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# Excluding purchases by businesses, the average amount spent

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TaN1213 wrote:
Excluding purchases by businesses, the average amount spent on a factory-new car has risen 30 per- cent in the last five years. In the average household budget, the proportion spent on car purchases has remained unchanged in that period. Therefore the average household budget must have increased by 30 percent over the last five years.

Which of the following is an assumption on which the argument relies?

(A)The average number of factory-new cars purchased per household has remained unchanged over the last five years.

(B)The average amount spent per car by businesses buying factory-new cars has risen 30 percent in the last five years.

(C)The proportion of the average household budgetspent on all car-related expenses has remained unchanged over the last five years.

(D)The proportion of the average household budget spent on food and housing has remained unchanged over the last five years.

(E)The total amount spent nationwide on factory new cars has increased by 30 percent over the last five years.

Clearly A..

let A be not true
If every household is buying two cars on average whereas earlier it was one car, the following will be the case..

Budget 1000 earlier
20% was being spent on car, so 200
each car costed 200 then

but now it has become 200*1.3=260..
and each house buys 2 cars so 260*2=520...
But 520 is 20% still, so 20% of new budget = 520, so budget = 2600
this increase is almost 160% and NOT 30%

so A has to be true
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chetan2u wrote:
TaN1213 wrote:
Excluding purchases by businesses, the average amount spent on a factory-new car has risen 30 per- cent in the last five years. In the average household budget, the proportion spent on car purchases has remained unchanged in that period. Therefore the average household budget must have increased by 30 percent over the last five years.

Which of the following is an assumption on which the argument relies?

(A)The average number of factory-new cars purchased per household has remained unchanged over the last five years.

(B)The average amount spent per car by businesses buying factory-new cars has risen 30 percent in the last five years.

(C)The proportion of the average household budgetspent on all car-related expenses has remained unchanged over the last five years.

(D)The proportion of the average household budget spent on food and housing has remained unchanged over the last five years.

(E)The total amount spent nationwide on factory new cars has increased by 30 percent over the last five years.

Clearly A..

let A be not true
If every household is buying two cars on average whereas earlier it was one car, the following will be the case..

Budget 1000 earlier
20% was being spent on car, so 200
each car costed 200 then

but now it has become 200*1.3=260..
and each house buys 2 cars so 260*2=520...
But 520 is 20% still, so 20% of new budget = 520, so budget = 2600
this increase is almost 160% and NOT 30%

so A has to be true

Could you elaborate on this calculate. I am very curious to learn this.

Sent from my Redmi Note 4 using GMAT Club Forum mobile app
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Option A.

Total money spent on cars , excluding business purchases (X) = Price per car (A) * No. of cars per household (B) * No. of households (C)

Average money spent on cars = X / (B*C) [ This figure has gone up by 30%) .............. (i)

Proportion of car expenses from the average household expense = constant

=> (X/C ) / (Total household expense/C) = constant ........... (ii)

As per the conclusion, the denominator of the above expression = total household expense/C = avg household expense has gone up by 30% ...... (iii)

For the conclusion to be valid, putting (ii) and (iii) together, the numerator X/C also needs to increase by 30%.

Hence in (i), B (no of cars per household) has to be constant

Hope this explains !
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