If 5

Question

If 5 < x < 10 and y = x + 5, what is the greatest possible integer value of x + y ?

A. 18
B. 20
C. 23
D. 24
E. 25

Source:   Nova GMAT  
Difficulty Level:   700

Bunuel · Accepted Answer

Please read and follow: 11-rules-for-posting-133935.html Pay attention to the points #3, 7 and 8. Original question is below: If 5 < x < 10 and y = x + 5, what is the greatest possible integer value of x + y ? A. 18 B. 20 C. 23 D. 24 E. 25 Since y=x+5 then x+y=x+(x+5)=2x+5 . So, we need to find the greatest possible integer value of 2x+5 . Multiply 5 < x < 10 by 2: 10<2x<20 . Now add 5 to each part of the inequality: 15<2x+5<25 . As you can see the greatest possible integer value of 2x+5 is 24. Answer: D. Hope it's clear.

cyberjadugar · Answer

Hi,

To find the greastest possible integer value of x + y,  it is not necessary that both x & y should be integers ,
 x, y should be chosen in such a way that their sum is an integral value .

so, to find, max value of (x + y)
x + y = 2x + 5
maximum value of x such that 2x is integer would be 9.5 (given, 5 < x < 10)
x + y (maximum) = 19 + 5 =24

Let me know if you need any more assistance on this topic.

Regards,

kashishh · Answer

Dear Bunuel,
1.)can't understand what is the need to take 2x+5? wont it be easy to calculate with x less than 10.?
2.) when x is not integer but x+y to be integer - we can take x=9.5 and y = 14.5 - giving 24 - is this right?

Bunuel · Answer

What do you mean by "need"? One can solve a question with different approaches and you can choose the approach you personally find easier.

shivanigs · Answer

Dear Bunuel,

Apologies for the wrongful post..did not know the rules.Have gone thru the same,will not happen again.Thanks for your help!

Regards

kashishh · Answer

Dear Bunuel,
sorry for the word 'need'. i just only wanted to know whether the way i did is right.
thanx for the reply.

Bunuel · Answer

Yes, the way you solved is totally OK.

amitbharadwaj7 · Answer

The question asks what is the greatest integer value of 2X+5, where 5<X<10, the greatest value of 2X which is integer will be achieved if X=9.5

Hence the greatest integer value of X+Y = 2x9.5+5=24, answer - D

Tango3 · Answer

I am getting it 23.

x = { 6,7,8,9} as 5<x<10

y=x+5 . Let's plug in values

x=6 y=11
x=7 y=12
x=8 y=13
x=9 y=14

Now as we have to find maximum value I chose x=9 and y=14

So x+y=9+14=23

Can someone let me know where I am making mistake here

shoumkrish · Answer

Hi  Tango3 , the question here asks for the max integer value of x+y, but nowhere it mentions x and y are integers.

x+y = x+(x+5) = 2x + 5. So, to make the sum an integer, x should assume the value 9.5

So the max sum is 24.

daniformic · Answer

If x=9.99
y=14.99
x+y=24.98
x+y≈25

Answer D

BrushMyQuant · Answer

5 < x < 10 and y = x + 5

=> 5 < x < 10 ...(1)

Adding 5 on both the sides we get
=> 5 + 5 < x + 5 < 10 + 5
=> 10 < x + 5 < 15
=> 10 < y < 15 ...(2)

(1) + (2) we get

5 + 10 < x + y < 10 + 15
=> 15 < x + y < 25

So, Max(x+y) = 24 based on the options

=> Answer will be D
Hope it helps!

Watch the following video to learn the Basics of Inequalities

bumpbot · Answer

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If 5 < x < 10 and y = x + 5, what is the greatest possible

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