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

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Bunuel
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If a = 2,879 + b, what is the value of the digit b? [#permalink] New post   09 Jul 2018, 00:50
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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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A
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Re: If a = 2,879 + b, what is the value of the digit b? [#permalink] New post   09 Jul 2018, 01:34
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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Re: If a = 2,879 + b, what is the value of the digit b? [#permalink] New post   09 Jul 2018, 09:43
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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.




Answer A.



Thanks,
GyM
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Re: If a = 2,879 + b, what is the value of the digit b? [#permalink] New post   09 Jul 2018, 09:47
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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Re: If a = 2,879 + b, what is the value of the digit b? [#permalink] New post   09 Jul 2018, 09:55
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.
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Re: If a = 2,879 + b, what is the value of the digit b? [#permalink] New post   09 Jul 2018, 10:03
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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Re: If a = 2,879 + b, what is the value of the digit b? [#permalink] New post   09 Jul 2018, 11:08
Can “digit” B be negative? I’m unsure. Experts to clarify please.


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If a = 2,879 + b, what is the value of the digit b? [#permalink] New post   09 Jul 2018, 19:37
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
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Re: If a = 2,879 + b, what is the value of the digit b? [#permalink] New post   09 Jul 2018, 20:49
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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? [#permalink] New post   11 Feb 2021, 18:35
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