The price of sugar is increased by 7%. By how much percent

Question

The price of sugar is increased by 7%. By how much percent should a home maker reduce her consumption of sugar to have no extra expenditure?

A. (700/107) %
B. (107/100) %
C. (100/107)%
D. (7/100)%
E. (100/700)%

Bunuel · Accepted Answer

Old price = $100 (assume);
Old consumption = 1 kg (assume).

New price = $107.

We want the spendings to remain at $100.
(New consumption)*107 = 100 --> (New consumption) = 100/107 kg.

Percent decrease = Change/Original *100 = (1 - 100/107)/1*100 = 700/107%.

Answer: A.

Else you can notice that the decrease in consumption must be very close to 7% (a bit less) and taking this into account only A makes sense.

vietnammba · Answer

Hi Bunuel,

Is this approach correct:

Old price: P
Old consumption: C
New Price: 107/100P
New consumption: C* (1-x) in which x is the percentage of change
PC = 107/100P* C *(1-x) => 107/100*(1-x) = 1 
1-x=100/107
x= 1-100/107 = 7/107
x% = 700/107%

mvictor · Answer

did half the work, and marked 100/107 ..eh..dumb me..
should have read the question more attentively..A is the correct answer.

Temurkhon · Answer

price and consumption are reversely proportional if spending is the same.

if price increases 107/100 times, consumption decreases 107/100 times, so final consumption becomes 100/107 of initial

107/107-100/107=7/107 => (7/107)*100/1=700/107

A

thefibonacci · Answer

assume she got 100 kg for 100 rs 
after increase in price she will get 100 kg for 107 rs 
she has to spend 100 rs only, so at new price she gets (100*100/107) for 100 rs
% change = 100 - (100*100/107) = 700/107 %

EMPOWERgmatRichC · Answer

Hi All,

The answer choices to this question are written in such a way that you can avoid most of the 'math work' and answer this question with a bit of logic.

We're told that the price of sugar is increased by 7%. We're asked by what percent a home maker should reduce her consumption of sugar to have no extra expenditure. In real basic terms, we need to reduct the amount of sugar by a certain percent so that no extra money is spent.

Since the price of sugar increased by 7%, we'll have to decrease the consumption by a value that's relatively close to 7% (but NOT 7% exactly). Now look at the answers and really think about what they 'translate' into:

A. (700/107) % = a little less than 7%
B. (107/100) % = a little more than 1%
C. (100/107)% = a little less than 1%
D. (7/100)% = less than 1/10 of 1%
E. (100/700)% = 1/7 of 1%

There's only one answer choice that makes any sense given the situation described...

Final Answer:  A

GMAT assassins aren't born, they're made,
Rich

naturalimproviser · Answer

Easy enough!

Just remember the formula - 
  
" If the price of an item goes up/down by x%, then the quantity consumed should be increased/reduced by (100x/(100+/-x))% so that the total expenditure remains the same."

That would be - 
(7*100/100+7)%
= (700/107)% 
 Option A

nigina93 · Answer

This can be solved with substituting numbers, (credits go to @rahul2013)
100usd per 1kg. I consume 10kg, so spend 1000 usd. Now, the price is 107, so 1000 (my total budget)/107=9.35kg now I can consume. 10kg-9.35=0.65*100%=6.35% or A

Archit3110 · Answer

let price of sugar be 100
new price ; 107
initial consumption of sugar was 1 kg so expenditure ; 100
now; new consumption*107=100
new consumption=100/107
% ∆ ; 1-100/107 /100 = 700/107%
IMO A

CrackverbalGMAT · Answer

This question is a special case of percentage increase and decrease. (There are 2 of them)

Since she has to reduce the consumption, we have to find the % decrease.

Let Original price = 100. Therefore New price = 107

% Decrease =  \frac{Difference}{Larger \space Number} * 100 = \frac{7}{107} * 100 = \frac{700}{107} %

Option A

Arun Kumar

Abhishek009 · Answer

7/(100+7)*100 = 700/107 %, Answer must be (A) { THere exists the shortcut formula}

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The price of sugar is increased by 7%. By how much percent

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