A, B, C and D are positive integers such that A/B = C/D. Is C divisibl

Question

A, B, C and D are positive integers such that A/B = C/D. Is C divisible by 5?

(1) A is divisible by 210
(2) B = 7^x, where x is a positive integer

AmoyV · Answer

1. A could be 210 and B couuld be 10.
C could be 42 and D could be 2.

Not Sufficient

2. A could be 14 and B 2
A could be 140 and B 14

Not Sufficient

1 and 2:
210=2*3*5*7---> A has atleast 1 factor of 5, which *if* not *divided away* by B will definitely be a value of C
B is the exponent of 7. So the factor of 5 in the numerator is preserved.

So C/D will *atleast* be 2*3*5=30. Hence, C will *atleast* be 2*3*5=30

Answer: C

Lucky2783 · Answer

A*D/B = C

(1) A is divisible by 210

A=2*3*5*7*K
 If B has one 5 then C may or may not have 5 , it depends on D. 
 If B has no 5 then , yes, C will have 5 .

Not Sufficient.

(2) B = 7^x, where x is a positive integer
 we know B has 7(s) , we do not know about A and D . 
 no sufficient.

together : 
 A has 5 and B does not have 5 so C will surely have one 5 .

Answer C .

Zhenek · Answer

our question can be interpreted as  \frac{A*D}{B} = 5*K ? where K, A, D, B - integers
#1 doesn't solve it coz B can be equal to A thus reducing the 210 completely and we are left with D which is unknown, INSUFFICIENT
#2 actually makes it look abit different, our denominator consists of 7's and if our numerator is divisible by 5 then so is C, but otherwise (if A*D is not divisible by 5) C is not , INSUFFICIENT
#1 + #2: combination of these makes our denominator a product of 7's which can't prevent number  \frac{210*Z*D}{7^x}  (A = 210*Z) from being divisibe by 5 due to number 210 alone being divisible by 5 and Z and D being positive integers thus giving us an explicit answer to the question. SUFFICIENT

C is the answer

sudh · Answer

Given  \frac {A}{B}\,=\,\frac {C}{D} 
 C\,=\,\frac{A*D}{B}

Statement (i):
A is divisible by 210
A  =\,210\,*\,integer ; no info about either B or D
Not sufficient

Statement (ii):
B  = 7^x , where  x  is a positive integer; no info about either A or D
Not sufficient

From (i) and (ii)
C  =\frac {30\,*\,7\,*\,integer\,*\,D}{7^x} 
 \,\,\,\,\,= 30\,*\,some\,\,integer ; C is divisible by 5

Answer C

Bunuel · Answer

VERITAS PREP OFFICIAL SOLUTION

Let’s discuss the solution till the point I assume you will be quite comfortable.

We need to find whether C is divisible by 5. So let’s separate the C out of the variables.

C = AD/B

Since C is an integer, AD will be divisible by B but what we don’t know is that after the division, is the quotient divisible by 5?

Statement 1:  A is divisible by 210

We still have no idea what B is so this statement alone is not sufficient. Let’s take an example of how the value of B could change our answer. Assume A is 210.

If B is 3, AD/B will be divisible by 5.

If B is 10, AD/B may not be divisible by 5 (depending on the value of D).

Statement 2:  B = 7^x, where x is a positive integer

We have no idea what A and D are hence this statement alone is not sufficient.

Using both together:  Now, this is where the trick comes in. Using both statements together, we see that C = (210*a*D)/(7^x)

Now we can say for sure that C will be divisible by 5.

fabricioka · Answer

C=AD/B
If we have at least one 5 as prime factor of C after the division the we can answer the question

Statement 1:
We know that A has at least (2,3,5 and 7 as prime factors). But we do not know the value of B. INSUFFICIENT

Statement 2: 
We know that B has only 7 as prime factor, but we know nothing about the other numbers. INSUFFICIENT

Statements 1 and 2: Because we have 2, 3, 5 and 7 as prime factors of A*D and 7 is the only prime factor os B, we know for sure that we have at least one "5" as prime factor of C. SUFFICIENT

stonecold · Answer

Excellent Question here we just need to make sure that either A or D has one 5 and that B does not cancel that 5 => C

vishumangal · Answer

Bunuel   VeritasKarishma 
Could anyone explain me this question 
On combining both statements if I take the value of X as 100 then in that case, C= A*D/B will not be Integer.....
 the How can the C be divided by 5
For eg take A = 210, D=1 and B = 7^35, In this case C will not be divided by 5.

As per my knowledge if something is divisible by some integer the it should yield the remainder as 0

KarishmaB · Answer

Using both statements together, A is divisible by 210 so A = 210m (where m is some positive integer)
B = 7^x where x is an integer.

So what will A/B look like?

\frac{A}{B} = \frac{210*m}{7*7*7* ...7*7}

\frac{A}{B} = \frac{7*2*3*5*m}{7*7*7* ...7*7}

\frac{A}{B} = \frac{2*3*5*m}{7*7*7* ... 7}

If m has factors of 7, some more 7s from the denominator could get cancelled but that is it. The lowest form of A/B will have at least 2, 3 and 5 in the numerator and MAY have some 7s in the denominator.

Since  \frac{A}{B} = \frac{C}{D} = \frac{2*3*5*...}{7*7*... *7} 
So C will have factors of 2, 3 and 5 too.

As for your example, if A = 210 and B = 7^35, D cannot be 1.

\frac{A}{B} = \frac{210}{7^{35}} = \frac{2*3*5}{7*7*... 7}

Now, if C = 2*3*5, D = 7*7*...*7
if C = 2*3*5*2, D = 2*7*7*...*7
and so on...

bumpbot · Answer

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A, B, C and D are positive integers such that A/B = C/D. Is C divisibl

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