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

Question

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

PKN · Answer

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)

GyMrAT · Answer

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

GyMrAT · Answer

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

yogithaan · Answer

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.

PKN · Answer

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.

jayantbakshi · Answer

Can “digit” B be negative? I’m unsure. Experts to clarify please.

Sent from my iPhone using GMAT Club Forum

PKN · Answer

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

Thank you all.

Posted from my mobile device

Bunuel · Answer

Stem says that b is a digit. Digits are: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

bumpbot · Answer

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

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

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