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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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New post 23 Jun 2016, 11:36
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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)

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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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New post 23 Jun 2016, 11:58
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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

Answer: D
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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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New post 23 Jun 2016, 12:04
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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

Hence answer will be (D)

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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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New post 24 Jun 2016, 03:20
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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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New post 02 Sep 2016, 11:00
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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New post 02 Sep 2016, 11:47
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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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New post 27 Oct 2016, 09:46
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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New post 14 Mar 2017, 14:09
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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New post 18 Mar 2017, 10:32
let's try smart numbers: 10 and 12
answer is D
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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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New post 20 Mar 2017, 06:54
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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

Answer: D
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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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New post 21 Mar 2017, 04:14
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
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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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New post 02 Sep 2018, 19:12
Let two numbers are x and x+2
As given:
S=x+x+2
S=2x+2
2x=S-2
x=(S-2)/2
So greater number is
x+2=((S-2)/2)+2
x+2=(S+2)/2
x+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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New post 18 May 2019, 00:41
let the 2 numbers be - a and b
& a > b

given
a+b=S
a-b=2
a-2=b

therefore
a + a - 2 = S

2a - 2 = S

2a= S+2
a= S/2 + 1

so answer D
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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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New post 10 Sep 2019, 13:05
a=5
b=3
5-3=2
5+3=8 (therefore s=8) (bigger number a=5)
.. let's test the options...
start with option
D) s/2+1 = 8/2+1
=5.. eureka.. bigger number is 5 .. hence proved...
if you try the remaining options, you don't end up getting ans 5.
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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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New post 17 Sep 2019, 03:15
@ Bunnel - Can you please check this answer. As the choice is supposed to be between the option A~E and not between the 2 numbers. Is the above explanation correct. Please Help!! How can S/2 +1 > S/2+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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New post 17 Sep 2019, 03:20
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Re: Two numbers differ by 2 and sum to S. Which of the following is the gr   [#permalink] 17 Sep 2019, 03:20
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