Is rst = 1 ? (1) rs = 1 (2) st = 1

Answer: "E" : Both statements not sufficient

Reason:
(plugging in method)

Statement 1: Say r = 1/3 and s = 3

satisfies statement 1 i.e. rs = 1 but cant comment about value of rst as t is still unknown.

Statement 2: Say t = 1/3 and s = 3

satisfies statement 1 i.e. st = 1 but cant comment about value of rst as t is still unknown.

Now if both statements are taken together, r=1/3 s=3 and t=1/3 => rst not equal to 1.

hence both the statements are not sufficient.

But from your response above combining the two statements tells us conclusively that rst not eqaul to 1. Therefore combining the two statements is sufficient to answer the question as a 'NO'. So shouldn't the answer be 'C'

Oh yes. My usual mistake . Thanks so much Loki. This goes directly to my error log.

So the answer is "C"

Ok, without a doubt my number property skills are my achillies heel when is comes to GMAT quant.

I was reviewing my error log today. Tell me why my logic is wrong.

95. Is rst=1

(1) rs=1
(2) st=1

I attacked it by rearranging the original equations, dividing both sides by t.

so, rs=1/t
then sub in rs=1
so, 1=1/t
then cross multiply t=1
Combined with what we already know (rs=1) we have 1*1=1
Therefore, sufficient.

Same logic can be applied to statment 2.
Therefore my answer was D.

OA is actually E and I understand how they got it, but I also fail to see why my strategy was wrong. I feel like I'm probably overlooking some basic rule that governs all equations here but if someone could help me out that'd be great.

Thanks

Okay, you can really deal with this much simpler. But, let's review what you've done.

I attacked it by rearranging the original equations, dividing both sides by t.
so, rs=1/t

your question then changes to -- Is rs=1/t?
1. Does this give the vale of t? No. Even if you use (1), you get -- 1=1/t -> t=1. Does this answer your question. No. A/D out
2. Similarly, does the value of st=1, help us in answering the question? No. B out

Hope this helps.

This is what I was missing. Normally I'd instinctively follow that, but I think cause it was in my error log I over-thought it and got fancy - effectively confusing myself. Ha!

Thanks for the quick repsonses guys, much appreciated!

i) rs=1
r=1/3 s=3 and t=7 so ans is no
r=1/3 s=3 and t=1 so ans is yes
not suff.

ii) st=1
s=1/3 and t=3 and r=7 so ans is no
r=1/3 s=3 and t=1 so ans is yes

not sufficient

combining both 1 and 2

s=1/3 r=3 and t=3 still it satisfies both eq but rst is not 1

if s=1 r=1 and t=1 it satisifies both eq. and rst is 1

so ans is E

i) rs=1
As we don't know anything about value of t so we cant answer if rst = 1. Insufficient.

ii) st=1
As we don't know anything about value of r so we cant answer if rst = 1. Insufficient.

Combining both 1 and 2

(rs)(st) = 1
(rst)s = 1
rst = 1/s

As we don't know the value of s. rst can be anything (1 or something else). we cannot answer "Is rst = 1?"

Insufficient
Ans: E

Its clear that 1 and 2 do not lead to a solution. then, Cant this be solved by observing that we have 2 equations and 3 unknown variables. hence not sufficient and hence E?

That's not entirely correct. Notice that we are asked to find whether rst = 1, not the values of the unknowns.

For example if the question were:

Is rst = 1 ?

(1) rs = 0
(2) st = 1

The answer would be A not E.

statement 1: don't know anything about t. not sufficient
statement 2: don't know anything about r. not sufficient

put them together: rst could equal (1)(1)(1) in which case would be 1. or rst could equal (1/2)(2)(1/2) in which case rst = 1/2. Not sufficient

Answer: E

I found that the easiest way to tackle this problem was as following:

(A) rs = 1 means r and s have same sign. Make a chart:


r s
+ +
- -

Clearly not sufficient

(B)

st = 1 means s and t have same sign. Make a chart:

s t
+ +
- -

Clearly not sufficient


combined:

r s t
+ + +
- - -

two different solutions: -1 or 1, hence (E)

Incredibly fast solution, took less than 15 seconds

Going through the solutions posted by students in this thread, I realized that this question is a good illustration of the perils of 'solve by substituting numbers' approach. A student considered one set of possible values of r, s and t and thought that since he was able to get a tangible value of the product rst that was not equal to 1, this meant the 2 statements together were sufficient. It didn't occur to him at that time (later he did realize this oversight) that other values of r, s and t were also possible that did lead to rst = 1.

To eliminate all this uncertainty about whether you've considered all possible sets of values for the different unknowns, I would like to suggest the algebraic way of thinking through this question. Here's how I would solve it:

The question asks if rst = 1 (Note to self: it's not mentioned that r, s and t are integers. So, they might very well be fractions)

1. rs = 1
But t = ? Don't know

Insufficient

2. st = 1
But r = ? Don't know

Insufficient.

1 + 2

The question asks about the product rst.
This product can be written as \(\frac{(rs)(st)}{s}\). Substituting the values of rs and st from St. 1 and 2, we get:

rst = \(\frac{(1)(1)}{s}\) = \(\frac{1}{s}\)

But s = ? Don't know

If s = 1, rst = 1
But if s = some other value, rst is not equal to 1.

So, clearly insufficient.

Answer: Option E

I hope this alternate solution was helpful for you

Best Regards

Japinder

1.) Tells us nothing about t - INS (eliminate A/D from grid)
2.) Tells us nothing about r - INS (eliminate B from grid)

Combined (left with C or E)
r*s = 1
s*t = 1

a.) 1*1*1 = 1 True
b.) 1/4 * 4 * 1/4 = 1 False

Therefore answer is E

Solution:

We need to determine whether RST = 1.

Statement One Alone:

RS = 1

Since we don’t know the value of T, knowing only that RS = 1 is not sufficient to determine whether RST = 1. We can eliminate answer choices A and D.

Statement Two Alone:

ST = 1

Since we don’t know the value of R, knowing only that ST = 1, is not sufficient to determine whether RST = 1. We can eliminate answer choice B.

Statements One and Two Together:

From statements one and two we know that RS = 1 and that ST = 1. Thus, we can say that:

RS = ST

RS – ST = 0

S(R – T) = 0

S = 0 or R = T

Because RS and ST both equal 1, S cannot be 0. Thus, R = T.

However, knowing that R = T is not enough information to determine whether RST = 1.

For example, if R = T = 1, then S = 1 (since RS = 1 and ST = 1), RST = 1.

However, if R = T = 2, then S = ½ (since RS = 1 and ST = 1), RST = 2  1.

The answer is E.

Target question: Is rst=1?

Statement 1: rs = 1
No information about t
INSUFFICIENT

Statement 2: st = 1
No information about r
INSUFFICIENT

Statements 1 and 2 combined
So, rs = 1 and st = 1
This means that rs/st = 1/1
Simplify to get r/t = 1
This tells us that r = t, so this is all that we can conclude one we combine the statements.

If r = t, there are still several values of r, s and t that satisfy the both statements. Here are two:
Case a: r = 1, s = 1 and t = 1, in which case rst = 1
Case b: r = 0.5, s = 2 and t = 0.5, in which case rst = 0.5
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent

I would urge all experts on forums to provide solutions like this one, we are learning and often experts forget we need layman basic terminology to really grip the concepts. I have read all the solutions and at the end, i understood from this post.

I have great respect for Bunnel, but man sometimes you forget that all do not share your level of expertise on this content. Using words helps us students a lot. Thank you for the post