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hard sufficiency

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hard sufficiency

by coolgirl26 » Sat Apr 18, 2009 5:11 pm
Hi, my friend sent me this problem to solve


X is a 2 digit number.. The ratio of units digit to tens digit is 1 to 2, what is the value of x


1. the sum of digits multipled by tens digit is 54

2. product of digits divided by 2 is 9

the answer is D



Please help me and show me the shortcuts needed to solve this problem..

THanks a bunch
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Source: — Data Sufficiency |
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by Feep » Sat Apr 18, 2009 5:27 pm
Let u = units digit, t = tens digit. Also, we know that t = 2u.

(1) gives us the additional relation of t (t + u) = 54. We have two equations and two unknowns, and so this can be solved. Do I want to solve it? No. But it can be.

(2) gives the additional relation ut/2 = 9, another happy equation, leaving us with two equations and two unknowns. Sufficient.

D.

(Subtle note: it might be worth checking that the two equations do not "row reduce", or rather, are not constant multiples of one another, as if they are, they are considered the same equation. Still, it's fairly obvious here that they are not.)
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by coolgirl26 » Sat Apr 18, 2009 5:42 pm
thank youuu
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by mayuran23 » Sat Apr 18, 2009 8:29 pm
hey guys

i've found that in some DS questions it's much easier to list out the options rather than go through the formula

in this case if the tens digit is twice the units digit, there're only 4 options

21
42
63
84

according to (1), 63 works since 6 * (6+3) = 54; sufficient
according to (2), 6*3 / 2 = 9; sufficient

D
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by Feep » Sat Apr 18, 2009 8:58 pm
Not a bad idea, but remember, you must test all the other solutions as well to make sure they DON'T work in that case. If more than one satisfies the conditions, then the data is insufficient.
I tutor GMAT/GRE level mathematics privately in the Los Angeles region, as well as via Skype for a discounted rate. Send me a message if you're interested.
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