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

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01 Nov 2019, 04:11
1
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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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Re: If A and B are positive integers and 5A -7(B + 3) = 2, what is the lea  [#permalink]

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01 Nov 2019, 05:07
3
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]

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01 Nov 2019, 06:00
2
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]

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01 Nov 2019, 14:46
2
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

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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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01 Nov 2019, 10:22
1
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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If A and B are positive integers and 5A -7(B + 3) = 2, what is the lea  [#permalink]

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Updated on: 26 Dec 2019, 05:05
1
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]

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01 Nov 2019, 13:47
1
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

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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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01 Nov 2019, 15:53
1

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]

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02 Nov 2019, 01:11
1
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]

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02 Nov 2019, 13:07
1
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

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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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03 Nov 2019, 15:50
1
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

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

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Updated on: 04 Nov 2019, 00:59
5a-7b=23
a=6 and b = 1
6-1 ;5
IMO C

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

Originally posted by Archit3110 on 01 Nov 2019, 05:54.
Last edited by Archit3110 on 04 Nov 2019, 00:59, 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]

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01 Nov 2019, 06:45
1
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

Since A - B has to be positive as per the answer choices, A > B.
So, let's take B = 1 (only then A > B as both are positive)
5A -7(B + 3) = 2
5A -7B - 21 = 2
5A - 7B = 23

5A - 7 * 1 = 23
A = 6

B = 1 and A = 6 are the least possible positive integer values
Hence A + B = 7

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

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01 Nov 2019, 15:55

5A -7(B + 3) = 2
or, 5A=23+7B.
or, A=23/5 + 7/5 B
So the difference between A & B is greater than 23/5 or 4.5.
So the minimum difference is 5 (since Integer-Integer=Integer and Minimum integer greater than 4.5 is 5)
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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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01 Nov 2019, 16:16
answer should be a , 5(a-b)+2b=23 for a-b to be minimum 2b must be equal to 18
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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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01 Nov 2019, 22:51
5A - 7B - 23 = 2
5A - 7B = 25
Because the result (25) is multiple of 5, 7B also should be multiple of 5. (Ex: 7*5= 35 (least number))
5A - 7*5 = 25
5A = 60
A = 12 and B =5
A-B= 12-5 = 7
Ans is: D
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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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13 Dec 2019, 07:36
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
Re: If A and B are positive integers and 5A -7(B + 3) = 2, what is the lea   [#permalink] 13 Dec 2019, 07:36
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