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# Two numbers differ by 2 and sum to S. Which of the following is the gr

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Two numbers differ by 2 and sum to S. Which of the following is the gr [#permalink]

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23 Jun 2016, 10:36
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Two numbers differ by 2 and sum to S. Which of the following is the greater of the numbers in terms of S ?
A. $$\frac{S}{2}$$-1

B. $$\frac{S}{2}$$

C. $$\frac{S}{2}$$+$$\frac{1}{2}$$

D. $$\frac{S}{2}$$+1

E. $$\frac{S}{2}$$+2

OG Q 2017 (Book Question: 139)
[Reveal] Spoiler: OA

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Re: Two numbers differ by 2 and sum to S. Which of the following is the gr [#permalink]

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23 Jun 2016, 10:58
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Let the two numbers be a and b.
Assume greater number = a.

a - b = 2.........(1)
a + b = S........(2)
(1) + (2) --> 2a = 2 + S --> a = 1 + S/2

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Re: Two numbers differ by 2 and sum to S. Which of the following is the gr [#permalink]

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23 Jun 2016, 11:04
AbdurRakib wrote:
Two numbers differ by 2 and sum to S. Which of the following is the greater of the numbers in terms of S ?
A. $$\frac{S}{2}$$-1

B. $$\frac{S}{2}$$

C. $$\frac{S}{2}$$+$$\frac{1}{2}$$

D. $$\frac{S}{2}$$+1

E. $$\frac{S}{2}$$+2

OG Q 2017 (Book Question: 139)

a - b = 2
a + b = s

So, 2a = 2 + s

Or, a = $$\frac{( 2 + s )}{2}$$

Or, a = 1 + s/2

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Re: Two numbers differ by 2 and sum to S. Which of the following is the gr [#permalink]

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24 Jun 2016, 02:20
Two numbers differ by 2 and sum to S.
(Let a and b be the two numbers) ;

a - b = 2
a + b = S
(Solving by combination) 2a = 2 + S
a = (2+ S )/ 2
a = 2/2 + S/2
a = 1 + S/2 or S/2 +1

Solving for b;
Substituting a in equation a - b = 2
S/2 +1 - b = 2
b = S/2 +1-2
b = S/2 - 1

Therefore "a" is greater than "b" . Hence Answer is D = (S/2 +1)...

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Re: Two numbers differ by 2 and sum to S. Which of the following is the gr [#permalink]

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02 Sep 2016, 10:00
Any chance this problem can be done by assuming no's?
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Re: Two numbers differ by 2 and sum to S. Which of the following is the gr [#permalink]

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02 Sep 2016, 10:47
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The easiest way to do this is just to pick numbers. Lets say the numbers are 4 and 2. S=6. So then We're looking for the answer to yield w/ 4.
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Re: Two numbers differ by 2 and sum to S. Which of the following is the gr [#permalink]

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27 Oct 2016, 08:46
For this question you can pick your own values.

1+3 = 4 --> x + x+2 = S

D is the only choice that provides us with 3 (the larger of the two numbers on the left hand side of the equation).
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Re: Two numbers differ by 2 and sum to S. Which of the following is the gr [#permalink]

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14 Mar 2017, 13:09
Assume x as the larger number

Then as per the question the two numbers are x and (x-2) (difference is 2)

(x-2)+x=s
2x-2=s
2x=s+2
x=s+2/2
x=s/2+2/2
x=s/2+1
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Re: Two numbers differ by 2 and sum to S. Which of the following is the gr [#permalink]

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18 Mar 2017, 09:32
let's try smart numbers: 10 and 12
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Re: Two numbers differ by 2 and sum to S. Which of the following is the gr [#permalink]

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20 Mar 2017, 05:54
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Expert's post
AbdurRakib wrote:
Two numbers differ by 2 and sum to S. Which of the following is the greater of the numbers in terms of S ?
A. $$\frac{S}{2}$$-1

B. $$\frac{S}{2}$$

C. $$\frac{S}{2}$$+$$\frac{1}{2}$$

D. $$\frac{S}{2}$$+1

E. $$\frac{S}{2}$$+2

We are given that two numbers differ by 2 and sum to S.

We can let the smaller number = x and the larger number = x + 2.

Since the two numbers sum to S, we have:

x + x + 2 = S

2x + 2 = S

2x = S - 2

x = (S - 2)/2 = S/2 -1

Thus, the greater number is x + 2 = S/2 - 1 + 2 = S/2 + 1

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Re: Two numbers differ by 2 and sum to S. Which of the following is the gr [#permalink]

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21 Mar 2017, 03:14
AbdurRakib wrote:
Two numbers differ by 2 and sum to S. Which of the following is the greater of the numbers in terms of S ?
A. $$\frac{S}{2}$$-1

B. $$\frac{S}{2}$$

C. $$\frac{S}{2}$$+$$\frac{1}{2}$$

D. $$\frac{S}{2}$$+1

E. $$\frac{S}{2}$$+2

OG Q 2017 (Book Question: 139)

let two numbe be a andb
a+b = S
a-b = 2
2a = s+2
a = s/2 +1
b = s/2 -1
Re: Two numbers differ by 2 and sum to S. Which of the following is the gr   [#permalink] 21 Mar 2017, 03:14
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