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Math Expert V
Joined: 02 Sep 2009
Posts: 59592
If the smaller of 2 consecutive odd integers is a multiple of 5, which  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 66% (01:51) correct 34% (01:37) wrong based on 779 sessions

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If the smaller of 2 consecutive odd integers is a multiple of 5, which of the following could NOT be the sum of these 2 integers?

A. –8
B. 12
C. 22
D. 52
E. 252

PS91602.01
Quantitative Review 2020 NEW QUESTION

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Re: If the smaller of 2 consecutive odd integers is a multiple of 5, which  [#permalink]

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7
1
Since all options are even and numbers are consecutive ,they can be found by dividing the options by two and adding and subtracting one.
For eg -12/2 =6,so numbers are 5 and 7.Since the smaller number is multiple of 5 ,condition is satisfied.
if we look at options one by one beginning with A, A and B satisfy.C does not .No need to check further since time is less.
Ans.C
##### General Discussion
GMAT Club Legend  V
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Posts: 4125
Re: If the smaller of 2 consecutive odd integers is a multiple of 5, which  [#permalink]

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Bunuel wrote:
If the smaller of 2 consecutive odd integers is a multiple of 5, which of the following could NOT be the sum of these 2 integers?

A. –8
B. 12
C. 22
D. 52
E. 252

The question asks "which of the following could NOT be the sum of these 2 integers"

So, if we find an answer choice that COULD be the sum of the 2 integers, we can ELIMINATE it.

-5 and -3 are two consecutive odd integers in which the smaller value (-5) is a multiple of 5
(-5) + (-3) = -8
ELIMINATE A

5 and 7 are two consecutive odd integers in which the smaller value (5) is a multiple of 5
5 + 7 = 12
ELIMINATE B

25 and 27 are two consecutive odd integers in which the smaller value (25) is a multiple of 5
25 + 27 = 52
ELIMINATE D

125 and 127 are two consecutive odd integers in which the smaller value (125) is a multiple of 5
125 + 127 = 252
ELIMINATE E

By the process of elimination, the correct answer is C

Cheers,
Brent
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Re: If the smaller of 2 consecutive odd integers is a multiple of 5, which  [#permalink]

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1
if we consider option :
10 & 12 ---

smaller no. is a multiple of 5
Sum = 10+12 = 22

so Ans c seems not correct
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Re: If the smaller of 2 consecutive odd integers is a multiple of 5, which  [#permalink]

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Our smaller integer is an odd multiple of 5, so is equal to 5x where x is odd. Our numbers are consecutive odd numbers, so the other is 5x+2. Their sum is thus 10x + 2, where x is odd. So if the answer is going to be positive (we can look at answer A later if we need to), the tens digit will be odd (since when we find 10x, we're just sticking a 0 on the end of some odd number), and the units digit will be 2. So we can't possibly get 22 as our answer.
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Re: If the smaller of 2 consecutive odd integers is a multiple of 5, which  [#permalink]

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kiran1989raj wrote:
if we consider option :
10 & 12 ---

smaller no. is a multiple of 5
Sum = 10+12 = 22

so Ans c seems not correct

Question says smallest odd integer so it should end with 5

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Re: If the smaller of 2 consecutive odd integers is a multiple of 5, which  [#permalink]

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Bunuel wrote:
If the smaller of 2 consecutive odd integers is a multiple of 5, which of the following could NOT be the sum of these 2 integers?

A. –8
B. 12
C. 22
D. 52
E. 252

PS91602.01
Quantitative Review 2020 NEW QUESTION

Since the two integers are consecutive odd integers, the larger integer is 2 more than the smaller integer.

Choice A: -5 + -3 = -8. This can work.

Choice B: 5 + 7 = 12. This can work.

Choice C: The only way to get the sum of two integers to be 22 when one integer is 2 more than the other is with 10 and 12. However, they are NOT consecutive odd integers. So 22 could NOT be the sum of the 2 consecutive odd integers

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Re: If the smaller of 2 consecutive odd integers is a multiple of 5, which  [#permalink]

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4
let's us take the two numbers as 2k+1 and 2k-1
the sum is 4k
k can be negative or positive integers.
only 22 is not a multiple of 4, rest all are.
hence option C.
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If the smaller of 2 consecutive odd integers is a multiple of 5, which  [#permalink]

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Bunuel wrote:
If the smaller of 2 consecutive odd integers is a multiple of 5, which of the following could NOT be the sum of these 2 integers?

A. –8
B. 12
C. 22
D. 52
E. 252

least odd multiple of 5: 5+7=12
next least odd multiple of 5: 15+17=32
thus, 22 can not be possible sum
C

Originally posted by gracie on 02 May 2019, 20:50.
Last edited by gracie on 28 Jul 2019, 14:10, edited 3 times in total.
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Re: If the smaller of 2 consecutive odd integers is a multiple of 5, which  [#permalink]

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1
Bunuel wrote:
If the smaller of 2 consecutive odd integers is a multiple of 5, which of the following could NOT be the sum of these 2 integers?

