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

It is currently 01 Jun 2020, 05:55

Close

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
Your Progress

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.

Close

Request Expert Reply

Confirm Cancel

What is the remainder when X is divided by 40?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 64153
What is the remainder when X is divided by 40?  [#permalink]

Show Tags

New post 17 Jul 2019, 07:00
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

62% (01:58) correct 38% (02:02) wrong based on 274 sessions

HideShow timer Statistics

Most Helpful Community Reply
CEO
CEO
User avatar
V
Joined: 03 Jun 2019
Posts: 2919
Location: India
GMAT 1: 690 Q50 V34
WE: Engineering (Transportation)
Premium Member Reviews Badge CAT Tests
Re: What is the remainder when X is divided by 40?  [#permalink]

Show Tags

New post 17 Jul 2019, 07:34
1
What is the remainder when positive integer X is divided by 40?

(1) 3X + 30 leaves remainder 93 when divided by 120.
(2) 5X - 10 leaves remainder 15 when divided by 20.

(1) 3X + 30 leaves remainder 93 when divided by 120.
3X+30 = 120k+93
3X = 120k +63
X=40k+21
21 is the remainder when positive integer x is divided by 40
SUFFICIENT

(2) 5X - 10 leaves remainder 15 when divided by 20.
5X-10 = 20k + 15
5X = 20K + 25 = 20Y+5
X = 4Y+1
NOT SUFFICIENT

IMO A
_________________
Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com
General Discussion
Intern
Intern
avatar
S
Joined: 18 Feb 2017
Posts: 14
Re: What is the remainder when X is divided by 40?  [#permalink]

Show Tags

New post 17 Jul 2019, 08:14
1
IMO A.

Statement 1: 3X + 30 leaves remainder 93 when divided by 120.
The numbers in this form would be 93,213,333,453...
X values for these would respectively would be - 30,70,110,150...
When these values are divided by 40, it always leaves a remainder as 30.
Hence, this statement is sufficient.

Statement 2: 5X - 10 leaves remainder 15 when divided by 20.
The numbers in this form would be 15,35,55,75...
X values for these would respectively would be - 5,9,13,17...
When these values are divided by 40, does not give a fixed value.
Hence, this statement is not sufficient.
Manager
Manager
avatar
G
Joined: 30 Nov 2017
Posts: 117
WE: Consulting (Consulting)
Premium Member
Re: What is the remainder when X is divided by 40?  [#permalink]

Show Tags

New post 17 Jul 2019, 08:16
1
The question states that what is the remainder when X is divided by 40

Statement 1: 3X + 30 leaves remainder of 93 when divided by 120

Let X = 21, therefore, 3(21) + 30 = 93
Thus, 93/120 gives remainder of 93
therefore, 93/40 gives remainder of 13

Let X = 61, therefore, 3(61) + 30 = 213
thus, 213/120 gives remainder of 93
therefore, 213/40 gives remainder of 13

similarly, let X = 101, therefore, 3(101) + 30 = 333
thus, 333/120 gives remainder of 93
therefore, 333/40 gives remainder of 13

Therefore this statement is sufficient (AD)

Statement 2: (5X - 10)/20 gives remainder of 15
let X = 5, therefore (5x5 - 10)/20 = 15/20 gives remainder of 15
therefore, 5/40 gives remainder of 5

let X = 9, therefore (5x9 - 10)/20 = 35/20 gives remainder of 15
therefore, 9/40 gives remainder of 9

Not sufficient

Hence answer choice A.
_________________
Be Braver, you cannot cross a chasm in two small jumps...
Intern
Intern
avatar
B
Joined: 16 Jun 2018
Posts: 2
Re: What is the remainder when X is divided by 40?  [#permalink]

Show Tags

New post 17 Jul 2019, 08:27
1
IMO A

Have to find: Remainder of \(X/40\)

Statement 1 -> \(\frac{(3X + 30)}{120}\) gives a remainder of 93. Substitute for X based on this statement. For X = 21, \(\frac{(3X + 30)}{120}\) gives the remainder of 93 and \(X/40\) gives a remainder of 21. For X = 101, \(\frac{(3X + 30)}{120}\) gives the remainder of 93 and \(X/40\) gives a remainder of 21 again. ---> Sufficient

Statement 2 -> \(\frac{(5X - 10)}{20}\) gives a remainder of 15. Substitute for X based on this statement. For X = 5, \(\frac{(5X - 10)}{20}\) gives the remainder 15 and \(X/40\) gives the remainder 5. For X = 9, \(\frac{(5X - 10)}{20}\) gives the remainder 15, but \(X/40\) gives the remainder 9. ---> Insufficient
Manager
Manager
User avatar
G
Joined: 18 Jun 2013
Posts: 103
Location: India
Concentration: Technology, General Management
GMAT 1: 690 Q50 V35
GPA: 3.2
WE: Information Technology (Consulting)
Reviews Badge
Re: What is the remainder when X is divided by 40?  [#permalink]

Show Tags

New post 17 Jul 2019, 09:44
1
To find,

Remainder of X when X is divided by 40.

