is considered infinite.
If there is a least integer that satisfies the inequality 9/x ≥ 2 what   [#permalink] 27 Jan 2020, 22:37
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