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If A and B are positive integers and 5A -7(B + 3) = 2, what is the lea

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Bunuel
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If A and B are positive integers and 5A -7(B + 3) = 2, what is the lea [#permalink] New post   01 Nov 2019, 04:11
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A
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C
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E

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If A and B are positive integers and 5A -7(B + 3) = 2, what is the least possible value of A-B?

(A) 1
(B) 3
(C) 5
(D) 7
(E) 9


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C
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Re: If A and B are positive integers and 5A -7(B + 3) = 2, what is the lea [#permalink] New post   01 Nov 2019, 05:07
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5A -7(B + 3) = 2
5A-7B-21=2
5A-7B=23

As A and B are positive intergers and from answer choices we know that A>B. lets do trial and error:
Lets say A=5, then B=-ve. not possible
Say A=6, then B=1
Therefore, A-B=5
Ans: C
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Re: If A and B are positive integers and 5A -7(B + 3) = 2, what is the lea [#permalink] New post   01 Nov 2019, 10:22
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If A and B are positive integers and 5A -7(B + 3) = 2, what is the least possible value of A-B?

5(A-B) = 23+2B
Least possible value of B is 1 => Least possible value of 5(A-B) is 23+2=25
IMO C
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Re: If A and B are positive integers and 5A -7(B + 3) = 2, what is the lea [#permalink] New post   01 Nov 2019, 06:00
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5A-7B=23

A and B are positive integers

5(6)-7(1)=23 (A=6, B=1)

A-B= 5

option C is the correct option
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Re: If A and B are positive integers and 5A -7(B + 3) = 2, what is the lea [#permalink] New post   01 Nov 2019, 08:24
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5A -7(B + 3) = 2,

Least value of B=1....then A=6

The least possible value of A-B=5


OA:B

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If A and B are positive integers and 5A -7(B + 3) = 2, what is the lea [#permalink] New post   Updated on: 26 Dec 2019, 05:05
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Substitutefrom given eauation, the value of A into A-B
We get A-B = (23+2B)/5 . For this expression to be minimum B must be minimum which is 1.
Hence expression = [23 + 2(1) ]/5 = 5 = C

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Originally posted by ShankSouljaBoi on 01 Nov 2019, 13:30.
Last edited by ShankSouljaBoi on 26 Dec 2019, 05:05, edited 1 time in total.
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Re: If A and B are positive integers and 5A -7(B + 3) = 2, what is the lea [#permalink] New post   01 Nov 2019, 13:47
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As per the question,

5A - 7B -21 = 2
=> 5A - 7B = 23
=> 5(A-B) = 23 + 2B
=> A-B = (23+2B)/5
Since A and B are positive integers and we have to find the minimum value of A-B, we have to consider the minimum possible value of B as per the previous expression.

Min. B = 1
Therefore, min. (A-B) = 5
Answer is (C)

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Re: If A and B are positive integers and 5A -7(B + 3) = 2, what is the lea [#permalink] New post   01 Nov 2019, 14:46
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A, B — positive integer
5A —7(B+3)= 2
—> what is the least possible value of A —B =???

5A —7B —21=2

5A —5B —2B =23

5*( A—B)= 23+ 2B

A —B= (23+ 2B)/5
—> in order A—B to be the least value, B should be equal to 1.

B=1 —> A —B = (23+2)/5= 5

The answer is C

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Re: If A and B are positive integers and 5A -7(B + 3) = 2, what is the lea [#permalink] New post   01 Nov 2019, 15:53
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C is my answer.

5A -7(B + 3) = 2
or, 5A=23+7B.
Min value of B=1, So min value A=6
So min value (A-B)=5
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Re: If A and B are positive integers and 5A -7(B + 3) = 2, what is the lea [#permalink] New post   02 Nov 2019, 01:11
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5A -7(B + 3) = 2
--> 5A - 7B = 23
--> 5A - 5B = 2B + 23
--> A - B = (2B + 23)/5

Least possible value of A - B is when B = 1
--> A - B = (2*1 + 23)/5 = 25/5 = 5

IMO Option C
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Re: If A and B are positive integers and 5A -7(B + 3) = 2, what is the lea [#permalink] New post   02 Nov 2019, 13:07
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Given : 5A -7(B + 3) = 2 and A,B are positive integers

5A - 7B - 21 = 2
5A - 7B = 23
5A - 5B -2B = 23
5(A-B) = 23 + 2 since the least positive value of B is 1
5(A-B) = 25
A-B = 5

Answer is C
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Re: If A and B are positive integers and 5A -7(B + 3) = 2, what is the lea [#permalink] New post   03 Nov 2019, 15:50
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Quote:
If A and B are positive integers and 5A -7(B + 3) = 2, what is the least possible value of A-B?

(A) 1
(B) 3
(C) 5
(D) 7
(E) 9


5A -7(B + 3) = 2
5A -7B = 2 + 21
5A = 23 + 7B
A = (23 + 7B) / 5

(A,B) = positive integers
A = (23 + 7B) / 5 = positive integer
B = 1; A = 23+7/5 = 30/5 = 6
B = 2; A ≠ integer
B = 6; A = 23+7(6)/5 = 65/3 = 13…

min. A-B = 6-1 = 5

Answer (C)
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Re: If A and B are positive integers and 5A -7(B + 3) = 2, what is the lea [#permalink] New post   13 Dec 2019, 07:36
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Bunuel wrote:

Competition Mode Question



If A and B are positive integers and 5A -7(B + 3) = 2, what is the least possible value of A-B?

(A) 1
(B) 3
(C) 5
(D) 7
(E) 9


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5A -7(B + 3) = 2
5A-7B = 23
B = (5A-23)/7
When A=6; B=1; A-B = 5
When A=13;B=6; A-B =7
A-B increases further e.g. A=20;B=11; A-B = 9

IMO C
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Re: If A and B are positive integers and 5A -7(B + 3) = 2, what is the lea [#permalink] New post   04 May 2020, 09:16
A and B are positive integers
5A-7(B+3)=2
So 5A-7B=2+21=23
Rewriting, 5(A-B)-2B=23
5(A-B)= 23+2B
Since we want the least answer, let us start with the least value for B say 1
5(A-B)= 23+2=25
so A-B=5
Hence C

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Re: If A and B are positive integers and 5A -7(B + 3) = 2, what is the lea [#permalink] New post   01 Jun 2021, 10:16
Finding the right combination is the key i guess and the right thing...luck is also great factor...........
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Re: If A and B are positive integers and 5A -7(B + 3) = 2, what is the lea [#permalink] New post   16 Feb 2024, 02:58
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Re: If A and B are positive integers and 5A -7(B + 3) = 2, what is the lea [#permalink]
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