If N is a positive Integer, is the units digit of N equal to zero?

Im not sure that Statement 1 is sufficient on it's own. All we know from st1 is that N has prime factors of 2,5,7, and possibly others. From this, N could be 14, or 70 ...

But statement 2 is good because it tells you exactly the value of N. Keep in mind you dont have to figure it out, but you just have to know that if you had time, you could get a value for N and see what its units digit is.

I think it's D.

St. 1 : 14 = 2 * 7, 35 = 5 * 7, hence, 2,5,7 are factors of N.
If N=70, 35 * 2 or 14 * 5
If N=105, 35*3, 14 isn't a factor of 105.
If N = 140, 35 * 4, 14 * 10

Thus, when 14 and 35 are factors of N, the unit's digit is always 0 ! Hence, Sufficient.

St.2 : N=(2^5)(3^2)(5^7)(7^6)

As you have 2*5 here, the unit's digit will always be 0. Hence, Sufficient.

Bunnel: If you could throw some light particularly on statement (1), it would be great.

I am still not clear how even statement (2) ensures that unit digit will be zero.

I opted B.

Bunnel..I am having doubts with statement 1. It just says 14 & 35 are factors of N, but it doesn't specify whether they are the only factors. If they aren't, then 1 isn't sufficient on its own. How can we infer that they are the only factors, when it's not clearly specified.

The question asks whether the units digit of N equals to zero. From (1) N is divisible by 2 and 5, hence it's divisible by 10, which means that the units digit of N is 0. We don't care about other factors of N at all.

Bunuel

When you say N is divisible by 2 and 5

If you take apart 14 and 35 say- 2 x 7 x 5 x 5 - is this correct method for making that conclusion?

N is divisible by 14, so it's divisible by 2.
N is divisible by 35, so it's divisible by 5.

Thus, it's divisible by 10.

Generally if a positive integer is divisible by positive integers x and y, then it must be divisible by the least common multiple of x and y. So, N above must be divisible by the LCM(14, 35), so by 70.

We need to determine whether the units digit of a positive integer N is zero. If N has a units digit of zero, then N must be divisible by 10. In other words, N must be divisible by both 2 and 5.

Statement One Alone:

14 and 35 are factors of N.

Since 14 is divisible by 2 and 35 is divisible by 5, N is divisible by both 2 and 5, and thus it has a units digit of zero. Statement one alone is sufficient. We can eliminate answer choices B, C, and E.

Statement Two Alone:

N = (2^5)(3^2)(5^7)(7^6)

We see that N is divisible by both 2 and 5 and thus has a units digit of zero. Statement two alone is also sufficient.

Answer: D

Forget the conventional way to solve DS questions.

We will solve this DS question using the variable approach.

DS question with 1 variable: Let the original condition in a DS question contain 1 variable. Now, 1 variable would generally require 1 equation to give us the value of the variables.

We know that each condition would usually give us an equation, and since we need 1 equation to match the number of variables and equations in the original condition, the equal number of equations and variables should logically lead to answer D.

To master the Variable Approach, visit https://www.mathrevolution.com and check our lessons and proven techniques to score high in DS questions.

Let’s apply the 3 steps suggested previously. [Watch lessons on our website to master these 3 steps]

Step 1 of the Variable Approach: Modifying and rechecking the original condition and the question.

We have to find whether the units digit of N equal to zero.

Second and the third step of Variable Approach: From the original condition, we have 1 variable (N). To match the number of variables with the number of equations, we need 1 equation. Since conditions (1) and (2) will provide 1 equation each, D would most likely be the answer.

Let’s take a look at each condition.

Condition(1) tells us that 14 and 35 are factors of N.

=> 14 = 2 * 7 and 35 = 5 * 7.

=>This means 'N' is divisible by 10 and it must have a unit digit equal to '0'

Since the answer is unique, the condition is sufficient by CMT 2.


Condition(2) tells us that N = \((2^5)(3^2)(5^7)(7^6)\)

=> Combiantion of 2 * 5 = 10 ensures that 'N' has unit digit as '0'

Since the answer is unique, the condition is sufficient by CMT 2.

Both conditions (1) and (2) alone are sufficient.

So, D is the correct answer.

Answer: D

Asked: If N is a positive Integer, is the units digit of N equal to zero?

(1) 14 and 35 are factors of N
N = 2*7*5*k = 70k ; where k is an integer
Unit digit of N = 0
SUFFICIENT

(2) N = (2^5)(3^2)(5^7)(7^6)
N = 2*5*k = 10k ; where k is an integer
Unit digit of N = 0
SUFFICIENT

IMO D

I am just reading all the reviews, and I did answer B on this one too, due the same reason since I didn´t see these are the only factors.
But it doesn´t matter the other factors, any number multiply by 10 will have a 0 unit.

With this said.
Statement one
14 and 35 as factors. Will mean 2 x 5 x 5 x 7. So we have 10 as a divisor. So it will mean that the number at some point will be multiply by 10 doesn´t matter the other factors. can be 231x10x223x13121 it will have a 0 unit.
Only numbers that multiply by 10 do not have a unit of 0 are the fractions, but it the statement says Positive integer.

Statement 2, since already explain as soon as we see that the number will be multiply by 10 we can assume is 0. with this said, we are able to see a 2 and a 5 as a prime factor. So at some point will be multiply by 10.

So D, each statement is valid on it is own.

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