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If x is an integer and y = –3x + 7, what is the least value of x for

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Bunuel
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If x is an integer and y = –3x + 7, what is the least value of x for [#permalink] If x is an integer and y = –3x + 7, what is the least value of x for   Updated on: 10 Jul 2019, 23:56
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If x is an integer and y = –3x + 7, what is the least value of x for which y is less than 1?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Source: Nova GMAT
Difficulty Level: 550
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C

Originally posted by Bunuel on 21 May 2017, 12:36.
Last edited by Sajjad1994 on 10 Jul 2019, 23:56, edited 1 time in total.
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Re: If x is an integer and y = –3x + 7, what is the least value of x for [#permalink] If x is an integer and y = –3x + 7, what is the least value of x for   21 May 2017, 12:48
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The least value of x for which y is less than 1 is 3.

y = -3x+7 = -3(3) + 7 = -2.

Option A and B yields positive value .

Option D and E gives -ve value but not the least value when compared to option C.

Hence answer is option C .
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Re: If x is an integer and y = –3x + 7, what is the least value of x for [#permalink] If x is an integer and y = –3x + 7, what is the least value of x for   21 May 2017, 17:08
Bunuel wrote:
If x is an integer and y = –3x + 7, what is the least value of x for which y is less than 1?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5


y=-3x+7
if y=1, then x=2
if y<1, then x>2
least value of x=3
C
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Re: If x is an integer and y = –3x + 7, what is the least value of x for [#permalink] If x is an integer and y = –3x + 7, what is the least value of x for   21 May 2017, 23:17
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If y < 1, it means
-3x + 7 <1
-3x < -6

Dividing both sides by -3
x > 2

Minimum integer value greater than 2 is 3. So minimum value x can take is 3.

Hence answer is C
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Re: If x is an integer and y = –3x + 7, what is the least value of x for [#permalink] If x is an integer and y = –3x + 7, what is the least value of x for   22 May 2017, 00:26
Quickest way to solve such question is using Ans option. Substitute answer options into the equation.

Ans : C
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Re: If x is an integer and y = –3x + 7, what is the least value of x for [#permalink] If x is an integer and y = –3x + 7, what is the least value of x for   22 May 2017, 00:42
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Bunuel wrote:
If x is an integer and y = –3x + 7, what is the least value of x for which y is less than 1?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

y = -3x + 7 < 1
3x > 6
x > 2

so for y<1, x>2..

So, x = 3

Show Spoiler
Answer C..
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Re: If x is an integer and y = –3x + 7, what is the least value of x for [#permalink] If x is an integer and y = –3x + 7, what is the least value of x for   23 May 2017, 09:17
If x is an integer and y = –3x + 7, what is the least value of x for which y is less than 1?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

two ways to solve the problem
1. Number plugging
y = –3x + 7
given that y < 1
–3x + 7 < 1
Now substitute the value of x such that the value of on left hand side of the equation must be less than 1
let say x =1 , then –3x + 7 = 4
x=2 , then –3x + 7 = 1
x=3 , then –3x + 7 = -2

the least value of x for which y is less than 1 , so x= 3

2 . solve the inequality
y = –3x + 7 , given that y < 1
therefore –3x + 7 < 1
x< -2
therefore for the minimum value of x is 3

C is the answer .

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Re: If x is an integer and y = –3x + 7, what is the least value of x for [#permalink] If x is an integer and y = –3x + 7, what is the least value of x for   23 May 2017, 17:18
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Bunuel wrote:
If x is an integer and y = –3x + 7, what is the least value of x for which y is less than 1?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5


Let’s analyze each answer choice:

A) x = 1

y = -3(1) + 7 = 4

B) x = 2

y = -3(2) + 7 = 1

C) x = 3

y = -3(3) + 7 = -2

Since -2 is the first negative value for y, we can stop here. The least value for x that makes y negative is 3.

Alternative solution:

Since y = –3x + 7 and we want y to be less than 1, we have:

–3x + 7 < 1

–3x < –6

x > 2

The least integer that is greater than 2 is 3, so x = 3.

Answer: C
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Re: If x is an integer and y = –3x + 7, what is the least value of x for [#permalink] If x is an integer and y = –3x + 7, what is the least value of x for   10 Jun 2018, 11:35
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Bunuel wrote:
If x is an integer and y = –3x + 7, what is the least value of x for which y is less than 1?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5


Back solving is the way to deal with this question. But before doing so, we have to mark the word least value of x and y is less than 1.

Only option C works. This the least value of x and for this value y is less than 1.

Thus the best answer is C.
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Re: If x is an integer and y = –3x + 7, what is the least value of x for [#permalink] If x is an integer and y = –3x + 7, what is the least value of x for   09 Jul 2020, 10:55
Bunuel wrote:
If x is an integer and y = –3x + 7, what is the least value of x for which y is less than 1?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Source: Nova GMAT
Difficulty Level: 550


Asked: If x is an integer and y = –3x + 7, what is the least value of x for which y is less than 1?

y = - 3x + 7

When x = 2; y = 1
When x=3; y = -2

IMO C
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Re: If x is an integer and y = –3x + 7, what is the least value of x for [#permalink]
09 Jul 2020, 10:55
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Bunuel
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