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

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

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New post Updated on: 03 Aug 2015, 00:45
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Question Stats:

41% (02:46) correct 59% (02:29) wrong based on 140 sessions

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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.

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Originally posted by VenoMfTw on 02 Aug 2015, 19:01.
Last edited by Bunuel on 03 Aug 2015, 00:45, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Alex spends 30% of his income on his children’s education, 20% on  [#permalink]

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New post 03 Aug 2015, 00:38
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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
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Re: Alex spends 30% of his income on his children’s education, 20% on  [#permalink]

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New post 03 Aug 2015, 01:38
1
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.



Given Alex spends E 30%, R 20% and H 10% ; Susie spends E 40%, R 25% and H 13%.
What should be inferred is, we do not know that the actual value of Alex and Susie Income, hence depending on that value, the %spending may vary.
Let Alex income be A, and Susie income be S

St 1: Given Alex spends more on recreation than Susie.
i.e, 20% of A > 25% of S
Assume A = 200, S=100, then 40>25. Hence Alex spends more than Susie on Recreation.
Assume A = 125, S= 128, then 25<32, Hence Susie spends more than Alex on Recreation.

Contrasting results, Hence Not sufficient.

St 2: Susie spends more on healthcare than Alex.
i.e, 13% of S > 10% of A. This is only possible when the Income of Susie is more than Alex.

Hence Susie will spend more on Recreation than Alex.

Hence Sufficient.

Option B
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Re: Alex spends 30% of his income on his children’s education, 20% on  [#permalink]

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New post 03 Aug 2015, 04:48
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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New post 03 Aug 2015, 08:32
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1
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.

Answer is B
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Re: Alex spends 30% of his income on his children’s education, 20% on  [#permalink]

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New post 03 Aug 2015, 09:13
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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Re: Alex spends 30% of his income on his children’s education, 20% on  [#permalink]

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Re: Alex spends 30% of his income on his children’s education, 20% on   [#permalink] 02 Dec 2018, 21:56
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