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# If r, s, t are different 1-digit positive integer and (ab) is defined

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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If r, s, t are different 1-digit positive integer and (ab) is defined [#permalink]

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06 Apr 2016, 05:33
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Question Stats:

51% (02:14) correct 49% (02:08) wrong based on 57 sessions

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If r, s, t are different 1-digit positive integer and (ab) is defined as 2-digit integer such that a is the tens digit and b is the units digit, t=?

1) The product of s and (rs) is (st)
2) The sum of s and (rs) is (rt)

* A solution will be posted in two days.
[Reveal] Spoiler: OA

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Manager
Joined: 24 Aug 2016
Posts: 68
Location: India
WE: Information Technology (Computer Software)
Re: If r, s, t are different 1-digit positive integer and (ab) is defined [#permalink]

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25 Sep 2016, 06:07
1) The product of s and (rs) is (st)

$$s * rs = st$$
==> $$s * ( 10*r + s) = s*10 + t$$
==> $$10rs + s^2 = 10s + t$$
==> $$10rs = 10s , s^2=t$$
==> $$r =1 , t = s^2$$ --{2,4} , { 3,9} , {1,1} -- Insufficient

2) The sum of s and (rs) is (rt)

$$s + rs = rt$$
==> $$s + r*10 + s = r*10 + t$$
==> $$r*10 + 2s = r*10 + t$$
==> $$r=2s$$ --{1,2} , { 2,4} , { 3,6} , { 4,8} -- Insufficient

If we combine (1) and (2) only {2,4} satisfies both the equation. t=4.

Ans. C
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Joined: 05 Jan 2017
Posts: 434
Location: India
Re: If r, s, t are different 1-digit positive integer and (ab) is defined [#permalink]

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23 Feb 2017, 03:51
PROMPT ANALYSIS
r, s,t are 1 digit natural number.

SUPERSET

The value of t could be from 1 to 9.

TRANSLATION
In order to find the value, we need:
Exact value of t.
Any equation to solve for t.
Any characteristics of t.

STATEMENT ANALYSIS

We will try to analyze with the help of cases.
St 1: Case#1: value of s = 3 and r =1, we get st = 39
Case #2: s=2 and r =1 we get st = 24. INSUFFICIENT. Option a and d eliminated.

St 2: Case#1: value of s = 3 and r =1, we get st = 16
Case #2: s=2 and r =1 we get st = 14. INSUFFICIENT. Option b eliminated.

ST 1 and St 2: combining the statement, we see that s*s is t and s+s is t. This can only happen if s =2, hence t =4. ANSWER.
Option C.
Re: If r, s, t are different 1-digit positive integer and (ab) is defined   [#permalink] 23 Feb 2017, 03:51
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