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

It is currently 19 Aug 2019, 05:06

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 
Manager
Manager
avatar
S
Joined: 29 Apr 2017
Posts: 54
Location: India
Concentration: Operations, Other
GMAT 1: 660 Q43 V38
GPA: 4
WE: Operations (Transportation)
Re: What is the remainder when X is divided by 40?  [#permalink]

Show Tags

New post 17 Jul 2019, 21:44
1
To find: Remainder when integer X is divided by 40 i.e. X=40q+R, R=?
Statement1: 3x+30 leaves a remainder 93 when divided by 120
i.e 3x+30=120q+93
=>3x=120q+63
=> x=40q+21
therefore, remainder = 21
Sufficient to answer

Statement 2: 5x-10 leaves a remainder 15 when divided by 20
i.e 5x-10=20q+15
=> 5x=20q+25
=> x =4q+5
=>x=4(q+1)+1 (i.e remainder can't be greater than divisor)
so possible x=1,5,9,13,................................,41,45,49,53.............
for all above x values, remainders are different for each when divided by 40 i.e 1,5,9,13,...................,1,5,9,13,........
So, statement 2 is not sufficient.

Answer: A
Manager
Manager
User avatar
G
Joined: 08 Jan 2018
Posts: 124
Re: What is the remainder when X is divided by 40?  [#permalink]

Show Tags

New post 17 Jul 2019, 21:58
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
Manager
Manager
User avatar
S
Joined: 12 Jan 2018
Posts: 112
Re: What is the remainder when X is divided by 40?  [#permalink]

Show Tags

New post 17 Jul 2019, 22:43
1
(1) 3X + 30 leaves remainder 93 when divided by 120.
First number that satisfies this is 93, 3x+30=93 => x=21. Next number would be 120+93=213; 213=3x+30=> x=61.
possible values of x=21,61,101 so on. Each leave a remainder of 21 when divided by 40. Sufficient.

(2) 5X - 10 leaves remainder 15 when divided by 20.
First number that satisfies this is 15, 5x-10=15 => 5. Next number would be 15+20=35; 35=5x-10=> x=9.
x:5,9,13,17...... Rach when divided by 40 can leave different remainder. Insufficient

Ans. A
_________________
"Remember that guy that gave up?
Neither does anybody else"
Manager
Manager
avatar
S
Joined: 24 Jan 2019
Posts: 103
Location: India
Concentration: Strategy, Finance
GPA: 4
Re: What is the remainder when X is divided by 40?  [#permalink]

Show Tags

New post 17 Jul 2019, 23:07
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
Intern
Intern
avatar
B
Joined: 09 Jul 2019
Posts: 38
Re: What is the remainder when X is divided by 40?  [#permalink]

Show Tags

New post 18 Jul 2019, 00:12
1
(1) After all cancellations, it is given
x= a*40+21,
x =21, 61, 101, 141, 181,....... divide 40, some quotient and remainder 21, sufficient
(2) After all cancellations, it is given
x=b*4+5
x=5, 9, 13, 17, 21, 25............ divide by 40, remainder 5, 9, 17, 21, 25, etc , insufficient
IMO A
Manager
Manager
User avatar
S
Joined: 06 Jun 2019
Posts: 114
Re: What is the remainder when X is divided by 40?  [#permalink]

Show Tags

New post 18 Jul 2019, 00:12
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:
Intern
Intern
avatar
B
Joined: 08 Jul 2019
Posts: 37
Re: What is the remainder when X is divided by 40?  [#permalink]

Show Tags

New post 18 Jul 2019, 01:46
1
What is the remainder when x is divided by 40?

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

Let’s create the formula of this statement:

30x+30 = 120a + 93
30x = 120a + 63
x = 40a + 21

We can see that if 40a + 21 is divided by 40, then the remainder is 21.
Therefore 1) is sufficient.

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

Let’s create the formula of this statement:

5x – 10 = 20b + 15
5x = 20b +25
X = 4b + 5

We can see that if 4b + 5 is divided by 40, then the remainder is different depending on b.
Therefore 2) is insufficient.

IMO A
Intern
Intern
avatar
B
Joined: 09 May 2019
Posts: 20
Re: What is the remainder when X is divided by 40?  [#permalink]

Show Tags

New post 18 Jul 2019, 02:27
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.

statement 1 - 3X+30 leaves remainder 93 when divided by 120
3X+3 can be written as 3(X+10)/120 = X+10/40 so this leaves remainder 93
So X/40 will leave remainder 93+10 = 103

Hence Statement one is sufficient

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

Suppose X = 13 then if we multiply both denominator and numerator by 2 then 10(X-2)/40 = 10*(13-2)/40 = 110/40 = 30 leaves remainder 30
Suppose X = 17 then if we multiply both denminator and numerator by 2 then 10(X-2)/40 = 10(17-2)/40 = 10*15/40 = 150/40 leaves remainder 30.

