GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 12 Nov 2019, 13:37 ### 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.  # What is the remainder when X^Y is divided by Z , Where X = 32, Y = 3[m

Author Message
TAGS:

### Hide Tags

Retired Moderator V
Joined: 27 Oct 2017
Posts: 1271
Location: India
GPA: 3.64
WE: Business Development (Energy and Utilities)
What is the remainder when X^Y is divided by Z , Where X = 32, Y = 3[m  [#permalink]

### Show Tags

2
12 00:00

Difficulty:   65% (hard)

Question Stats: 55% (02:17) correct 45% (02:30) wrong based on 78 sessions

### HideShow timer Statistics

Weekly Quant Quiz Question -9

What is the remainder when X^Y is divided by Z , Where X = 32, Y = (32)^(32) and Z = 13?
a) 4
b) 5
c) 6
d) 7
e) 8

ONLY TEXT SOLUTIONS ARE ALLOWED.

_________________
Intern  S
Joined: 16 May 2018
Posts: 16
Location: India
Re: What is the remainder when X^Y is divided by Z , Where X = 32, Y = 3[m  [#permalink]

### Show Tags

4
Should be 6, since 32÷13 gives 6 As remainder, and then x^y would be in the form of 32*32*32.... hence comes out to be 6

Posted from my mobile device
Intern  B
Joined: 11 Jun 2018
Posts: 12
GMAT 1: 760 Q50 V44 Re: What is the remainder when X^Y is divided by Z , Where X = 32, Y = 3[m  [#permalink]

### Show Tags

3
Hey all, hoping someone can clarify one aspect of this for me as I'm hitting my head against a wall here!

My thought process is: When expanding the binomial (26+6)^M the last term will be 6^M.

6^M/13 doesn't always leave remainder 6. e.g. 6^2/13 = remainder 10... So how can we confidently say it does.

What simple fact am i missing here!
Senior PS Moderator D
Status: It always seems impossible until it's done.
Joined: 16 Sep 2016
Posts: 732
GMAT 1: 740 Q50 V40 GMAT 2: 770 Q51 V42 Re: What is the remainder when X^Y is divided by Z , Where X = 32, Y = 3[m  [#permalink]

### Show Tags

1
What is the remainder when X^Y is divided by Z , Where X = 32, Y = (32)^(32) and Z = 13?
a) 4
b) 5
c) 6
d) 7
e) 8

Ans:
x^y => 32^(32^32)

Write 32 as 26+6

The exponent is a very large integer call it M.

x^y => (26+6)^M

In the binomial expansion of the above binomial entity every term will have a factor of 26 except the last term. Hence 13 will divide all the terms except 6.

The remainder will be 6.

Hence IMO Option (C) is correct.

Best,
_________________
Regards,

“Do. Or do not. There is no try.” - Yoda (The Empire Strikes Back)
Manager  G
Joined: 23 Aug 2016
Posts: 101
Location: India
Concentration: Finance, Strategy
GMAT 1: 660 Q49 V31 GPA: 2.84
WE: Other (Energy and Utilities)
Re: What is the remainder when X^Y is divided by Z , Where X = 32, Y = 3[m  [#permalink]

### Show Tags

What is the remainder when X^Y is divided by Z , Where X = 32, Y = (32)^(32) and Z = 13?
a) 4
b) 5
c) 6
d) 7
e) 8

By calculation the cyclicity of remainders when 13 divides 32 and powers of 32= 6,10,8,4 therefore as 32 is a factor of therefore the remainder is
4
_________________
Thanks and Regards,

Honneeey.

In former years,Used to run for "Likes", nowadays, craving for "Kudos". :D
RC Moderator V
Joined: 24 Aug 2016
Posts: 782
GMAT 1: 540 Q49 V16 GMAT 2: 680 Q49 V33 Re: What is the remainder when X^Y is divided by Z , Where X = 32, Y = 3[m  [#permalink]

### Show Tags

Ans C-----6 (13*2 +6) =32
_________________
Please let me know if I am going in wrong direction.
Thanks in appreciation.
Intern  B
Joined: 18 Oct 2017
Posts: 21
Location: India
Re: What is the remainder when X^Y is divided by Z , Where X = 32, Y = 3[m  [#permalink]

### Show Tags

Ans is C, 6

X* Y = (32) raised to the power of 33

This can be written as (26+6) to the power of 33.

