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Intern  Joined: 25 Jun 2013
Posts: 14
Concentration: General Management, Operations
GMAT 1: 690 Q47 V38 GPA: 3.2
WE: Account Management (Computer Software)
The price of sugar is increased by 7%. By how much percent  [#permalink]

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Difficulty:   75% (hard)

Question Stats: 52% (01:43) correct 48% (01:41) wrong based on 251 sessions

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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)%
Math Expert V
Joined: 02 Sep 2009
Posts: 58453
Re: The price of sugar is increased by 7%. By how much percent  [#permalink]

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DarkKnight06 wrote:
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)%

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%.

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.
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Re: The price of sugar is increased by 7%. By how much percent  [#permalink]

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Bunuel wrote:
DarkKnight06 wrote:
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)%

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%.

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.

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%
Board of Directors P
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Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30 GPA: 3.92
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Re: The price of sugar is increased by 7%. By how much percent  [#permalink]

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did half the work, and marked 100/107 ..eh..dumb me..
should have read the question more attentively..A is the correct answer.
Director  G
Joined: 23 Jan 2013
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Schools: Cambridge'16
Re: The price of sugar is increased by 7%. By how much percent  [#permalink]

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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
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Joined: 22 Jan 2014
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WE: Project Management (Computer Hardware)
Re: The price of sugar is increased by 7%. By how much percent  [#permalink]

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DarkKnight06 wrote:
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)%

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 %
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: The price of sugar is increased by 7%. By how much percent  [#permalink]

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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...

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Intern  B
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Schools: Queen's MBA'20
GMAT 1: 610 Q44 V30 GMAT 2: 650 Q44 V35 GRE 1: Q160 V150 GPA: 3
Re: The price of sugar is increased by 7%. By how much percent  [#permalink]

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DarkKnight06 wrote:
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)%

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
Manager  P
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The price of sugar is increased by 7%. By how much percent  [#permalink]

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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
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Re: The price of sugar is increased by 7%. By how much percent  [#permalink]

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DarkKnight06 wrote:
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)%

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 Re: The price of sugar is increased by 7%. By how much percent   [#permalink] 14 Sep 2019, 04:18
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