Hence 5X-10 leaves remainder 15 when divided by 20 , but it cannot be determined for sure what is the remainder when it X is divided by 40
Hence insufficient

Ther Answer is A
Manager
Manager
avatar
B
Joined: 07 Jul 2019
Posts: 54
Re: What is the remainder when X is divided by 40?  [#permalink]

Show Tags

New post 18 Jul 2019, 02:31
1
What is remainder when x/40? Formula for remainders is a/b=integer+r. We will apply this formula for both statements.
1. When 120 divides 3x+30, remainder is 93. Substitute number to formula above.
(3x+30)/120=integer+93
3x+30=120*i+93 , we can multiply by 1/3 all sides to get easier numbers to calculate
x=40*i+21,
x/40=i+21, remainder is 21 A is good
2. When 20 divides 5x-10, remainder is 15. Substitute number to formula
(5x-10)/20=integer+15
5x-10=20*integer+15 , multiply by 1/5
x=4*integer+5
x/4=integer+5, different values possible.
IMO A
Director
Director
avatar
P
Joined: 20 Jul 2017
Posts: 633
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, 02:31
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
Senior Manager
Senior Manager
User avatar
P
Status: eternal student
Joined: 06 Mar 2018
Posts: 279
Location: Kazakhstan
GPA: 3.87
GMAT ToolKit User Premium Member CAT Tests
Re: What is the remainder when X is divided by 40?  [#permalink]

Show Tags

New post 18 Jul 2019, 03:15
1
What is the remainder when positive integer X is divided by 40?

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

Let's imagine if we 3x+30 divide by 120 we have reminder of 83 are 21, 61, 101....
(arithmetic progression: add 40 to previous term)
21/40=21 is reminder,
61/40=21 is reminder and so on...
Reminder is always equal to 21.
Sufficient. :)


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

Let's imagine if we 5x-10 divide by 20 we have reminder of 15 are 5, 9, 13...
(arithmetic progression: add 4 to previous term)
We've always got different reminders, so insufficient. :(

A is the answer. :heart
_________________
My SC approach flowchart

(no one is ideal, please correct if you see any mistakes or gaps in my explanation, it will be helpful for both of us, thank you)

___________________
Practice makes perfect!


It is pointless to try to study if it is not fun, then it becomes a chore. At that point, you will either hate your studies or became afraid of them.
Manager
Manager
avatar
G
Joined: 27 May 2010
Posts: 200
Re: What is the remainder when X is divided by 40?  [#permalink]

Show Tags

New post 18 Jul 2019, 03:35
1
(1) 3X + 30 leaves remainder 93 when divided by 120.
(2) 5X - 10 leaves remainder 15 when divided by 20.

Statement1: (3x + 30 - 93)/120 is an integer
Implies (x - 21)/40 is an integer.
Therefore reminder = 21.
Sufficient.

Statement2: (5x - 10 -15)/20 is an integer
(5x-25)/20 is an integer
(x-5)/4 is an integer
Not sufficient since we cannot determine reminder when divided by 40.

Option A.
_________________
Please give Kudos if you like the post
Senior Manager
Senior Manager
User avatar
D
Joined: 25 Sep 2018
Posts: 393
Location: United States (CA)
Concentration: Finance, Strategy
GMAT 1: 640 Q47 V30
GPA: 3.97
WE: Investment Banking (Investment Banking)
Re: What is the remainder when X is divided by 40?  [#permalink]

Show Tags

New post 18 Jul 2019, 04:19
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
_________________
Why do we fall?...So we can learn to pick ourselves up again
Manager
Manager
avatar
S
Joined: 22 Oct 2018
Posts: 74
CAT Tests
Re: What is the remainder when X is divided by 40?  [#permalink]

Show Tags

New post 18 Jul 2019, 04:25
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:
We have to find
\(\frac{x}{40}\) = Q +\(\frac{R}{40}\)

From the first statement:
\(\frac{(3x+30)}{120}\) = Q +\(\frac{93}{120}\)

\(\frac{x}{40}\) = Q +\(\frac{21}{40}\) Hence sufficient.


