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# Alex spends 30% of his income on his children’s education, 20% on

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Re: Alex spends 30% of his income on his children’s education, 20% on [#permalink]
anceer wrote:
In simple approach we have to compare health care to health care i.e. 30% to 40%.
We have a reference of recreation 20% to 25%
and healthcare 10% to 13%.

From statement 1
A’s 20% > S’s 25%
So A’s 30% must be > S’s 37.5%

Whereas Susie spends 40%, we have an answer.

From statement 2
A’s 10% < S’s 13%
So A’s 30% must be < S’s 39%

So I think we can get an answer from statement 2

Finally both the answer from st 1 and st 2 contradicts each other.
CAN ANY ONE EXPLAIN WHAT IS WRONG IN THIS APPROACH

Look below for the comments for the mistaken assumptions:

Per statement 1, 0.2A>0.25B --> A>1.25 B

What the question is asking : which one is greater ? 0.3A or 0.4B ?? ---> 0.3A > 0.4 B ONLY IF A > 1.33 B but per statement 1 A>1.25 B . SO A may or may be not > 1.33 B . What if A = 1.3 B (NO) or A = 1.27 B (NO) or A = 1.4 B (Yes). Thus you do not get a definite answer as to which one is greater.

Per statement 2, 0.13B>0.1A ---> B>0.77 A and from out analysis in statement 1 , 0.3A > 0.4 B ONLY IF A > 1.33 B or B > 0.7 A which we get from statement 2. Thus statement 2 is sufficient.

Hence B is the correct answer. Statement 2 says A< 1.3 B while statement says A>1.25 B . How are they contradictory? The value of A could = 1.28 B .

Hope this helps.
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Re: Alex spends 30% of his income on his children’s education, 20% on [#permalink]
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Just reading the stimulus without looking at the Statements, we can re-phrase the question to be How much werre Alex and Susie's incomes. That would solve the problem for us. Additionally, we might be able to solve the problem if we can figure out their incomes relative to each other.

Now, understanding that the information in each statement is FACTUAL, Stmt 1 tells us that Alex spent more \$ on recreation than Susie. So, algebraically, we can say 0.2A > 0.25S. Manipulating the inequality will give us either A > 1.25S, or 0.8A > B. What we are trying to answer though is 0.3A greater than or less than 0.4S. Using the same algebraic manipulation, we get A in terms of B as A is either greater or less than 1.33B. Using Stmt 1, we know A > 1.25B. But, do we know whether A > 1.33B? No, we cannot definitivelt say this - thus, Stmt 1 is NOt SUFFICIENT

Stmt 2, which is also FACTUAL, tells us that 0.1A < 0.13B. Manipulating this like above, we get that A < 1.3B. From the initial question, we are asked (putting it in the algebraic terms) is A is greater or less than 1.33B. Stmt 2 answers this. Stmt 2 is SUFFICIENT.

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Re: Alex spends 30% of his income on his children’s education, 20% on [#permalink]
anceer wrote:
In simple approach we have to compare health care to health care i.e. 30% to 40%.
We have a reference of recreation 20% to 25%
and healthcare 10% to 13%.

From statement 1
A’s 20% > S’s 25%
So A’s 30% must be > S’s 37.5%
Whereas Susie spends 40%, we have an answer.

From statement 2
A’s 10% < S’s 13%
So A’s 30% must be < S’s 39%
So I think we can get an answer from statement 2

Finally both the answer from st 1 and st 2 contradicts each other.
CAN ANY ONE EXPLAIN WHAT IS WRONG IN THIS APPROACH

anceer

Statement 1 :
0.2 A > 0.25 B
20 A > 25 B
A > 1.25 B

Now coming to the question steam amount spent on children
3A and 4S
From st 1 we get A > 1.25 B
So if A = 1.3B then 3A = 3.9S ==> Thus 3A(3.9S) < 4S
If A = 2B Then 3A = 6S --> Thus 3A(6S) > 4S

We end up with 2 different possibilities.
Hence not suff.

Hope it is clear
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Alex spends 30% of his income on his children’s education, 20% on [#permalink]
VenoMfTw wrote:
Alex spends 30% of his income on his children’s education, 20% on recreation and 10% on healthcare. The corresponding percentage for Susie are 40%, 25%, and 13%. Who spends more on children’s education?

(1) Alex spends more on recreation than Susie.
(2) Susie spends more on healthcare than Alex.

Let the income of Alex and Susie be A and S.
Children’s education: Alex spends 30%, and Susie spends 50%.
So we are looking at whether 30% of A is greater than 40% of S.

$$\frac{30A}{100}>\frac{40S}{100}$$

Is $$\frac{A}{S}>\frac{4}{3}=1.33$$?

(1) Alex spends more on recreation than Susie.

Recreation : Alex spends 20%, and Susie spends 25%.

$$\frac{20A}{100}>\frac{25S}{100}$$

$$\frac{A}{S}>\frac{5}{4}=1.25$$
So if A/S is 1.5, then yes. But A/S can also be 1.26, then no.
Insufficient

(2) Susie spends more on healthcare than Alex.
Healthcare: Alex spends 10%, and Susie spends 13%.

$$\frac{10A}{100}<\frac{13S}{100}$$

$$\frac{A}{S}<\frac{13}{10}=1.3$$
But 1.3<1.33, so our answer is always NO.
Sufficient

B
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Re: Alex spends 30% of his income on his childrens education, 20% on [#permalink]
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Re: Alex spends 30% of his income on his childrens education, 20% on [#permalink]
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