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Henry purchased 3 items during a sale. He received a 20 percent discou 18 Sep 2022, 08:59
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DrVanNostrand
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Henry purchased 3 items during a sale. He received a 20 percent discount off the regular price of the most expensive item and a 10 percent discount off the regular price of each of the other 2 items. Was the total discount of these three items greater than 15 percent of the sum of the regular prices of the 3 items?

(1) The regular price of the most expensive item was $50, and the regular price of the next most expensive item was $20
(2) The regular price of the least expensive item was $15

Let the regular prices be a, b, and c, so that a > b > c.

Basically the questions: is \(0.2a+0.1b+0.1c>0.15(a+b+c)\)? --> is \(a>b+c\)?

(1) The regular price of the most expensive item was $50 and the regular price of the next most expensive item was $20 --> \(a=50\), \(b=20\), \(c\leq{20}\) (as the second most expensive item was $20 then the least expansive item, the third one, must be less than or equal to 20). So the question becomes: is \(50>20+c\) --> is \(c<30\)? As we got that \(c\leq{20}\), hence the above is always true. Sufficient.

(2) The regular price of the least expensive item was $15. Clearly insufficient.

Answer: A.


Hi Bunuel. First of all, thanks for the tremendous help that you have been providing to us all.

Coming back to the question, I don't think the answer is A ( it should be C ). Algebraically, what you have said is right. However, if we take specific numerical values, the answer ranges from "Yes" ( for c= 20 ) to "No" ( for c = 10 ). Also, inequality provides us with a range of values. For some, the answer is ">15%" and for some that sanwer is "<15%".

Kindly explain.
Show more

Answer is A. Imagine A=50 B=20 C=20, when you calculate the total discount of the sum you do 90*0.15%= 13.5 . the discount of ABC is 14. so 14>13.5 . What happens if you reduce C? 14 goes down, but 13.5 goes down as well, as it is not 90*0.15% anymore, you'll have to subtract from 90 the same amount you subtract from C. Therefore A.
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Henry purchased 3 items during a sale. He received a 20 percent discou 08 Jan 2024, 05:05
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docabuzar
Henry purchased 3 items during a sale. He received a 20 percent discount off the regular price of the most expensive item and a 10 percent discount off the regular price of each of the other 2 items. Was the total amount of the 3 discounts greater than 15 percent of the sum of the regular prices of the 3 items?


(1) The regular price of the most expensive item was $50, and the regular price of the next most expensive item was $20

(2) The regular price of the least expensive item was $15


Show Spoiler
Attachment:
Henry discount on items.GIF
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Hi KarishmaB
Could you kindly explain this question with Weight Average or Allegation method please?
Thanks
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Henry purchased 3 items during a sale. He received a 20 percent discou 08 Jan 2024, 05:30
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Kimberly77
docabuzar
Henry purchased 3 items during a sale. He received a 20 percent discount off the regular price of the most expensive item and a 10 percent discount off the regular price of each of the other 2 items. Was the total amount of the 3 discounts greater than 15 percent of the sum of the regular prices of the 3 items?


(1) The regular price of the most expensive item was $50, and the regular price of the next most expensive item was $20

(2) The regular price of the least expensive item was $15


Show Spoiler
Attachment:
Henry discount on items.GIF

Hi KarishmaB
Could you kindly explain this question with Weight Average or Allegation method please?
Thanks
Show more

This is a 0 calculation 30 sec question in case you use weighted averages.

20% discount on the most expensive item
10% discount on the two cheaper ones

Discounts are given on regular prices (marked prices) of items so weights will be the regular prices.
When will the overall discount be 15%? When the weights of the two are equal (right in the centre of 20 and 10). This means that if the price of the most expensive item is equal to the price of the other two items combined, then overall discount will be 15%.

(1) The regular price of the most expensive item was $50, and the regular price of the next most expensive item was $20

This tells us that the price of the most expensive was $50 but the price of the next most expensive was $20 so the price of the cheapest item will be less than $20. Hence price of the two cheaper items will certainly be less than $50. Hence the average discount will be closer to 20% than to 10% i.e. the overall discount will be more than 15%. We can answer 'Yes'.
This statement alone is sufficient.

(2) The regular price of the least expensive item was $15

We don't know the prices of the other two items. Hence we cannot say what the overall discount will be.
This statement alone is not sufficient.

Answer (A)

Check this video for more on weighted averages and how to use them: https://youtu.be/_GOAU7moZ2Q
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Henry purchased 3 items during a sale. He received a 20 percent discou 18 Jan 2024, 00:55
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KarishmaB
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docabuzar
Henry purchased 3 items during a sale. He received a 20 percent discount off the regular price of the most expensive item and a 10 percent discount off the regular price of each of the other 2 items. Was the total amount of the 3 discounts greater than 15 percent of the sum of the regular prices of the 3 items?


(1) The regular price of the most expensive item was $50, and the regular price of the next most expensive item was $20

(2) The regular price of the least expensive item was $15


Show Spoiler
Attachment:
Henry discount on items.GIF

Hi KarishmaB
Could you kindly explain this question with Weight Average or Allegation method please?
Thanks

This is a 0 calculation 30 sec question in case you use weighted averages.

20% discount on the most expensive item
10% discount on the two cheaper ones

Discounts are given on regular prices (marked prices) of items so weights will be the regular prices.
When will the overall discount be 15%? When the weights of the two are equal (right in the centre of 20 and 10). This means that if the price of the most expensive item is equal to the price of the other two items combined, then overall discount will be 15%.

