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Difficulty: 555-605 Level,    Arithmetic,                         
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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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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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Two numbers differ by 2 and sum to S. Which of the following is the gr [#permalink]
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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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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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Lets have two numbers a and b, Sum is "S", Average is S/2
Differance between b & a is 2

b=S/2 + 1
and
a=S/2 - 1

Larger is b

Ans 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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Ugh, the actual math here wasn't the problem for me.

Understanding that the question was asking for the numbers in relation to the previous terms did not click for me on first blush.

Time and time again I find myself taking math questions literally and verbal questions figuratively. It's maddenning!

If the question had worded the problem "Which of the following is the greater of the two numbers in terms of S?" it would have been obvious what to solve. But the wording stresses the following numbers, which just seems diabolical.

Is this just a lack of having a deeper knowledge of the question types and how they might appear? Does this type of trip-up get any easier to overcome? Honestly, I feel like it's just an arms race of finding cheat codes sometimes.

Posted from my mobile device
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Re: Two numbers differ by 2 and sum to S. Which of the following is the gr [#permalink]
kwizzical wrote:
Ugh, the actual math here wasn't the problem for me.

Understanding that the question was asking for the numbers in relation to the previous terms did not click for me on first blush.

Time and time again I find myself taking math questions literally and verbal questions figuratively. It's maddenning!

If the question had worded the problem "Which of the following is the greater of the two numbers in terms of S?" it would have been obvious what to solve. But the wording stresses the following numbers, which just seems diabolical.

Is this just a lack of having a deeper knowledge of the question types and how they might appear? Does this type of trip-up get any easier to overcome? Honestly, I feel like it's just an arms race of finding cheat codes sometimes.

Posted from my mobile device


So true its maddenning at times :lol: :lol:
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Two numbers differ by 2 and sum to S. Which of the following is the gr [#permalink]
x - y = 2 ——> we can assume that x is the greater of the two numbers

x + y = s —-> y = s - x

x - (s - x) = 2
2x - s = 2
2x = s + 2

x = s/2 + 1

Option 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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