From Statement 2;

\(\frac{(5x-10)}{20}\) = Q + \(\frac{15}{20}\)

\(\frac{x}{4}\) = Q +\(\frac{5}{4}\)

Hence insufficient.
Therefore A IMO
Manager
Manager
avatar
S
Joined: 07 Dec 2018
Posts: 111
Location: India
Concentration: Technology, Finance
GMAT 1: 670 Q49 V32
Re: What is the remainder when X is divided by 40?  [#permalink]

Show Tags

New post 18 Jul 2019, 04:48
1
Given : x=40a+r ..........................(1)

We need to find r.

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

3x+30 = 120b+93
3(x+10) = 120b+93
x+10=40b+31
x=40b+21..........................(2)

If we compare equation (1) & (2)
r=21
Sufficient.

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


5x-10 = 20c+15
x-2=4c+3
x=4c+5...................(3)

Equation (1) & (3) are not comparable.
Insufficient.

So, Ans should be (A)
Manager
Manager
avatar
S
Joined: 25 Jul 2018
Posts: 188
CAT Tests
What is the remainder when X is divided by 40?  [#permalink]

Show Tags

New post 18 Jul 2019, 04:49
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.

Statement1:

3X+30=120*a+93 (a is quotient)
3X=120a+93-30
3X=120a+63
3X/3=120a/3+63/3
X=40a+21
Well, if we divided X by 40, remainder will be 21.
Sufficient

Statement2:

5X - 10=20a+15 (a is quotient)
5X=20a+15+10
5X=20a+25
5X/5=20a/5+25/5
X=4a+5
Well, it depends on 'a' if we divide X by 40.
if a≥8, the remainder will be 5.
if a<8, the remainder will be different from 5.
Insufficient

Answer choice is A.
Manager
Manager
avatar
S
Joined: 01 Oct 2018
Posts: 111
Re: What is the remainder when X is divided by 40?  [#permalink]

Show Tags

New post 18 Jul 2019, 06:57
1
What is the remainder when positive integer X is divided by 40?

X = 40*k + a
a = ?

(1) 3X + 30 leaves remainder 93 when divided by 120.
3X + 30 = 120*k1 + 93
3X=120*k1+63
We know that X = 40*k + a
120 / 40 = 3, so 40 can be included in 120 3 times
That's mean a = 23
SUFFICIENT
(2) 5X - 10 leaves remainder 15 when divided by 20.
5X - 10=20*k2 + 15
5X = 20*(k2+1) + 5
As: X = 40*k + a
20 can be included in 40 2 times, so exists 2 possible remainders of a:
a = 5 and a = 25
INSUFFICIENT

ANSWER A
Intern
Intern
avatar
B
Joined: 30 Nov 2018
Posts: 11
Location: India
Schools: HEC MiM '21
GPA: 4
CAT Tests
Re: What is the remainder when X is divided by 40?  [#permalink]

Show Tags

New post 18 Jul 2019, 07:23
1
Option A

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

here 3x when divided by 120 will leave a remainder of 63 (ie 3 x 21).. In that case x when divided by 120 will leave a remainder of 21

(2) 5X - 10 leaves remainder 15 when divided by 20.
here 5x will leave a remainder of 5 when divided by 20... the are many possible values for such cases.. X can be 5, 9 etc... hence it is insufficient !!
Intern
Intern
avatar
B
Joined: 11 Jun 2014
Posts: 23
Re: What is the remainder when X is divided by 40?  [#permalink]

Show Tags

New post 18 Jul 2019, 07:27
1
Answer A
Statement i= sufficient
3x+30=120k+93
x=40k+21 remainder 21
statement ii not sufficient
5x-10=20I+15
x=4I+5, 5,13 are remaninders not sufficient
Intern
Intern
User avatar
S
Joined: 24 Mar 2018
Posts: 48
Location: India
Concentration: Operations, Strategy
Schools: ISB '21
WE: Project Management (Energy and Utilities)
Re: What is the remainder when X is divided by 40?  [#permalink]

Show Tags

New post 18 Jul 2019, 07:52
1
X=40k+r where r is the remainder

Statement 1:
3X+30= 120k+3r+30
3r+30 = 93
3r=63
r=21
Sufficient.

Statement 2:
5X-10=200k+5r-10
Wen 5X-10 is divided by 20, 200k is reduced to 10k. But we don't know about 5r-10
If 5r-10 <20, 5r-10=15; r=5
If 5r-10>20, lets say, 5r-10 = 35, r=9
Not sufficient.

Hence, option (A).
GMAT Club Bot
Re: What is the remainder when X is divided by 40?   [#permalink] 18 Jul 2019, 07:52

Go to page   Previous    1   2   3   4   [ 80 posts ] 

Display posts from previous: Sort by

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