130 can be expressed as the sum of which of the following?

Question

I. 4 consecutive integers
II. 5 consecutive integers
III. 6 consecutive integers

(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) II and III only

CrackverbalGMAT · Accepted Answer

Statement I: 130/4 = 32.5--> So sum of the middle 2 numbers should be 65 which is the sum of 32 and 33. The 4 numbers are 31 + 32 + 33 + 34 = 130

Statement II: 130/5 = 26--> The middle number is 26 with the other 4 being 2 behind and 2 ahead of 26. The 5 numbers are 24 + 25 + 26 + 27 + 28 = 130

Statement III: 130/6 = 21.67--> So sum of the middle 2 numbers should be 43.33 which then cannot have integers.

Option C

Arun Kumar

wishmasterdj · Answer

or, just visualize the series

4 consecutive -> a, a+1, a+2, a+3, = 4a +6
Similarly, 5 consecutive = 5a+10 and 6 consecutive = 6a+15

Equate each of them to 130 and you find only cases 1 and 2 are possible, as the third one leaves a non integer value, violating the question's constraint.

mysteriouswoman · Answer

Bunuel  please explain. Can't understand the sum

LucienH · Answer

The formula of the sum of a consecutive number series is 
n(first number+ last number)/2

here we are looking for consecutive INTEGERS, so the sum must be divisible by the number of terms

start with the first case: 
Let x be the first number: 
130 = 4*(x+x+3)/2
as you can see, 130*2 must be divisible by 4, otherwise these won't be integers. 
260 is divisible by 4, so I is true

Repeat this process with all options

GulfTube · Answer

i) 4a+6=130 => a=31
ii) 5a+10=130 => a=24
iii) 6a+15=130 => a=19.2 not an integer

Answer C

Another way:

CONCEPT: 
 If n is odd, where n is the number of terms in sequence of consecutive integers, the sum of consecutive integers is always divisible by n

If n is even, the sum of consecutive integers is divisible by n/2.

i) 4 consecutive integers n=4
n/2=2, 130 is divisible by 2 hence 130 can be sum of 4 consecutive integers.

ii) 5 consecutive integers n=5
130 is divisible by 5 hence 130 can be sum of 5 consecutive integers.

iii) 6 consecutive integers n=6
n/2=3, 130 is not divisible by 3 hence 130 cannot be sum of 6 consecutive integers.

vasu1104 · Answer

S-1 a+a+1+a+2+a+3 = 130 
4a + 6 =130 
4a = 124
a= 31
correct.

S-2
5a + 10 =130
5a = 120
a= 24
correct

S-3
6a+ 15=130
6a = 115

not possible.

only S-1 & 2 possible.

choice C

digvijay1111 · Answer

This question can be solved quickly by using the concept of parity or ODD and EVEN. 
Question stem says "can be" so we need to explore possibilities that could happen 
130 is an even number
I. 4 consecutive integers = 2 odds and 2 evens which is a guarantee and summation of Even+Odd+Even+Odd / Odd+Even+Odd+Even ; will give us Even as an answer so either ways we get a definite yes
II. 5 consecutive integers can be = Odd+Even+Odd+Even+Odd / Even+Odd+Even+Odd+Even ; 1 of them gives us Even and 1 of them gives us Odd but since question says "can be" so we can say yes
III. 5 consecutive integers can be = Even+Odd+Even+Odd+Even+Odd / Odd+Even+Odd+Even+Odd+Even ; Either ways we get Odd so we can say definite no.

130 can be expressed as the sum of which of the following?

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GMAT Problem Solving (PS) Questions

130 can be expressed as the sum of which of the following?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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