If the smaller of 2 consecutive odd integers is a multiple of 5, which

Question

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

IanStewart · Accepted Answer

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.

StudiosTom · Answer

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

BrentGMATPrepNow · Answer

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

kiran1989raj · Answer

if we consider option :
10 & 12 ---

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

so Ans c seems not correct

ScottTargetTestPrep · Answer

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

Let’s consider the answer choices.

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

Answer: C

ScottTargetTestPrep · Answer

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.

Answer: C

fighting750 · Answer

I don't know the function of "smaller"

Bunuel · Answer

The "smaller" refers to the first of the two consecutive odd integers. For example, if you have two consecutive odd integers like 5 and 7, 5 is the smaller one. The question is asking about a situation where the smaller integer is a multiple of 5, and you need to determine which of the given options cannot be the sum of those two consecutive odd integers.

mbaprepavi · Answer

Let the two consecutive odd integers be
2k-1 and 2k+1

We have that 2k-1 = 5p
Therefore 2k = 5p+1

Sum of the two integers is 4k = 10p+2

Now check the options.
Keep in mind that 2k -1 is still odd. So P CANNOT be EVEN

Therefore, C

HarshZsssh · Answer

we are looking for consecutive odd integers only 10 and 12 are even

GmatKnightTutor · Answer

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

Some quick trial and error using multiples of 5 around half the value of the answer choices could be helpful.

-5 + (-3) = -8

0 is even so we can't use it.

5 + 7 = 12

10 + 12 is 22... but since 10 is an even integer, this one fails.

We don’t really have to check the others at this point!

(C) is your answer.

MagnusSamIBA · Answer

The sum of two consecutive odd numbers, where the smaller one is a multiple of 5, always ends in 2. Try a few: 5+7 = 12, 15+17 = 32, 25+27 = 52. See the pattern? It always ends in 2.

Now check the answer choices. 12, 22, 52, and 252 all end in 2, so they work. But –8 doesn’t.

Final answer: A (–8).

ShreyasVartak · Answer

Where does 22 come in the pattern... it dosen't so that the Correct answer.

Also to get -8 we just need -5 and -3.

AdarshSambare · Answer

Hi  MagnusSamIBA ,

The question did not say positive, so you also need to consider negative odd number.
Consider: -5,-3 as smallest number should be multiple of 5
-5+ -3 = -8
So, it cannot be -8 (A)

Now consider 5x be the smallest number, so second number will be 5x+2 (x should be odd)
=5x+5x+2
=10x+2
Now check the option:
22 = 10x+2
20=10x
x = 2
This cannot happen
So the answer is 22

gmatstudent100 · Answer

it says consecutive odd integers

abhikc3004 · Answer

Consider the no. to be x and x+2. 
Thus, 2x + 2 = the answer choices. Obtain values of x and see which of them is an even number. 
For A, B: x obtained is an odd number, hence we omit. 
For C: 2x + 2 = 22 => x = 10. This is even, and does not satisfy our condition. 
 Hence, option C.  
No need to assess D and E

Bunuel  - is there a quicker approach than this? I understand this works for smaller numbers but for larger numbers this may not very suitable.

egmat · Answer

Hi abhikc3004,

You're right that plugging in numbers gets clumsy once the answer choices get large. There  is  a one-line algebraic characterization that works no matter how big the numbers get, and IanStewart hinted at it above. Let me make it fully general.

Set it up once

The smaller integer must be  both odd and a multiple of 5  - so it's an odd multiple of  5 , which we can write as  5x  where  x is odd .

The two consecutive odd integers are then  5x  and  5x + 2 , so:

Sum = 5x + (5x + 2) = 10x + 2 , with x odd.

The quick test

For any candidate sum S, just solve for x:

x = (S - 2) / 10

A sum is possible only if that x comes out as an  odd integer . That single check replaces all the guessing:

- A:  (−8 − 2)/10 = −1  - odd ✓
- B:  (12 − 2)/10 = 1  - odd ✓
- C:  (22 − 2)/10 = 2  -  even ✗ 
- D:  (52 − 2)/10 = 5  - odd ✓
- E:  (252 − 2)/10 = 25  - odd ✓

Only  C  fails, and it takes seconds even for the big number  252  - no listing of integers required.

The insight to carry forward: whenever a problem stacks conditions like "odd"  and  "multiple of  5 ," write the number in a form that bakes both in ( 5x , x odd), then reduce the whole thing to one algebraic test. That scales to any size.

Quick check to lock it in:  which of these could be such a sum -  102  or  152 ? Run (S- 2 )/ 10 : you get  10  (even, no) and  15  (odd, yes). Same one test, instantly.

Answer: C

If the smaller of 2 consecutive odd integers is a multiple of 5, which

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