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If a is divisible by 2, is b + 5 an integer?

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If a is divisible by 2, is b + 5 an integer?  [#permalink]

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If a is divisible by 2, is b + 5 an integer?

(1) The median of a and b is not an integer.
(2) The average (arithmetic mean) of 3a, b, and b + 10 is an even integer.

Something that occasionally throws me off and I often forget. When we get a variable on the gmat, what can we assume about it? Just that it is a real, rational number? We CANNOT automatically assume it's an integer correct?

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Originally posted by manimgoindowndown on 28 Feb 2013, 13:11.
Last edited by Bunuel on 01 Mar 2013, 00:52, edited 3 times in total.
Moved to DS forum and edited the question. Edited OA.
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Re: If a is divisible by 2, is b + 5 an integer?  [#permalink]

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New post 28 Feb 2013, 22:22
Right. We only know that b is real and rational. If we could assume variables were integers, we wouldn't need any additional statements at all to answer the question, "Is b + 5 an integer?"
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Re: If a is divisible by 2, is b + 5 an integer?  [#permalink]

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New post 28 Feb 2013, 22:48
manimgoindowndown wrote:
If a is divisible by 2, is b + 5 an integer?

(1) The median of a and b is not an integer.
(2) The average (arithmetic mean) of 3a, b, and b + 10 is an even integer.

Something that occasionally throws me off and I often forget. When we get a variable on the gmat, what can we assume about it? Just that it is a real, rational number? We CANNOT automatically assume it's an integer correct?


answer should be Option(b) as

from (1) :- either b is an odd integer or a real number of type x.y ...........hence not sufficient.
from (2) : (3a+b+b+10)/3 = 2k (let say)
so, 3a + 2b = 6k - 10
b = (3(2k-a) - 10)/2
b= 3(2k - a)/2 -5
as k is even, so 2k is also even also even - even is an even hence (2k-a) is divisible by 2
so, b = 3*some_integer - 5
hence b = integer...............hence condition 2 is sufficient

hence answer should be option(b)
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Re: If a is divisible by 2, is b + 5 an integer?  [#permalink]

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New post 28 Feb 2013, 22:55
jbisht wrote:
manimgoindowndown wrote:
If a is divisible by 2, is b + 5 an integer?

(1) The median of a and b is not an integer.
(2) The average (arithmetic mean) of 3a, b, and b + 10 is an even integer.

Something that occasionally throws me off and I often forget. When we get a variable on the gmat, what can we assume about it? Just that it is a real, rational number? We CANNOT automatically assume it's an integer correct?


answer should be Option(b) as

from (1) :- either b is an odd integer or a real number of type x.y ...........hence not sufficient.
from (2) : (3a+b+b+10)/3 = 2k (let say)
so, 3a + 2b = 6k - 10
b = (3(2k-a) - 10)/2
b= 3(2k - a)/2 -5
as k is even, so 2k is also even also even - even is an even hence (2k-a) is divisible by 2
so, b = 3*some_integer - 5
hence b = integer...............hence condition 2 is sufficient

hence answer should be option(b)


I bolded two parts of your explanation. You originally indicated that 2k was even. k itself may be even or odd. You later asserted that k was even.
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Re: If a is divisible by 2, is b + 5 an integer?  [#permalink]

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New post 28 Feb 2013, 23:19
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manimgoindowndown wrote:
If a is divisible by 2, is b + 5 an integer?

(1) The median of a and b is not an integer.
(2) The average (arithmetic mean) of 3a, b, and b + 10 is an even integer.



I don't think the given OA is correct. Anyways, let a = 2p,where p is any integer.

From F.S 1, we have that\(\frac{(a+b)}{2}\) = Not an integer

or\(\frac{2p}{2}+\frac{b}{2} = p+\frac{b}{2}\)= Not an integer. Assuming, b = 3 , we satisfy the fact statement and get a YES for the question stem. Again assuming b=1.2, we satisfy the fact statement but get a NO for the question stem.Insufficient.

From F.S 2, we have \(3a+b+(b+10)/3\) = 2k, where k is again an integer.

Thus,\(3a/3 + (b+5)/3+(b+5)/3\) = 2k

or 2/3*(b+5) = 2k-a = 2k-2p = 2(k-p)[an integer]

or (b+5) = An integer*3 = integer.

Sufficient.

