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# John received a 10% raise each month for three consecutive months. Wha

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Math Expert
Joined: 02 Sep 2009
Posts: 46280
John received a 10% raise each month for three consecutive months. Wha [#permalink]

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10 Jan 2016, 08:27
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5% (low)

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97% (00:40) correct 3% (00:37) wrong based on 76 sessions

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John received a 10% raise each month for three consecutive months. What was his salary after the three raises if his starting salary was $1,000 per month? A.$1,248
B. $1,300 C.$1,331
D. $1,410 E.$1,463

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Re: John received a 10% raise each month for three consecutive months. Wha [#permalink]

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10 Jan 2016, 08:42
1,000 + 100 (10%) = 1,100
1,100 + 110 (10%) = 1,210
1,210 + 121 (10%) = 1,331

Ans C
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Re: John received a 10% raise each month for three consecutive months. Wha [#permalink]

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16 May 2016, 13:25
1000 * 1.1 * 1.1 * 1.1 = 1000 * 1.331 = 1331
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John received a 10% raise each month for three consecutive months. Wha [#permalink]

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28 May 2017, 19:08
We can consider the 10 percent increase as of following: $$\frac{11}{10} *\frac{11}{10}*\frac{11}{0} or (\frac{11}{10})^3$$

$$(\frac{11}{10}*\frac{11}{10}*\frac{11}{10})*1000=1331$$

The correct option: C
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Re: John received a 10% raise each month for three consecutive months. Wha [#permalink]

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04 Sep 2017, 21:51
Bunuel - How can I apply this consecutive interest/rate changes formula below to problems like this?

a+b+$$\frac{ab}{100}$$. Or is it that this formula applies only when there are two consecutive rate/interest changes? TIA.
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Re: John received a 10% raise each month for three consecutive months. Wha [#permalink]

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04 Sep 2017, 22:12
Bunuel wrote:
John received a 10% raise each month for three consecutive months. What was his salary after the three raises if his starting salary was $1,000 per month? A.$1,248
B. $1,300 C.$1,331
D. $1,410 E.$1,463

We can apply the concept of CI as the 10% raise each month is on the salary of that month. And each month's salary includes last month's salary plus the 10% hike.

Thus, applying CI formula,
Amount = P[1+(10/100)]^3
= 1000(11/10)^ 3 = 1331.

Sent from my iPhone using GMAT Club Forum mobile app
Math Expert
Joined: 02 Sep 2009
Posts: 46280
Re: John received a 10% raise each month for three consecutive months. Wha [#permalink]

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04 Sep 2017, 23:50
Blackbox wrote:
Bunuel - How can I apply this consecutive interest/rate changes formula below to problems like this?

a+b+$$\frac{ab}{100}$$. Or is it that this formula applies only when there are two consecutive rate/interest changes? TIA.

Yes, $$a+b+\frac{ab}{100}$$ gives the effective percentage change over TWO periods, not three. So, for this problem if it were "...for TWO consecutive months...", then the effective percentage change would be $$a+b+\frac{ab}{100}=10+10+\frac{100}{100}=21\%$$. But you can find it directly with 1.1^2 = 1.21. So, you should use this formula if there are two periods and a and b are different from each other.

For more check "Successive Percentage Changes" chapter in Percentages, Interest and More.

Hope it helps.
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Re: John received a 10% raise each month for three consecutive months. Wha [#permalink]

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05 Sep 2017, 00:41
Bunuel wrote:
John received a 10% raise each month for three consecutive months. What was his salary after the three raises if his starting salary was $1,000 per month? A.$1,248
B. $1,300 C.$1,331
D. $1,410 E.$1,463

1,000*1.1^3=1,331
Manager
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Concentration: Finance, Marketing
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John received a 10% raise each month for three consecutive months. Wha [#permalink]

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05 Sep 2017, 06:30
Bunuel wrote:
Blackbox wrote:
Bunuel - How can I apply this consecutive interest/rate changes formula below to problems like this?

a+b+$$\frac{ab}{100}$$. Or is it that this formula applies only when there are two consecutive rate/interest changes? TIA.

Yes, $$a+b+\frac{ab}{100}$$ gives the effective percentage change over TWO periods, not three. So, for this problem if it were "...for TWO consecutive months...", then the effective percentage change would be $$a+b+\frac{ab}{100}=10+10+\frac{100}{100}=21\%$$. But you can find it directly with 1.1^2 = 1.21. So, you should use this formula if there are two periods and a and b are different from each other.

For more check "Successive Percentage Changes" chapter in Percentages, Interest and More.

Hope it helps.

Thank you for the explanation.
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Re: John received a 10% raise each month for three consecutive months. Wha [#permalink]

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07 Sep 2017, 16:48
Bunuel wrote:
John received a 10% raise each month for three consecutive months. What was his salary after the three raises if his starting salary was $1,000 per month? A.$1,248
B. $1,300 C.$1,331
D. $1,410 E.$1,463

John’s salary after 3 months is 1000(11/10)(11/10)(11/10) = 11 x 11 x 11 = \$1331.

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Re: John received a 10% raise each month for three consecutive months. Wha   [#permalink] 07 Sep 2017, 16:48
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