We know,

Dividend = Divisor * Quotient + Remainder

Let us check the two options -

Option 1: 3X + 30 leaves remainder 93 when divided by 120.

=> 3*X + 30 = 120 * Quotient + 93
=> X + 10 = 40 * Quotient + 31
=> X = 40 * Quotient + 21

Hence, X whenever divided by 40 will give a remainder of 21.

Hence option 1 is sufficient.

Option 2: 5X - 10 leaves remainder 15 when divided by 20.

=> 5*X - 10 = 20 * Quotient + 15
=> X - 2 = 4 * Quotient + 3
=> X = 4 * Quotient + 5
=> X = 4 * Quotient + 4 + 1
=> X = 4 * (Quotient + 1) + 1

Hence, X whenever divided by 4 will give a remainder of 1.

Now, if X is 5 (satisfying above condition in option 2) then it will give a remainder of 5 when divided by 40.
Now, if X is 9 (satisfying above condition in option 2) then it will give a remainder of 9 when divided by 40.
Now, if X is 45 (satisfying above condition in option 2) then it will give a remainder of 5 when divided by 40.
Now, if X is 53 (satisfying above condition in option 2) then it will give a remainder of 13 when divided by 40.

Hence, option 2 is insufficient.

Answer: A
Manager
Manager
avatar
G
Joined: 08 Jan 2018
Posts: 148
Location: India
Concentration: Operations, General Management
GMAT 1: 680 Q50 V32
WE: Project Management (Manufacturing)
Re: What is the remainder when X is divided by 40?  [#permalink]

Show Tags

New post 17 Jul 2019, 10:02
1
IMO-A

Remainder when positive integer X is divided by 40

(1) 3X + 30 leaves remainder 93 when divided by 120.

3X+30= 120K + 93
=> X+10= 40K + 31 [K = integer]
=> X-21 = 40K
=> X-21= { 0, 40, 80, ........40K}
=> X= 21, 61, 81,....40K+21
Remainder (X/40)= 21

Sufficient

(2) 5X - 10 leaves remainder 15 when divided by 20.
=>.5X-10=20K+15
=> 5X= 20K+25
=> X= 4K+5
=> X= {5,9,13,17...........4K+5}
Remainder (X/40)= {5,9,13,17.....}

Not Sufficient
Manager
Manager
avatar
B
Joined: 24 Jun 2019
Posts: 66
Re: What is the remainder when X is divided by 40?  [#permalink]

Show Tags

New post 17 Jul 2019, 11:19
1
What is the remainder when positive integer X is divided by 40?

40q+r = X ..... q is quotient and r is remainder. We have to find r.

(1) 3X + 30 leaves remainder 93 when divided by 120.

120q+93 = 3X + 30
120q+63 = 3X
40q+21 = X ... This is in the same form as 40q+r=X

Therefore r = 21

(1) IS SUFFICIENT

(2) 5X - 10 leaves remainder 15 when divided by 20.

20q+15 = 5X-10

20q + 25 = 5X

4q + 5 = X

It is not possible to represent X in the form of 40q+r....

X could be 9 with remainder 9, or x could be 45 with remainder 5.

(2) IS NOT SUFFICIENT

ANSWER: A - 1 Alone is SUFFICIENT
DS Forum Moderator
User avatar
V
Joined: 19 Oct 2018
Posts: 1860
Location: India
Premium Member
Re: What is the remainder when X is divided by 40?  [#permalink]

Show Tags

New post 17 Jul 2019, 12:30
1
Statement 1
3x+30= 120k+93, where k is no-negative integer.
x+10=40k+31
x= 40k+21

We will always get 21 as a remainder, when x is divided by 40.
Sufficient

Statement 2
5x-10=20a+15, where a is non-negative integer
x-2=4a+3
x=4a+5

Hence, x can be 5, 9, 13, 17...and so on
If x=5, we will get 5 as a remainder, when x is divided by 40.
If x=9, we will get 9 as a remainder, when x is divided by 40.


Insufficient.
CR Forum Moderator
avatar
D
Joined: 18 May 2019
Posts: 811
GMAT ToolKit User Premium Member
Re: What is the remainder when X is divided by 40?  [#permalink]

Show Tags

New post 17 Jul 2019, 14:17
1
We are to find the remainder when a positive integer x is divided by 40.

