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# Does rst = 1? (1) rs = –1 (2) rt = –1

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Math Expert
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Does rst = 1? (1) rs = –1 (2) rt = –1  [#permalink]

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28 Aug 2017, 04:02
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Difficulty:

35% (medium)

Question Stats:

84% (01:10) correct 16% (01:12) wrong based on 47 sessions

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Does rst = 1?

(1) rs = –1
(2) rt = –1

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Re: Does rst = 1? (1) rs = –1 (2) rt = –1  [#permalink]

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28 Aug 2017, 04:11
Bunuel wrote:
Does rst = 1?

(1) rs = –1
(2) rt = –1

(1) no info abt t..not sufficient

(2) no info abt s...not sufficient

on combining
s=-1/r
t=-1/r
r*-1/r*-1/r = 1/r
1/r is not necessarily equal to 1
not sufficient
E
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Re: Does rst = 1? (1) rs = –1 (2) rt = –1  [#permalink]

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28 Aug 2017, 05:34
Ques : is rst=1

1. rs= -1 => No information. Not sufficient
2. rt= -1 => No information. Not sufficient

1+2
'rs= -1 and rt= -1;

we can only conclude that :
r= +ve and both s and t are -ve
s= -1/r and t= -1/r

OR

r= -ve and both s and t are +ve
s= -1/r and t= -1/r

so rst = r*(-1/r)*(-1/r) =1/r

Not sufficeint

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Re: Does rst = 1? (1) rs = –1 (2) rt = –1  [#permalink]

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28 Aug 2017, 05:39
(1) rs = –1. No info on t ; insuff
(2) rt = –1. No info on s; insuff

Combining r^2st=1 i.e; rst=1/r; no idea if r=-1 . So insufficient. E
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Does rst = 1? (1) rs = –1 (2) rt = –1  [#permalink]

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28 Aug 2017, 12:28
It can be easily seen that both the statements can't answer the Q independently. So lets combine the two statements.

As per A: rs=-1 --> r=-1/s and As per B: rt=-1, substitute value of r --> (-1/s)*t=-1 --> t=s. No lets test the equations with some numbers.
Test 1: let t=s=1/2 ans r=-2, all equations are satisfied but rst is not equal to 1
Test 2: let t=s=1 and r=-1, all equations are satisfied and rst is equal to 1
Test 3: let t=s=1/2 ans r=-4, all equations are satisfied and rst is equal to 1

So it can't be uniquely established if rst=1 or not, hence, the answer is E.
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Re: Does rst = 1? (1) rs = –1 (2) rt = –1  [#permalink]

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28 Aug 2017, 20:31
Bunuel wrote:
Does rst = 1?

(1) rs = –1
(2) rt = –1

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

There are 3 variables and 0 equation. Thus the answer E is most likely.

Consider both conditions together.
We have two kinds of solutions as follows.

r = 1, s = -1, t = -1. Then we have rst = 1.
r = -1, s = 1, t = 1. The we have rst = -1.
We don't have a unique solution.

Both conditions together are not sufficient.
The answer is E as expected.

For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80 % chance that E is the answer, while C has 15% chance and A, B or D has 5% chance. Since E is most likely to be the answer using 1) and 2) together according to DS definition. Obviously there may be cases where the answer is A, B, C or D.
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Re: Does rst = 1? (1) rs = –1 (2) rt = –1  [#permalink]

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29 Aug 2017, 01:45
Similar question: https://gmatclub.com/forum/is-rst-90398.html
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Re: Does rst = 1? (1) rs = –1 (2) rt = –1   [#permalink] 29 Aug 2017, 01:45
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