Using binomial expression, we will get (6) power of 33

We now have to check it’s divisibity by 13. Thus remainder is 6

Posted from my mobile device
Manager  B
Joined: 03 Sep 2018
Posts: 237
Location: Netherlands
GMAT 1: 710 Q48 V40 GPA: 4
Re: What is the remainder when X^Y is divided by Z , Where X = 32, Y = 3[m  [#permalink]

### Show Tags

This question is incorrect.

$$32^{{32}^{32}}$$ mod $$13$$ is $$9$$ (checked with wolfram alpha)

So how do we get to $$R=9$$?
_________________
Good luck to you.
Manager  B
Joined: 18 Apr 2018
Posts: 93
What is the remainder when X^Y is divided by Z , Where X = 32, Y = 3[m  [#permalink]

### Show Tags

Hi @gladiator56, thanks for your explanation but I will appreciate if you can explain a bit on this part ""

The exponent is a very large integer call it M.

x^y => (26+6)^M

In the binomial expansion of the above binomial entity every term will have a factor of 26 except the last term. Hence 13 will divide all the terms except 6.""

""From what I know 13 will be divisible by all terms except 6^M and not just 6. Did you just assume or check for cyclicity of remainder of 6^M as well before arriving at OA. I am simply asking the same question MattyE is asking ?. Thanks.

Posted from my mobile device

Originally posted by Kem12 on 12 Jan 2019, 14:20.
Last edited by Kem12 on 12 Jan 2019, 15:40, edited 1 time in total.
Manager  B
Joined: 03 Sep 2018
Posts: 237
Location: Netherlands
GMAT 1: 710 Q48 V40 GPA: 4
Re: What is the remainder when X^Y is divided by Z , Where X = 32, Y = 3[m  [#permalink]

### Show Tags

Kem12 wrote:
Hi @gladiator56, thanks for your explanation but I will appreciate if you can explain a bit on this part ""

The exponent is a very large integer call it M.

x^y => (26+6)^M

In the binomial expansion of the above binomial entity every term will have a factor of 26 except the last term. Hence 13 will divide all the terms except 6.""

From what I know 13 will be divisible by all terms except 6^M and not just 6. Did you just assume or check for cyclicity of remainder of 6^M as well before arriving at OA. I am simply asking the same question MattyE is asking ?. Thanks.

Posted from my mobile device

Kem12 Question is incorrect IMO, as are all answers. The remainder is 9 which you can easily check if you plug in the numbers as x mod y into wolfram alpha
_________________
Good luck to you.
Intern  B
Joined: 29 Aug 2017
Posts: 25
What is the remainder when X^Y is divided by Z , Where X = 32, Y = 3[m  [#permalink]

### Show Tags

gmatbusters wrote:

Weekly Quant Quiz Question -9

What is the remainder when X^Y is divided by Z , Where X = 32, Y = (32)^(32) and Z = 13?
a) 4
b) 5
c) 6
d) 7
e) 8

ONLY TEXT SOLUTIONS ARE ALLOWED.

Attachments temp_image_20190305_214258_608e6bc4-9a02-4777-83c4-94ecdb0238be_2728651704854327533.jpg [ 129.89 KiB | Viewed 528 times ] temp_image_20190305_214253_dd109b64-252e-4945-909d-e03fc189a667_2154424710377754276.jpg [ 186.9 KiB | Viewed 527 times ] What is the remainder when X^Y is divided by Z , Where X = 32, Y = 3[m   [#permalink] 05 Mar 2019, 09:17
Display posts from previous: Sort by

# What is the remainder when X^Y is divided by Z , Where X = 32, Y = 3[m  