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

Question

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)

JeffTargetTestPrep · Accepted Answer

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

Kurtosis · Answer

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

Abhishek009 · Answer

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)

sashiim20 · Answer

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)...

Joc456 · Answer

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.

ramlala · Answer

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

kwizzical · Answer

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

ShilpiAgnihotrii · Answer

So true its maddenning at times :lol:

e3thekid · Answer

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

Posted from my mobile device

GmatKnightTutor · Answer

Let’s say the two numbers are "x" and "y" respectively and that x is greater than y.

Based on the provided info, we can create two expressions:

x – y = 2
x + y = S

The question basically asks us what x is in terms of S.

By rearranging the first expression, we get:

x = 2 + y

By rearranging the second expression, we can see that y = S – x

If we replace y with (S – x) in  x = 2 + y , we get:

x = 2 + (S – x)
x = 2 + S – x
2x = 2 + S
x = 1 + S/2

(D) is your answer.

PGTLrowanhand · Answer

https://www.youtube.com/watch?v=c2ylb6NXVfI 
Here's my video solution.

MarkGMATMentor · Answer

This is a good example of a problem where  multiple approaches work well to solve.

1. Reasoning approach:  Note that the answer choices share a remarkable similarity: they all contain an  \frac{S}{2}  term, which would represent the average of the two numbers. Since the two numbers differ by 2, one number must be 1 below the average and the other must be 1 above the average. Thus, the greater number is the average plus 1, or  \frac{S}{2} + 1  (choice D).

2. Picking numbers approach : Pick two easy numbers that differ by 2. Let’s pick 3 and 5. Thus, S = 8. Now plug 8 in for S in the answer choices to see which results in the greater of the two numbers, 5:

(A) S/2 - 1 --> 8/2 – 1 = 3
(B) S/2 --> 8/2 = 4
(C) S/2 + 1/2 --> 8/2 + 1/2 = 9/2
(D) S/2 + 1 --> 8/2 + 1 = 5
(E) S/2 + 2 --> 8/2 + 2 = 6

Only choice D results in 5, so it’s correct.

3. Algebraic approach:  Let’s call the greater number x and the smaller number x – 2. Now let’s build an equation and solve for x:

x + (x – 2) = S  Since S is the sum of the two numbers.

2x – 2 = S  Combine like terms.

2x = S + 2  Add 2 to both sides.

x = S/2 + 1  Divide both sides by 2. This is answer choice D.

If you can see it, the reasoning approach is the fastest and cleanest here, and you should always be looking for reasoning approaches. But the picking numbers and algebraic approaches are also both reasonably fast.

It’s important to stay flexible and be comfortable with many approaches.  That way, if you can’t see how to solve any particular problem one way, or if your chosen method ends up being unworkable, you can quickly shift to another.

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

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GMAT Problem Solving (PS) Questions

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

Prep Toolkit

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