(1) The regular price of the most expensive item was $50, and the regular price of the next most expensive item was $20

This tells us that the price of the most expensive was $50 but the price of the next most expensive was $20 so the price of the cheapest item will be less than $20. Hence price of the two cheaper items will certainly be less than $50. Hence the average discount will be closer to 20% than to 10% i.e. the overall discount will be more than 15%. We can answer 'Yes'.
This statement alone is sufficient.

(2) The regular price of the least expensive item was $15

We don't know the prices of the other two items. Hence we cannot say what the overall discount will be.
This statement alone is not sufficient.

Answer (A)

Check this video for more on weighted averages and how to use them: https://youtu.be/_GOAU7moZ2Q
Show more

Brilliant explanation always KarishmaB thanks.
One question regarding 10% discount on the two cheaper ones, not sure why are we only using 10 for thinking here in below sentence and not 20 (as it's 10% each for 2 items) or other numbers ? Could you help clarify? Thanks

When will the overall discount be 15%? When the weights of the two are equal (right in the centre of 20 and 10)
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Brilliant explanation always KarishmaB thanks.
One question regarding 10% discount on the two cheaper ones, not sure why are we only using 10 for thinking here in below sentence and not 20 (as it's 10% each for 2 items) or other numbers ? Could you help clarify? Thanks

When will the overall discount be 15%? When the weights of the two are equal (right in the centre of 20 and 10)
Show more

It comes down to knowing what the weights are in weighted averages. When we are averaging discount percentages, the weights will be marked price.

Discount percentage = Discount/Marked price

You should check this post first if you haven't seen it: https://anaprep.com/arithmetic-weights- ... d-average/

So it doesn't matter whether we have 1 item or 2 items or 4. What matters is the overall marked price on which we are giving the discount.

So if there are two discounts 20% and 10% and they average out to 15%, it means that the marked price on which 20% was given was equal to marked price on which 10% was given say $100 each. So 20% on 100 is $20 and 10% on 100 is $10 and overall we have $30 on $200 which is a discount of 15%.

It does not matter how many items there were. Say there was 1 item with marked price $100 on which 20% was given and there were 2 items with marked price $50 each on which 10% was given. Still discount would be 20 + 5 + 5 = $30 on marked price of $200 giving a 15% overall discount.
Even if we say we had 4 of the cheaper items of $25 each, still the logic stays the same.
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Henry purchased 3 items during a sale. He received a 20 percent discou 18 Jan 2024, 02:22
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KarishmaB
Kimberly77

Brilliant explanation always KarishmaB thanks.
One question regarding 10% discount on the two cheaper ones, not sure why are we only using 10 for thinking here in below sentence and not 20 (as it's 10% each for 2 items) or other numbers ? Could you help clarify? Thanks

When will the overall discount be 15%? When the weights of the two are equal (right in the centre of 20 and 10)

It comes down to knowing what the weights are in weighted averages. When we are averaging discount percentages, the weights will be marked price.

Discount percentage = Discount/Marked price

You should check this post first if you haven't seen it: https://anaprep.com/arithmetic-weights- ... d-average/

So it doesn't matter whether we have 1 item or 2 items or 4. What matters is the overall marked price on which we are giving the discount.

So if there are two discounts 20% and 10% and they average out to 15%, it means that the marked price on which 20% was given was equal to marked price on which 10% was given say $100 each. So 20% on 100 is $20 and 10% on 100 is $10 and overall we have $30 on $200 which is a discount of 15%.

It does not matter how many items there were. Say there was 1 item with marked price $100 on which 20% was given and there were 2 items with marked price $50 each on which 10% was given. Still discount would be 20 + 5 + 5 = $30 on marked price of $200 giving a 15% overall discount.
Even if we say we had 4 of the cheaper items of $25 each, still the logic stays the same.
Show more

Brilliant thanks KarishmaB and get it.
What an innovative way of your solutions always !!!
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Why is the 2 not sufficient. How are we straight away deciding its not sufficient
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viswanath1

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Henry purchased 3 items during a sale. He received a 20 percent discount off the regular price of the most expensive item and a 10 percent discount off the regular price of each of the other 2 items. Was the total discount of these three items greater than 15 percent of the sum of the regular prices of the 3 items?

(1) The regular price of the most expensive item was $50, and the regular price of the next most expensive item was $20
(2) The regular price of the least expensive item was $15

Let the regular prices be a, b, and c, so that a > b > c.

Basically the questions: is \(0.2a+0.1b+0.1c>0.15(a+b+c)\)? --> is \(a>b+c\)?

(1) The regular price of the most expensive item was $50 and the regular price of the next most expensive item was $20 --> \(a=50\), \(b=20\), \(c\leq{20}\) (as the second most expensive item was $20 then the least expansive item, the third one, must be less than or equal to 20). So the question becomes: is \(50>20+c\) --> is \(c<30\)? As we got that \(c\leq{20}\), hence the above is always true. Sufficient.

(2) The regular price of the least expensive item was $15. Clearly insufficient.

Answer: A.
Why is the 2 not sufficient. How are we straight away deciding its not sufficient
Show more

Because Statement (2) only tells us the least expensive item is $15 (c = 15), but we know nothing about the prices of the other two items. So we cannot evaluate whether the total discount is more than 15% of the total regular price. Without knowing a and b, the question cannot be answered.

You can go through the full thread for a detailed breakdown and examples.
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This can also be looked at as a weighted average question. Given the percent discounts on each of the items if each of the items are priced equally then the average % discount will be slightly greater than 13%. Option A tells us that the most expensive item is discounted the most therefore this is sufficient.
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