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# If a = 2,879 + b, what is the value of the digit b?

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Math Expert
Joined: 02 Sep 2009
Posts: 51072
If a = 2,879 + b, what is the value of the digit b?  [#permalink]

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08 Jul 2018, 23:50
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Difficulty:

85% (hard)

Question Stats:

27% (01:13) correct 73% (01:20) wrong based on 55 sessions

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If a = 2,879 + b, what is the value of the digit b?

(1) a is divisible by 7.
(2) a is divisible by 2.

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Status: Learning stage
Joined: 01 Oct 2017
Posts: 931
WE: Supply Chain Management (Energy and Utilities)
Re: If a = 2,879 + b, what is the value of the digit b?  [#permalink]

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09 Jul 2018, 00:34
Bunuel wrote:
If a = 2,879 + b, what is the value of the digit b?

(1) a is divisible by 7.
(2) a is divisible by 2.

Given a = 2,879 + b
We have range of 'b' from -9 to 9 since 'b' is a digit.
So, 'a' ranges from 2879-9 to 2879+9, i.e, 2870 to 2889.
Question stem: b=?

st1:-a is divisible by 7

So a=2870,2877, and 2884 when b=-9, -2, and 5 respectively.

Since b has more than one values, hence insufficient.

st2:-a is divisible by 2
So a=2870,2872, .......,2884,2886,2888 when b=-9, -7,.......,5,7,9 respectively.
Since b has more than one values, hence insufficient.
Now, combining st1 and st2, we have
a=2870 and 2884 when b=-9 and 5 respectively.
Since b has more than one values, hence insufficient.

Hence, insufficient.

Ans. (E)
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PKN

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Joined: 14 Dec 2017
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Re: If a = 2,879 + b, what is the value of the digit b?  [#permalink]

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09 Jul 2018, 08:43
3
Bunuel wrote:
If a = 2,879 + b, what is the value of the digit b?

(1) a is divisible by 7.
(2) a is divisible by 2.

Given a = 2879 + b, b is a digit, b = {0,1,......8,9}

We have find value of digit b = ?

Statement 1: a is divisible by 7

Hence, (2879 + b) is divisible by 7

When 2879 is divided by 7, we get remainder as 2.

So for a to be a multiple of 7, (2+b) = 7k

b = 5, 12, 19,....

Statement 1 is Sufficient

Statement 2: a is divisible by 2

Hence, (2879 + b) is divisible by 2

When 2879 is divided by 2, we get remainder as 1.

So for a to be a multiple of 2, (1+b) = 2k

b = 1, 3, 5, 7, 9....

Statement 2 is Not Sufficient.

Thanks,
GyM
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Re: If a = 2,879 + b, what is the value of the digit b?  [#permalink]

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09 Jul 2018, 08:47
PKN wrote:
Bunuel wrote:
If a = 2,879 + b, what is the value of the digit b?

(1) a is divisible by 7.
(2) a is divisible by 2.

Given a = 2,879 + b
We have range of 'b' from -9 to 9 since 'b' is a digit.
So, 'a' ranges from 2879-9 to 2879+9, i.e, 2870 to 2889.
Question stem: b=?

st1:-a is divisible by 7

So a=2870,2877, and 2884 when b=-9, -2, and 5 respectively.

Since b has more than one values, hence insufficient.

st2:-a is divisible by 2
So a=2870,2872, .......,2884,2886,2888 when b=-9, -7,.......,5,7,9 respectively.
Since b has more than one values, hence insufficient.
Now, combining st1 and st2, we have
a=2870 and 2884 when b=-9 and 5 respectively.
Since b has more than one values, hence insufficient.

Hence, insufficient.

Ans. (E)

PKN are digits considered to be negative as well?

I thought in decimal system we consider digits to be {0 to 9}. If they are considered negative as well, then good job on the solution. E is the right answer.

