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Math Expert V
Joined: 02 Sep 2009
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What is the remainder when X is divided by 40?  [#permalink]

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Difficulty:   65% (hard)

Question Stats: 63% (01:56) correct 37% (02:01) wrong based on 247 sessions

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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. This question was provided by Experts Global for the Game of Timers Competition _________________
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Re: What is the remainder when X is divided by 40?  [#permalink]

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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
##### General Discussion
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Re: What is the remainder when X is divided by 40?  [#permalink]

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Case A
3x + 30 = 120y + 93
x + 10 = 40y + 31
So, x = 40y + 21 Sufficient

Case B
5x - 10 = 20y + 15
x-2 = 4y + 3
x=4y+5, Insufficient A
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Re: What is the remainder when X is divided by 40?  [#permalink]

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Quote:
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.

Option D
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Re: What is the remainder when X is divided by 40?  [#permalink]

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both together are sufficient.

C is the right answer IMO
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Re: What is the remainder when X is divided by 40?  [#permalink]

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What is the remainder when positive integer X is divided by 40?

This is an easy question. Nothing to analyze in the stem lets move to the statements.

(1) 3X + 30 leaves remainder 93 when divided by 120.
This choice is correct, cause X will take values like 39, 79, etc, which will always have remainder as 39.
Hence this is sufficient.

(2) 5X - 10 leaves remainder 15 when divided by 20.
This statement is insufficient. Cause X will have multiple values like 5, 9, etc and hence the remainder will also be different.

Hence the answer choice A is correct.
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Re: What is the remainder when X is divided by 40?  [#permalink]

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Statement 1-

3x+30=120m+93

X= 40k+ 21, thus when divided by 40, will leave 21

Statement 2-
5x-10 = 20k + 15

X= 4k + 5

Not sufficient

Posted from my mobile device
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Re: What is the remainder when X is divided by 40?  [#permalink]

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we know from statement 1: 3x+30 = 93, x= 21, similarly 3x+3 = 213, x = 61.
so x can be 21, 61,101,....
In all these cases, we get a reminder of 21 when x is divided by 40. so suff

from statement 2: in similar lines, x can be 5,9,13,17,21,25...
as multiple values, multiple reminders, not suff

so A
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Re: What is the remainder when X is divided by 40?  [#permalink]

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(1) 3X + 30 leaves remainder 93 when divided by 120.
Sufficient.
3x+30=120k+93
3x=120k+63
x=40k+21
Thus remainder will be 21
(2) 5X - 10 leaves remainder 15 when divided by 20.
Not sufficient.
5x-10=20m+15
5x=20m+25
x=4m+5
Thus we have plenty of possible remainders: 5, 9, 13...

IMO A
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Re: What is the remainder when X is divided by 40?  [#permalink]

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Answer is: D. both statements are sufficient.

What is the remainder when positive integer X is divided by 40?

(1) 3X + 30 leaves remainder 93 when divided by 120.
X must be odd.
(2) 5X - 10 leaves remainder 15 when divided by 20.
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Re: What is the remainder when X is divided by 40?  [#permalink]

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From A
3x + 30 = 120A +93 (where A is an positive integer)
3x = 120A +63
x = 40A +21

Divide (40A +21)/40
Remainder = 21

A is sufficient.

From B

5x- 10 = 20B +15 (Where B is positive integer)
5x = 20B +25
X = 4B +5

divide (4B +5)/40
Take B=40 Then Remainder = 5
Take B as 1 then Remainder = 9

No single answer B is insufficient

Only A can sufficiently gives the answer.

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What is the remainder when X is divided by 40?  [#permalink]

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What is the remainder when positive integer X is divided by 40?

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

3X +30 = 120K+93

X+ 10 = 40K+ 31

X = 40K + 21, so remainder will be always 21

So,sufficient

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

5X -10 = 20K+15

5X = 20K + 25

x = 4K + 5

So reminder will vary based on value ok K, so not sufficient.

Originally posted by Mizar18 on 17 Jul 2019, 08:44.
Last edited by Mizar18 on 17 Jul 2019, 19:57, edited 1 time in total.
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What is the remainder when X is divided by 40?  [#permalink]

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For 1: $$\frac{3X+30-93}{120}$$ =y
X+10-31=40y
X-21=40y

So, remainder is 21
Sufficient

For 2: $$\frac{5X-10-15}{20}$$ =y
X-2-3=4y
X-5=4y
Insufficient

Hence A

Originally posted by kitipriyanka on 17 Jul 2019, 08:48.
Last edited by kitipriyanka on 17 Jul 2019, 10:18, edited 1 time in total.
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Re: What is the remainder when X is divided by 40?  [#permalink]

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A.

From st 1, mathematically it can be written as, 3x+30 = 120n1+93 => x = 40n1 + 21, clearly remainder is 21 when x is divided by 40 - Sufficient

From st 2, mathematically it can be written as, 5x-10 = 20n2+15 => x = 4n2 + 5, so can have values such as 9, 13,17 .. which are all remainders when x is divided by 40 - Not Sufficient
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Re: What is the remainder when X is divided by 40?  [#permalink]

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X = 40k + N, we are asked to find the remainder:

1. 3X + 30 leaves remainder 93 when divided by 120.
3X + 30 = 120k +93
3X = 120k + 63
If K = 1 , 3X = 183 => X = 61
If K = 2, 3X = 303 => X = 101
Not Sufficient.

2. 5X - 10 leaves remainder 15 when divided by 20.
5X - 10 = 20k + 15
5X = 20k + 25
If K =1, 5X = 45 => X = 9
If K = 2, 5X = 65 = > X = 13

Not sufficient.

Thus we can't find a unique number which will give us a unique remainder.

Please hit kudos if you like the solution.
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GMAT 1: 640 Q45 V35 GMAT 2: 660 Q48 V33 Re: What is the remainder when X is divided by 40?  [#permalink]

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What is the remainder when positive integer X is divided by 40?

(1) 3X + 30 leaves remainder 93 when divided by 120. - Sufficient, Min X Number that satisfies the requirement is (93-30)/3=21 which leaves a remainder of 21 when divided by 40. When X=181 (21+40*4) the above becomes (543+30)/120 still gives a remainder of 93 when divided by 120 and 21 when divided by 40. Remainder will always be 21

(2) 5X - 10 leaves remainder 15 when divided by 20. Insufficient; When Min X Number that satisfies the requirement is (25-10)/3=5 which leaves a remainder of 5 when divided by 40; When X=9 also satisfies the requirement but gives a remainder of 9 when divided by 40. Two values for X have 2 different remainders

IMO A
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GMAT 1: 590 Q44 V22 Re: What is the remainder when X is divided by 40?  [#permalink]

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3x+30 when divided by 120 leaves a remainder 93 i.e
3x+30+27 (120-93=27) is divisible by 120
3x+57 is divisible by 120
3(x+19)is divisible by 120
x+19 is divisible 40
i.e 21 is the remainder hence A is sufficient

5x-10 leaves remainder 15 when divided by 20
ie 5x-5 is divisible by 20
5(x-1) is divisible by 20
x-1 is divisible by 4 but we calculate the remainder when x is divided by 40
Hence insufficient

IMO A
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Re: What is the remainder when X is divided by 40?  [#permalink]

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Question is asking what is the remainder when positive integer X is divided by 40?

St.1 - 3X + 30 leaves remainder 93 when divided by 120. If the number is 93 then X=21, then X/40 remainder is 21.
Lets try with another number that satisfies the condition, X=61, then 61*3+30=213/120 Remainder is 93, then X/40 Remainder is 21. In both the cases X/40 remainder is 21. Sufficient.

St.2 - 5X - 10 leaves remainder 15 when divided by 20. If the number is 15 then X=5, then X/40 remainder is 5, but if the number is 35 then X=9, then X/40 remainder is 9. Two different answers therefore the statement is Insufficient.

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Correct answer is A; explanation is given in the attachment
Attachments IMG_20190717_213525.JPG [ 1.03 MiB | Viewed 1670 times ]

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Re: What is the remainder when X is divided by 40?  [#permalink]

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Quote:
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.

GIVEN: rof x/40?

(1) 3X + 30 leaves remainder 93 when divided by 120: 3x+30/120 rof 93… 3x+30={93,213,333,453,…} x={21,(fraction),101,141…}; rof x/40={21,21,21…} sufficient.
(2) 5X - 10 leaves remainder 15 when divided by 20: 5x-10/20 rof 15… 5x-10={15,35,55,75,…} x={5,9,13…}; insufficient. Re: What is the remainder when X is divided by 40?   [#permalink] 17 Jul 2019, 09:11

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