A. –8
B. 12
C. 22
D. 52
E. 252

PS91602.01
Quantitative Review 2020 NEW QUESTION

ANSWER - Let the first odd integer be 2n+1, next would be - 2n+3
adding these two - 2n+1+2n+3 = 4n+4 = 4 (n+1)
So, we can say that solution will be multiple of 4.
Only option C is not multiple of 4, hence the ANSWER.

Please give KUDOS if you like the solution.
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Re: If the smaller of 2 consecutive odd integers is a multiple of 5, which  [#permalink]

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Bunuel wrote:
If the smaller of 2 consecutive odd integers is a multiple of 5, which of the following could NOT be the sum of these 2 integers?

A. –8
B. 12
C. 22
D. 52
E. 252

PS91602.01
Quantitative Review 2020 NEW QUESTION

We can check the answer choices:

-5 + (-3) = -8, so A works.

5 + 7 = 12, so B works

We see that there is no way to get 22.

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Re: If the smaller of 2 consecutive odd integers is a multiple of 5, which  [#permalink]

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Bunuel wrote:
If the smaller of 2 consecutive odd integers is a multiple of 5, which of the following could NOT be the sum of these 2 integers?

A. –8
B. 12
C. 22
D. 52
E. 252

PS91602.01
Quantitative Review 2020 NEW QUESTION

let odd numbers be x and x+2
Now x=5K

Sum of two odd integers- 2x+2= 2(X+1)

Now let's see if
2(5K+1) = 22 (Option C)

5K + 1= 11
5K=10, K=2.
But if k=2 then x won't be an odd number. So C.
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Re: If the smaller of 2 consecutive odd integers is a multiple of 5, which  [#permalink]

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Bunuel wrote:
If the smaller of 2 consecutive odd integers is a multiple of 5, which of the following could NOT be the sum of these 2 integers?

A. –8
B. 12
C. 22
D. 52
E. 252

PS91602.01
Quantitative Review 2020 NEW QUESTION

There are two methods to solve this question. One through value substitution and other through Algebraic equation.

Approach 1:
Two odd numbers with the smallest odd number is the multiple of 5. hence below are few possible sets.
{5,7}, {15, 17), {25, 27}, {35, 37} {125, 127] etc., When try the sum of the below sets, we could get, 12, 32, 52, 72, etc.. hence we know for sure 22 does not fit into this list. Hence Option is the answer.

Approach 2: Algebraic Equation

A: lowest Odd number multiple of 5 -> 5 (multiple of 5) 2n+1 (odd number) => 5 (2n+1) represents digits 5, 15, 25, 35 etc --
B: Next consequtive odd integer => 5(2n+1) +2

Question: Sum of A+B => 5 (2n+1) + 5 (2n+1) +2
=> 10n+5+10n+5+2
=> 20n +12
now apply values for n= -1, 0, 1, 2, 3 etc.,
n= -1 : 20 (-1)+12 = -8
n= 0 : 20 (0)+ 12 = 12
n= 1 : 20(1)+ 12 = 32
n = 2 : 20 (2)+12 = 52
Similarly
n=12 : 20 (12) + 12 = 252

Hence Option C is not the possible sum. Hope this helps.

==================================================
Please provide your feedback if I miss any logic here. It will help to improve my score.
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Re: If the smaller of 2 consecutive odd integers is a multiple of 5, which  [#permalink]

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5n + 5n+2 represents two consecutive odd integers in which the first is a multiple of 5.

10n +2 (sum) = each answer choice

solve for n and if n is odd, it should work, but if n is even we know it Cannot be our answer as the pair of integers are odd
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If the smaller of 2 consecutive odd integers is a multiple of 5, which  [#permalink]

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Here is my approach:

The three consecutive integers: 5k (odd), 5k+1 (even), 5k+2 (odd)
The mean = sum of these 2 integers devided by 2 = (10k+2)/2 must be even

Only 22/2 = 11, which is not even. So is the answer.

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Re: If the smaller of 2 consecutive odd integers is a multiple of 5, which  [#permalink]

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Hi GMATPrepNow
Isn't it true that a multiple of a number has to be equal or greater than that number.
For example multiple of 5 are as follows:
5 * 1 = 5 (equal to 5)
5 * 2 = 10 (greater than 5 from here onwards)
.
.
.
and so on...
As -5 < 5, how can -5 be a multiple of 5 in option A?

Thank you,
Dablu
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Re: If the smaller of 2 consecutive odd integers is a multiple of 5, which  [#permalink]

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gurudabl wrote:
Hi GMATPrepNow
Isn't it true that a multiple of a number has to be equal or greater than that number.
For example multiple of 5 are as follows:
5 * 1 = 5 (equal to 5)
5 * 2 = 10 (greater than 5 from here onwards)
.
.
.
and so on...
As -5 < 5, how can -5 be a multiple of 5 in option A?

Thank you,
Dablu

A multiple of a number is that number multiplied by an integer. And we know that an integer can be negative or positive (or a zero). As a result, a multiple of a number can be greater than, equal to, or less than that number.

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--- One day you will thank yourself for not giving up --- Re: If the smaller of 2 consecutive odd integers is a multiple of 5, which   [#permalink] 12 Nov 2019, 07:15
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