1. 3x +30 leaves a remainder of 93 when divided by 120.
(3x+30)/120 = 120m + 93
(X+10)/40=40m+31
If m=0 x+10=31 hence x=21
21/40 leaves R=21
If m=1, x+10=71 hence x=61
61/40 leaves R=21
If m=10, x+10=431 hence x=421.
421/40 leaves R=21. Therefore statement 1 on it’s own is sufficient.

2: 5x-10 leaves Remainder of 15 when divided by 20.
(5x-10)/20= 20m+15
(x-2)/4 = 4m + 3
When m=0 x-2=3 hence x=5
5/40 leaves R=5
When m=1, x-2=7 hence x=9
9/40 leaves a remainder of 9. Hence not sufficient.

The answer is therefore A.

Posted from my mobile device
Director
Director
avatar
V
Joined: 30 Sep 2017
Posts: 923
GMAT 1: 720 Q49 V40
GPA: 3.8
Premium Member Reviews Badge
What is the remainder when X is divided by 40?  [#permalink]

Show Tags

New post 17 Jul 2019, 18:07
1
Question: What is the remainder when positive integer X is divided by 40?

(1) (3X + 30) leaves remainder 93 when divided by 120.
\((3X + 30) = 120Q + 93\), where \(93\) is the remainder and positive integer quotient \(Q \geq{0}\)
<=> \(X = 40Q + 21\)
Therefore, when positive integer X is divided by \(40\), the remainder is \(21\)
SUFFICIENT

(2) (5X - 10) leaves remainder 15 when divided by 20.
\((5X - 10) = 20Q + 15\), where \(15\) is the remainder and positive integer quotient \(Q \geq{0}\)
<=> \(X = 4Q + 5\)
We only know that when positive integer X is divided by \(4\), the remainder is \(5\) . Unfortunately, we have no sufficient information on what the remainder is when positive integer X is divided by \(40\).
NOT SUFFICIENT


Answer is (A)
Manager
Manager
avatar
P
Joined: 30 May 2019
Posts: 83
CAT Tests
Re: What is the remainder when X is divided by 40?  [#permalink]

Show Tags

New post 17 Jul 2019, 19:48
1
What is the remainder when positive integer X is divided by 40?

(1) 3X + 30 leaves remainder 93 when divided by 120.
(2) 5X - 10 leaves remainder 15 when divided by 20.


We need to find remainder when \(\frac{x}{40}.\)

St 1) \(\frac{3x+30}{120}\)= q+93 (get rid of 120)
3x+30=120q+93
3x=120q+63 (divide by 3)
x=40q+21
Now let's plug in some number for q.
If q=0, x is 21 (remainder when \(\frac{x}{40}\))
If q=1, x is 61 (\(\frac{61}{40}\) remainder is 21)
If q=2, x is 101 (\(\frac{101}{40}\) remainder is again 21)
For any number substituted for q, we will always get remainder of 21 because q is multiple of 40 and thus will divide 40 evenly leaving remainder of 21 always. Thus, st 1 is sufficient

St 2) \(\frac{5x-10}{20}\)=q+15 (get rid of 20)
5x-10=20q+15
5x=20q+25 (divide by 5)
x=4q+5
If q=0, x is 5 (\(\frac{5}{40}\) remainder is 5)
If q=1, x is 9 (\(\frac{9}{40}\) remainder is 9)
We already have two different values, thus st 2 is NOT sufficient
Answer is A
Manager
Manager
User avatar
G
Joined: 08 Jan 2018
Posts: 90
Re: What is the remainder when X is divided by 40?  [#permalink]

Show Tags

New post 17 Jul 2019, 20:58
1
Given, X is a positive integer.
We need to find the remainder of X/40.

(1) 3X + 30 leaves remainder 93 when divided by 120.
3X + 30 = 120 * A + 93, where A is the quotient
3X = 120*A + 63 -> (a)

Substituting values of A in (a):
A = 1
3X = 120 + 63 => X = 61
Remainder of \(\frac{X}{40}\) = \(\frac{61}{40}\) = 21 -> [1]

A = 2
3X = 240 + 63 => X = 101
Remainder of \(\frac{X}{40}\) = \(\frac{101}{40}\) = 21 -> [2]

From [1] and [2] we find the pattern will keep continuing. Thus, the Remainder of \(\frac{X}{40}\)is 21.

Sufficient

(2) 5X - 10 leaves remainder 15 when divided by 20.
5X – 10 = 20 * B + 15, where B is the quotient.
5X = 20*B + 25 -> (b)

Substituting values of B in (b):
B = 1
5X = 20 + 25 => X = 9
Remainder of \(\frac{X}{40}\) = \(\frac{9}{40}\) = 9 -> [3]

B = 2
5X = 40+ 25 => X = 13
Remainder of \(\frac{X}{40}\) = \(\frac{13}{40}\) = 13 -> [4]

From [3] and [4] we find that it does not give a unique solution.

