If r, s, and t are positive integers and rst = 343, what is the value

343=1*7*7*7

(1) r < s < t .... 1*7*49, t=49....Sufficient
(2) rs = 7 ..... t=49...sufficient

Answer 'D'.

VERITAS PREP OFFICIAL SOLUTION:

Question Type: What Is the Value? This questions asks for the value of the integer t.

Given information in the question stem or diagram: r, s, and t are positive integers, and rst = 343.

Statement 1: “r < s < t.” This statement not only puts the variables in ascending order but also subtly guarantees that the variables are all different numbers— no repeats. It would be a good idea at this point to get the prime factors of 343. 343 = 7^3. The only factors of 343 are 1, 7, 49, and 343. Even before you get to Statement 1, you might recognize from the question stem that the only possible sets of values for r, s, and t are 1 • 1 • 343, 1 • 7 • 49, and 7 • 7 • 7. With Statement 1 the only possible set is 1 • 7 • 49, so t must be 49.The answer is A or D.

Statement 2: “rs = 7.” This means that 7t = 343. In order for rst to equal 343, t must = 49. This statement is clearly sufficient. The correct answer is D.

Note: This is a great example of another important construct discussed in the lesson portion of this book. Statement 2 is a very easy statement: T is clearly equal to 49, and this is quite obviously sufficient. Whenever you have one clearly sufficient statement, the other one will almost always be hard and counterintuitive! The first statement does not seem sufficient at first glance, but with a careful analysis of factors, you see that it is indeed sufficient. The easy 2nd statement is a hint to dig deeper in the first statement and leverage every piece of information that is available.

I have a question. In the first statement, there's no information in the question that points to r,s or t being different numbers. Why can't we assume all of them are 7? This crossed my mind and hence, I marked 'B' as the answer.

Can someone please explain whether we have to assume that r, s and t are different numbers?

Hi,

the statement 1 tells us that r<s<t, this tells us that all THREE are different integers where t is the largest and r is the smallest...

343= 7*7*7

Factors of 343= 1,7,49,343

(1) r < s < t
That means t= 49
Sufficient

(2) rs = 7
rst=343
t= 343/rs
sufficient

D is the answer

If r, s, and t are positive integers and rst = 343, what is the value of t?
(1) r < s < t
(2) rs = 7

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