Thanks,
GyM
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Joined: 30 Aug 2016
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Re: If a = 2,879 + b, what is the value of the digit b?  [#permalink]

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09 Jul 2018, 08:55
Bunuel wrote:
If a = 2,879 + b, what is the value of the digit b?

(1) a is divisible by 7.
(2) a is divisible by 2.

It is given that that b is a digit. This implies b={0,1,2,...,9}

Conisder
Statement 1:
a is divisible by 7 implies a=((2877) + 2+b)/7 yields a whole number

(2+b)/7 = an integer i.e, when b is 5.

Hence, Statement 1 is sufficient.
Statement 2:
a is divisible by 2 implies a=((2879) + 1+b)/2 yields a whole number

(1+b)/2 = an integer i.e, when b is {1,3,5,7,9}.

That gives multiple solutions. Hence, Insufficient.

The answer has to be A.
Director
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Re: If a = 2,879 + b, what is the value of the digit b?  [#permalink]

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09 Jul 2018, 09:03
GyMrAT wrote:
PKN wrote:
Bunuel wrote:
If a = 2,879 + b, what is the value of the digit b?

(1) a is divisible by 7.
(2) a is divisible by 2.

Given a = 2,879 + b
We have range of 'b' from -9 to 9 since 'b' is a digit.
So, 'a' ranges from 2879-9 to 2879+9, i.e, 2870 to 2889.
Question stem: b=?

st1:-a is divisible by 7

So a=2870,2877, and 2884 when b=-9, -2, and 5 respectively.

Since b has more than one values, hence insufficient.

st2:-a is divisible by 2
So a=2870,2872, .......,2884,2886,2888 when b=-9, -7,.......,5,7,9 respectively.
Since b has more than one values, hence insufficient.
Now, combining st1 and st2, we have
a=2870 and 2884 when b=-9 and 5 respectively.
Since b has more than one values, hence insufficient.

Hence, insufficient.

Ans. (E)

PKN are digits considered to be negative as well?

I thought in decimal system we consider digits to be {0 to 9}. If they are considered negative as well, then good job on the solution. E is the right answer.

Thanks,
GyM

Hi GyMrAT,
You are correct . In decimal system digits are from 0-9.
However, since 'b' is involved in an arithmetic operation (a=2879+b), I considered both faces of polarity.
If we go by words of the question stem, it says "what is the value of digit b",then negative digits are not allowed.
Bunuel, chetan2u Could you please clarify?

Thanking you.
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Regards,

PKN

Rise above the storm, you will find the sunshine

Intern
Status: GMAT in August 2018
Joined: 05 Mar 2018
Posts: 46
Location: India
WE: Law (Consulting)
Re: If a = 2,879 + b, what is the value of the digit b?  [#permalink]

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09 Jul 2018, 10:08
Can “digit” B be negative? I’m unsure. Experts to clarify please.

Sent from my iPhone using GMAT Club Forum
Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 931
WE: Supply Chain Management (Energy and Utilities)
If a = 2,879 + b, what is the value of the digit b?  [#permalink]

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09 Jul 2018, 18:37
jayantbakshi wrote:
Can “digit” B be negative? I’m unsure. Experts to clarify please.

Sent from my iPhone using GMAT Club Forum

OA is A.Good learnings for me.
I need to revise concepts and start again.

Thank you all.

Posted from my mobile device
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

Math Expert
Joined: 02 Sep 2009
Posts: 51072
Re: If a = 2,879 + b, what is the value of the digit b?  [#permalink]

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09 Jul 2018, 19:49
PKN wrote:
jayantbakshi wrote:
Can “digit” B be negative? I’m unsure. Experts to clarify please.

Sent from my iPhone using GMAT Club Forum

OA is A.Good learnings for me.
I need to revise concepts and start again.

Thank you all.

Posted from my mobile device

Stem says that b is a digit. Digits are: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
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Re: If a = 2,879 + b, what is the value of the digit b? &nbs [#permalink] 09 Jul 2018, 19:49
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