Not Sufficient

Answer A
Intern
Intern
avatar
S
Joined: 24 Jan 2019
Posts: 36
Location: India
Concentration: Strategy, Finance
GMAT 1: 730 Q51 V38
GPA: 4
Re: What is the remainder when X is divided by 40?  [#permalink]

Show Tags

New post 17 Jul 2019, 22:07
1
What is the remainder when positive integer X is divided by 40?

(1) 3X + 30 leaves remainder 93 when divided by 120.

Assume 'a' is the quotient.
We can write 3X+30 as:

3X + 30 = 120*a + 93

simplify this for X,
3X = 120*a + 63
X = 40*a + 21.....................when X is divided by 40, remainder will be "21"

First can answer the question.

(2) 5X - 10 leaves remainder 15 when divided by 20.

Just like we did in first part, assume 'b' is the quotient.

5X-10 = 20*b +15
5X = 20*b + 25 = 20*(b+1) + 5

X = 4*(b+1) + 1......................from this we can not answer the question.

So, second can not answer the question.



ANSWER : A
Manager
Manager
User avatar
P
Joined: 06 Jun 2019
Posts: 136
Re: What is the remainder when X is divided by 40?  [#permalink]

Show Tags

New post 17 Jul 2019, 23:12
1
What is the reminder of \(\frac{x}{40}\) ?

ST1. \(3x + 30\) leaves remainder \(93\) when divided by \(120\).

If \(3x + 30 = 120k + 93\) is simplified, we get \(x = 40k + 21\). Now the question is what is the reminder of \(\frac{(40k + 21)}{40}\) ?

If simplified we get \(k + \frac{21}{40}\), thus regardless of \(k\) the reminder is \(21\).

Sufficient

ST2. \(5x - 10\) leaves remainder \(15\) when divided by \(20\).

If \(5x-10=20p + 15\) is simplified, we get \(x=4p+5\). Now the question is what is the reminder of \(\frac{(4p + 5)}{40}\) ?

If \(p=1\), then the remainder is \(9\). If \(p=2\), then the remainder is \(13\).

Insufficient


Hence A
_________________
Bruce Lee: “I fear not the man who has practiced 10,000 kicks once, but I fear the man who has practiced one kick 10,000 times.”
GMAC: “I fear not the aspirant who has practiced 10,000 questions, but I fear the aspirant who has learnt the most out of every single question.” :lol:
SVP
SVP
avatar
V
Joined: 20 Jul 2017
Posts: 1506
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Re: What is the remainder when X is divided by 40?  [#permalink]

Show Tags

New post 18 Jul 2019, 01:31
1
(1) 3X + 30 leaves remainder 93 when divided by 120.
--> 3X + 30 = 120M + 93, for any integer M
--> 3X = 120M + 63
--> X = 40M + 21

So, Remainder = 21

Sufficient


(2) 5X - 10 leaves remainder 15 when divided by 20.
--> 5X - 10 = 20N + 15, for any integer N
--> 5X = 20N + 25
--> X = 4N + 5
--> Possible values of X = 5, 9, 13, 17, . . . . .

So, Possible Remainders = 5, 9, 13, 17 . . . . .

Insufficient

IMO Option A

Pls Hit Kudos if you like the solution
SC Moderator
User avatar
V
Joined: 25 Sep 2018
Posts: 871
Location: United States (CA)
Concentration: Finance, Strategy
GPA: 3.97
WE: Investment Banking (Investment Banking)
Premium Member Reviews Badge CAT Tests
Re: What is the remainder when X is divided by 40?  [#permalink]

Show Tags

New post 18 Jul 2019, 03:19
1
What is the remainder when positive integer X is divided by 40?

(1) 3X + 30 leaves remainder 93 when divided by 120.
(2) 5X - 10 leaves remainder 15 when divided by 20.

Solution :

Question Stem analysis:

We are required to find out remainder when 40 is divided by X,
IMP property : Dividend = Quotient X divisor + Remainder.


Statement one analysis:

We can form the equation using the above stated property,
3X + 30 = 120Q + 93.
3X = 120Q + 63
X= 40Q + 21
If we divide 40Q + 21 by 40, we know that 40Q is divisible by 40, and 21 when divided by 40 leaves a remainder of 21.
Hence statement one alone is sufficient. we can eliminate C & E.

Statement two alone:

We can form the equation using the above stated property,
5X- 10 =20Q + 15,
5X= 20Q+ 25
X = 4Q + 5
In this, we don't know if 40Q is divisible by 40, for eg, if Q=10, then yes we have a remainder of 5, if Q= 1, then the remainder is different. Hence without knowing the value of Q, this statement is insufficient.

Answer must be A
_________________
GMAT Club Bot
Re: What is the remainder when X is divided by 40?   [#permalink] 18 Jul 2019, 03:19

What is the remainder when X is divided by 40?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne