When x is divided by 3, the remainder is 2, and when y is divided by 7

Question

When x is divided by 3, the remainder is 2, and when y is divided by 7, the remainder is 4. What is the remainder when x + y is divided by 21?

(1) x^2 divided by 7 leaves a remainder of 4.
(2) y – 4 is divisible by 3.

Balajikarthick1990 · Answer

X can be 2,5 and y can be 18 so reminder is different in both..SO E

Takdir · Answer

can someone give a solution with equations ?

chetan2u · Answer

Hi,

if you are looking for solution with equation..

the main statement tells us..
 A) x=3a+2.... x could be 2,5,8,11,14,17....
B) y=7b+4.... y could be 4,11,18,25...

statements..
I)  x^2=7c+4 .....  x^2  could be 4,11,18,25.....
so x can be  \sqrt{4},\sqrt{11},\sqrt{18},\sqrt{25} ... or  2,\sqrt{11},\sqrt{18},5 ...
 not required to go beyond this as we see ATLEAST two values of x possible 2,5... 
insuff

II.  it will give you some value of y..
nothing about x  
insuff

combined..

whatever be the value of y..
y+2 and y+5 will surely give different REMAINDER when div by 21.. 
hence insuff

E

RandomStoryteller · Answer

Hi,
I guess Answer is C.

x when divided by 3, Remainder is 2.
x = 3a + 2

y when divided by 7, remainder is 4.
y = 7b + 4

Remainder when x + y divided by 21?
x + y = 3a + 2 + 7b+ 4
x + y = 3a + 7b+ 6.
If a is divisible by 7 and b is divisible by 3 then Remainder = 6.

A. x2 / 7 , Remainder = 4.
x = (3a + 2). x2 = 9a2 +6a + 4.
a is divisible by 7, so that remainder is 4.

B. y - 4 is divisible by 3
y = 7b + 4 ; y-4 = 7b
7b is divisible by 3, so b is divisible by 3.

C. a = divisible by 7, b = divisible by 3.
x + y = 3a + 7b + 6 when divided by 21 should give remainder 6.

The OA is E, Please can someone tell why C is incorrect?

Jazzmin · Answer

Try the numbers x=5 and y=4 it gives a remainder of 9 when divided by 21
But when you take x=23 and y=4, it gives a remainder of 6 when divided by 21

SchruteDwight · Answer

Bunuel   chetan2u 
So what I don't understand is that my algebraic solution would indicate C as the correct answer. Please let me know where I went wrong:

Stem:  x=3q+2  and  y=7p+4   –>   x+y=3q+7p+6 
Hence, our question becomes: is  3q+7p=21k . This is the case whenever  3q  is divisible by  7  and  7p  is divisible by  3 .

Statement I:  x^2=9q^2+12q+4=7L+4 –> q=7L 
Still,  Not sufficient as no information is given about y

Statement II:  y-4=3m . Now from the stem, we know that  y=7p+4  hence, this statement tells us that  7p=3m 
Still,  Not sufficient as no information is given about x

Statement I&II combined: 
From I) we know that  3q  is divisible by  7 , hence,  3q  must be a multiple of  21 
From II) we know that  7p  is divisible by  3 , hence,  7p  must be a multiple of  21

Thus,  x+y=(3q+7p)+6= 21b+6

Please let me know where I went wrong!

SchruteDwight · Answer

no one has any idea why above solution is incorrect?

chetan2u · Answer

You are wrong here..

Statement I:  x^2=9q^2+12q+4=7L+4 –> q=7L 
Still,  Not sufficient as no information is given about y

x^2=9q^2+12q+4=7L+4 –>9q^2+12q=7L......3q(3q+4)=7L ..
When q is multiple of 7, 3q(3q+4)=21a(21a+4)=7L.... possible 
 Here 3q is divisible by 7 
When 3q+4 is multiple of 7, say q is 1....3*1(3*1+4)=3*(7).... possible
 Here 3q=3 and it is not divisible by 7

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When x is divided by 3, the remainder is 2, and when y is divided by 7

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