GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 23 Feb 2020, 15:27 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If m is a natural number less than or equal to 100

Author Message
TAGS:

### Hide Tags

Manager  G
Joined: 20 Aug 2017
Posts: 104
If m is a natural number less than or equal to 100  [#permalink]

### Show Tags

1
5 00:00

Difficulty:   25% (medium)

Question Stats: 75% (02:01) correct 25% (02:27) wrong based on 24 sessions

### HideShow timer Statistics

If m is a natural number less than or equal to 100, what is the probability that $$(7^m + 11^m)$$ is divisible by 5?

A. $$\frac{1}{4}$$

B. $$\frac{3}{7}$$

C. $$\frac{8}{25}$$

D. $$\frac{13}{50}$$

E. $$\frac{3}{8}$$
VP  V
Joined: 19 Oct 2018
Posts: 1304
Location: India
Re: If m is a natural number less than or equal to 100  [#permalink]

### Show Tags

last digit of 7^{4k+1} is 7
last digit of 7^{4k+2} is 9
last digit of 7^{4k+3} is 3
last digit of 7^{4k} is 1

Last digit of 11^m is always 1

m=4k+1, last digit of (7^m + 11^m)= 7+1=8( not divisible by 5}
m=4k+2, last digit of (7^m + 11^m)= 9+1=0( divisible by 5}
m=4k+3, last digit of (7^m + 11^m)= 3+1=4( not divisible by 5}
m=4k, last digit of (7^m + 11^m)= 1+1=2( not divisible by 5}

probability that $$(7^m + 11^m)$$ is divisible by 5, 0<m≤100= 1/4

uchihaitachi wrote:
If m is a natural number less than or equal to 100, what is the probability that $$(7^m + 11^m)$$ is divisible by 5?

A. $$\frac{1}{4}$$

B. $$\frac{3}{7}$$

C. $$\frac{8}{25}$$

D. $$\frac{13}{50}$$

E. $$\frac{3}{8}$$
Intern  B
Joined: 31 Aug 2017
Posts: 2
If m is a natural number less than or equal to 100  [#permalink]

### Show Tags

We need to find a number which has last digit either 0 or 5 in order to be divisible with 5.

The last digit of 11^m will always be 1

The last digit of 7^m will be (7, 49, 343, 2401, 16807), this means that 7 has a cyclexity of 4. We are only interested in values where last digit is 9, so that the sum has last digit as 0 (9 + 1).

Therefore the total possible values of m (that are less than or equal to 100) will be 100/4 = 25.

The probability will be 25/100 or 1/4. If m is a natural number less than or equal to 100   [#permalink] 29 Dec 2019, 03:59
Display posts from previous: Sort by

# If m is a natural number less than or equal to 100   