Kim has 40 percent more money than Sal and Sal has 20 percent less money than Phil. If Sal and Phil have a combined total of $1.80, how much money does Kim have?


(A) $1.00
(B) $1.12
(C) $1.20
(D) $1.32
(E) $1.40

Source: Test 55, S7, Q12, P28

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Hi All,

This question has a really subtle Number Property rule built into it - THAT rule, when combined with TESTing THE ANSWERS, can help you to quickly answer this question.

First, it's worth noting that answer choices all involve 'cents' as part of the formatting, so we have to calculate down to the penny. We're told that Kim has 40% more money than Sal....Algebraically, that means...

K = 1.4(S)

1.4 = 14/10 = 7/5, so in real-world terms, that means for every 5 cents that Sal has, Kim has 7 cents. This is useful information, since the prompt asks for the amount of money that KIM has and now we know that she has some multiple of 7 cents. Working through the answer choices, there are ONLY 2 answers that are a multiple of 7 cents: Answers B and E. Answer E seems like the 'nicer' answer, so I'll TEST that one first...

Answer E: $1.40

IF....
Kim = $1.40
Sal = $1.00

We're told that Sal has 20% less money than Phil, which would mean that Phil has MORE than $1.00. Combined, Sal and Phil would total OVER $2.00, but the prompt states that their total is $1.80. Since this clearly does NOT match up with what we're told, Answer E is incorrect, which leaves just one answer...

Final Answer:

GMAT assassins aren't born, they're made,
Rich
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If ratios are involved (A has X percent more or less than B = a ratio), the moment we see a "counting number" we should pounce.

Sal and Phil have a combined total of $1.80. Thus: \((S+P)=$1.80\)

And: Sal has 20 percent less money than Phil: \(S = 0.80P\)
Substitute that value for \(S\). Now we have
\(0.8P+P=$1.80\)
\(1.8P=$1.80\)
\(P=\frac{$1.80}{1.8}=$1.00\)

Sal? \(S=0.80P=(0.8*$1.00)=$0.80\)

Kim? She has 40 percent more money than Sal.
\(K=1.4S\)
\(K=(1.4*$0.80)=$1.12\)

Answer B
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P =100,S= 80,K= 80*120/100= 112 ( assume).
P+S= 100+80= 180
So k = 1.8*112/180= 1.12

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