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Retired Moderator
Joined: 07 Jun 2014
Posts: 4806
GRE 1: Q167 V156
WE:Business Development (Energy and Utilities)
Aloysius spends 50% of his income on rent, utilities, and
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02 Jun 2018, 03:41
02 Jun 2018, 03:41
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Question Stats:
75% (00:50) correct
24% (00:45) wrong based on 65 sessions
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Aloysius spends 50% of his income on rent, utilities, and insurance, and 20% on food. If he spends 30% of the remainder on video games and has no other expenditures, what percent of his income is left after all of the expenditures?
(A) 30%
(B) 21%
(C) 20%
(D) 9%
(E) 0%
_________________
(A) 30%
(B) 21%
(C) 20%
(D) 9%
(E) 0%
_________________
Sandy
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Re: Aloysius spends 50% of his income on rent, utilities, and
[#permalink]
03 Jun 2018, 08:23
03 Jun 2018, 08:23
Let us say Aloysius income is x then,
50% is spent on rent
20% is spent on food
Therefore, 70% is spent in total before anything is spent on video games.
Remaining = 100-70 = 30%
Out of this 30% is spent on video games
Therefore, Final Remaining income = 70% of 0.30x = 0.30x * 0.70 = 0.21 or 21%
_________________
50% is spent on rent
20% is spent on food
Therefore, 70% is spent in total before anything is spent on video games.
Remaining = 100-70 = 30%
Out of this 30% is spent on video games
Therefore, Final Remaining income = 70% of 0.30x = 0.30x * 0.70 = 0.21 or 21%
_________________
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Retired Moderator
Joined: 07 Jun 2014
Posts: 4806
GRE 1: Q167 V156
WE:Business Development (Energy and Utilities)
Re: Aloysius spends 50% of his income on rent, utilities, and
[#permalink]
11 Jul 2018, 15:49
11 Jul 2018, 15:49
Expert Reply
Explanation
The 50% spent on rent, utilities, and insurance and the 20% spent on food are both percents of the total, so sum the percents: 50% + 20% = 70%. After these expenditures, Aloysius has 30% left.
He then spends 30% of the remaining 30% on video games. 30% of 30% = 0.30 × 0.30 = 0.09, or 9% of the total, so 30% – 9% = 21% of his income remains.
Alternatively, use smart numbers. If Aloysius’s income is $100, he would spend $50 on rent, utilities, and insurance, and $20 on food, for a total of $70. Of his remaining $30, he would spend 30%, or $9, on video games, leaving $21, or 21%, of the original amount.
_________________
The 50% spent on rent, utilities, and insurance and the 20% spent on food are both percents of the total, so sum the percents: 50% + 20% = 70%. After these expenditures, Aloysius has 30% left.
He then spends 30% of the remaining 30% on video games. 30% of 30% = 0.30 × 0.30 = 0.09, or 9% of the total, so 30% – 9% = 21% of his income remains.
Alternatively, use smart numbers. If Aloysius’s income is $100, he would spend $50 on rent, utilities, and insurance, and $20 on food, for a total of $70. Of his remaining $30, he would spend 30%, or $9, on video games, leaving $21, or 21%, of the original amount.
_________________
Sandy
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Re: Aloysius spends 50% of his income on rent, utilities, and
[#permalink]
20 Jul 2018, 09:43
20 Jul 2018, 09:43
sandy wrote:
Aloysius spends 50% of his income on rent, utilities, and insurance, and 20% on food. If he spends 30% of the remainder on video games and has no other expenditures, what percent of his income is left after all of the expenditures?
(A) 30%
(B) 21%
(C) 20%
(D) 9%
(E) 0%
(A) 30%
(B) 21%
(C) 20%
(D) 9%
(E) 0%
Total income : 100
Rent m utilities = 50
Food = 20
Remaining = 100 - 50 - 20 =30
video games = 30*30% = 9
So, (30-9) = 21
The correct answer is B.
Re: Aloysius spends 50% of his income on rent, utilities, and
[#permalink]
21 Jun 2023, 05:50
21 Jun 2023, 05:50
To solve this problem, we can first calculate the total percentage of Aloysius’ income that he spends on rent, utilities, insurance, and food. This is 50% + 20% = 70%. This means that he has 100% - 70% = 30% of his income left after these expenditures. He then spends 30% of this remainder on video games, which is equal to 0.3 * 30% = 9%. Therefore, after all of the expenditures, Aloysius has 30% - 9% = 21% of his income left. So the correct answer is (B) 21%.
gmatclubot
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