GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 20 Oct 2019, 12:31

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 07 Feb 2011
Posts: 89
If a is divisible by 2, is b + 5 an integer?  [#permalink]

### Show Tags

Updated on: 01 Mar 2013, 01:52
4
00:00

Difficulty:

55% (hard)

Question Stats:

68% (02:14) correct 32% (02:10) wrong based on 137 sessions

### HideShow timer Statistics

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?

_________________

Originally posted by manimgoindowndown on 28 Feb 2013, 14:11.
Last edited by Bunuel on 01 Mar 2013, 01:52, edited 3 times in total.
Moved to DS forum and edited the question. Edited OA.
Manager
Joined: 12 Jul 2011
Posts: 122
Concentration: Strategy, Sustainability
Schools: Booth '15 (M)
WE: Business Development (Non-Profit and Government)
Re: If a is divisible by 2, is b + 5 an integer?  [#permalink]

### Show Tags

28 Feb 2013, 23:22
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?"
_________________
Intern
Joined: 16 Jan 2013
Posts: 19
Re: If a is divisible by 2, is b + 5 an integer?  [#permalink]

### Show Tags

28 Feb 2013, 23:48
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?

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

Manager
Joined: 12 Jul 2011
Posts: 122
Concentration: Strategy, Sustainability
Schools: Booth '15 (M)
WE: Business Development (Non-Profit and Government)
Re: If a is divisible by 2, is b + 5 an integer?  [#permalink]

### Show Tags

28 Feb 2013, 23:55
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?

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

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.
_________________
Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 590
Re: If a is divisible by 2, is b + 5 an integer?  [#permalink]

### Show Tags

01 Mar 2013, 00:19
1
1
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.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 58434
Re: If a is divisible by 2, is b + 5 an integer?  [#permalink]

### Show Tags

01 Mar 2013, 01:51
2
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.

Hope it's clear.
_________________
Manager
Joined: 12 Jul 2011
Posts: 122
Concentration: Strategy, Sustainability
Schools: Booth '15 (M)
WE: Business Development (Non-Profit and Government)
Re: If a is divisible by 2, is b + 5 an integer?  [#permalink]

### Show Tags

01 Mar 2013, 10:30
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.
_________________
Current Student
Joined: 18 Oct 2014
Posts: 801
Location: United States
GMAT 1: 660 Q49 V31
GPA: 3.98
Re: If a is divisible by 2, is b + 5 an integer?  [#permalink]

### Show Tags

05 Jun 2016, 14:37
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.

_________________
I welcome critical analysis of my post!! That will help me reach 700+
Retired Moderator
Joined: 25 Feb 2013
Posts: 1178
Location: India
GPA: 3.82
Re: If a is divisible by 2, is b + 5 an integer?  [#permalink]

### Show Tags

23 Feb 2018, 21:15
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
Re: If a is divisible by 2, is b + 5 an integer?   [#permalink] 23 Feb 2018, 21:15
Display posts from previous: Sort by