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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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Math Expert
Joined: 02 Sep 2009
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A, B, C and D are positive integers such that A/B = C/D. Is C divisibl  [#permalink]

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16 Apr 2015, 04:46
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54% (01:56) correct 46% (01:55) wrong based on 263 sessions

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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

Kudos for a correct solution.

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Re: A, B, C and D are positive integers such that A/B = C/D. Is C divisibl  [#permalink]

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16 Apr 2015, 05:08
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Bunuel wrote:
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

Kudos for a correct solution.

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

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Re: A, B, C and D are positive integers such that A/B = C/D. Is C divisibl  [#permalink]

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16 Apr 2015, 07:09
1
Bunuel wrote:
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

Kudos for a correct solution.

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 .

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

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17 Apr 2015, 06:34
1
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

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Re: A, B, C and D are positive integers such that A/B = C/D. Is C divisibl  [#permalink]

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17 Apr 2015, 23:36
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

Math Expert
Joined: 02 Sep 2009
Posts: 58320
A, B, C and D are positive integers such that A/B = C/D. Is C divisibl  [#permalink]

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20 Apr 2015, 05:49
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1
Bunuel wrote:
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

Kudos for a correct solution.

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.

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.
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Re: A, B, C and D are positive integers such that A/B = C/D. Is C divisibl  [#permalink]

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28 Jan 2016, 15:59
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
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Re: A, B, C and D are positive integers such that A/B = C/D. Is C divisibl  [#permalink]

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16 Mar 2016, 06:12
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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
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Re: A, B, C and D are positive integers such that A/B = C/D. Is C divisibl  [#permalink]

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17 Jan 2019, 13:11
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Re: A, B, C and D are positive integers such that A/B = C/D. Is C divisibl   [#permalink] 17 Jan 2019, 13:11
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