B.
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Re: If a is divisible by 2, is b + 5 an integer?  [#permalink]

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New post 01 Mar 2013, 00:51
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NonYankee wrote:
manimgoindowndown wrote:
If a is divisible by 2, is b + 5 an integer?

(1) The median of a and b is not an integer.
(2) The average (arithmetic mean) of 3a, b, and b + 10 is an even integer.

Something that occasionally throws me off and I often forget. When we get a variable on the gmat, what can we assume about it? Just that it is a real, rational number? We CANNOT automatically assume it's an integer correct?


Right. We only know that b is real and rational. If we could assume variables were integers, we wouldn't need any additional statements at all to answer the question, "Is b + 5 an integer?"


From the stem we cannot assume that b is a rational number, it could be an irrational as well, for example \(\sqrt{2}\).

If no other constraint is given about a variable, then all we can say that it's a real number.

If a is divisible by 2, is b + 5 an integer?

Notice that:
a is divisible by 2 implies that a is an even number.
The question basically asks whether b is an integer.

(1) The median of a and b is not an integer. b may or may not be an integer. Consider: a=2 and b=3 for an YES answer and a=2 and b=1/2 for a NO answer. Not sufficient.

(2) The average (arithmetic mean) of 3a, b, and b + 10 is an even integer --> \(3a+b+(b+10)=3*even\) --> \(2b+10=3*even-3a\) --> since a is even, then \(2b+10=3*even-3*even\) --> \(2(b+5)=3(even-even)=3*even\) --> \(b+5=3*\frac{even}{2}=3*integer=integer\). Sufficient.

Answer: B.

Hope it's clear.
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Re: If a is divisible by 2, is b + 5 an integer?  [#permalink]

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New post 01 Mar 2013, 09:30
Bunuel wrote:
From the stem we cannot assume that b is a rational number, it could be an irrational as well, for example \(\sqrt{2}\).


You make a good point. In any case, it's not an integer.
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Re: If a is divisible by 2, is b + 5 an integer?  [#permalink]

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New post 05 Jun 2016, 13:37
manimgoindowndown wrote:
If a is divisible by 2, is b + 5 an integer?

(1) The median of a and b is not an integer.
(2) The average (arithmetic mean) of 3a, b, and b + 10 is an even integer.

Something that occasionally throws me off and I often forget. When we get a variable on the gmat, what can we assume about it? Just that it is a real, rational number? We CANNOT automatically assume it's an integer correct?


a = even

b+5 is an integer?

(1) The median of a and b is not an integer.

a+b/2 is not an integer.

Its given that a is even. The above expression can not be an integer if b is odd or fraction.

(2) The average (arithmetic mean) of 3a, b, and b + 10 is an even integer

3a+b+b+10/2= integer

3a+2b+10/2= integer

3a is even (a is even), 2 b is even and 10 is even. To have above equation as an integer b must be an integer.

Hence b+5 will be an integer.

B is the answer
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Re: If a is divisible by 2, is b + 5 an integer?  [#permalink]

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New post 23 Feb 2018, 20:15
manimgoindowndown wrote:
If a is divisible by 2, is b + 5 an integer?

(1) The median of a and b is not an integer.
(2) The average (arithmetic mean) of 3a, b, and b + 10 is an even integer.

Something that occasionally throws me off and I often forget. When we get a variable on the gmat, what can we assume about it? Just that it is a real, rational number? We CANNOT automatically assume it's an integer correct?


From the question stem it is clear that \(a\) is \(Even\) and we need to know whether \(b\) is integer

Statement 1: implies \(\frac{a+b}{2} =\) Non Integer (NI). if \(a=2\) & \(b=1.5\), then median is non integer and \(b+5\) is also a non integer

but if \(a=2\) & \(b=3\), then median is non integer but \(b+5\) is an integer. Hence we have both a Yes & a NO. Insufficient

Statement 2: implies \(\frac{3a+b+b+10}{3}=Even => 3a+2b+10=3*Even\)

\(=>2b=Even-10-3a\). Now as \(a\) is even so \(3a\) is even and \(10\) is also even

so \(2b=Even-Even-Even=Even => b=\frac{Even}{2}=Integer\). Hence \(b+5\) will be an integer. Sufficient

Option B
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Re: If a is divisible by 2, is b + 5 an integer? &nbs [#permalink] 23 Feb 2018, 20:15
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