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805+ (Hard)|   Tables|            
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ashutosh_73
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For each of 18 recent purchases that included each of Products AD Updated on: 15 Sep 2026, 12:38
Originally posted by ashutosh_73 on 17 Mar 2024, 21:36.
Last edited by Bunuel on 15 Sep 2026, 12:38, edited 1 time in total.
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Product A: Sufficient Product B: Sufficient Product C: Sufficient
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

95% (hard)

Question Stats:

64% (02:56) correct 36% (03:05) wrong based on 1068 sessions

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For each of 18 recent purchases that included each of Products A–D, the table shows the product subtotals (the unit price for that product multiplied by the number of units bought as part of that purchase). For example, the table shows that, in the purchase corresponding to Receipt 1, €14.0 of the total purchase was due to the purchase of units of Product D. For each product, the number of units bought was always an integer and the unit price was the same for each of the 18 purchases.

Product subtotals (in €)
ReceiptABCD
160502414
260352163
357101859.5
45430321
55427.516.535
648151270
742453049
836302417.5
936202735
1030501249
11247.52442
1218451256
1318301249
141825963
151851814
161242.51835
17123067
186401870

For each of the following products, select Sufficient if the information provided is sufficient to determine whether the unit price of the product exceeds €3. Otherwise, select Insufficient.
Sufficient Insufficient
Product A
Product B
Product C
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Product A: Sufficient Product B: Sufficient Product C: Sufficient
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For each of 18 recent purchases that included each of Products AD 30 Jul 2024, 23:28
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ashutosh_73
For each of 18 recent purchases that included each of Products A–D, the table shows the product subtotals (the unit price for that product multiplied by the number of units bought as part of that purchase). For example, the table shows that, in the purchase corresponding to Receipt 1, €14.0 of the total purchase was due to the purchase of units of Product D. For each product, the number of units bought was always an integer and the unit price was the same for each of the 18 purchases.



For each of the following products, select Sufficient if the information provided is sufficient to determine whether the unit price of the product exceeds €3. Otherwise, select Insufficient.

­
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­The units of any product bought are a positive integer value.

Product A - In a receipt, someone bought x units and gave €54. In another receipt, someone bought more than x units and gave €57.
This means that the one who gave €3 extra bought 1 or 2 or 3 or 4 or 5 etc. units of A extra.
So cost of each unit of A is at most €3 and can go down to €0.01 per unit theoretically. Hence cost of each unit of A is not more than €3.
Select Sufficient

Product B - In a receipt, someone bought x units and gave €27.5. In another receipt, someone bought more than x units and gave €30.
This means that the one who gave €2.5 extra bought 1 or 2 or 3 or 4 or 5 etc. units of B extra.
So cost of each unit of B is at most €2.5 and can go down to €0.01 per unit theoretically. Hence cost of each unit of B is not more than €3.
Select Sufficient

Product C - In a receipt, someone bought x units and gave €16.5. In another receipt, someone bought more than x units and gave €18.
This means that the one who gave €1.5 extra bought 1 or 2 or 3 or 4 or 5 etc. units of C extra.
So cost of each unit of C is at most €1.5 and can go down to €0.01 per unit theoretically. Hence cost of each unit of C is not more than €3.
Select Sufficient
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For each of 18 recent purchases that included each of Products AD 18 Mar 2024, 04:13
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Product A

Check Receipt 3 in which total spend for Product A is 57 which is 19*3 (both prime numbers)
All numbers in Product A column are multiples of 3
i.e. Each product price must be €3
SUFFICIENT

Product B

Check Receipt 5, 11, 15 in which total spend for Product B are 27.5, 7.5, 5 i.e. GCD is 2.5
All numbers in Product B column are multiples of 2.5
i.e. Each product price must be €2.5
SUFFICIENT

Product C

Check Receipt 4 & 5 in which total spend for Product C are 3 and 16.5 i.e. GCD is 1.5
All numbers in Product A column are multiples of 1.5
i.e. Each product price must be €1.5
SUFFICIENT
ashutosh_73
For each of 18 recent purchases that included each of Products A–D, the table shows the product subtotals (the unit price for that product multiplied by the number of units bought as part of that purchase). For example, the table shows that, in the purchase corresponding to Receipt 1, €14.0 of the total purchase was due to the purchase of units of Product D. For each product, the number of units bought was always an integer and the unit price was the same for each of the 18 purchases.



For each of the following products, select Sufficient if the information provided is sufficient to determine whether the unit price of the product exceeds €3. Otherwise, select Insufficient.

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For each of 18 recent purchases that included each of Products AD 26 May 2024, 13:08
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Official Explanation from the Book

Evaluate
RO1
Each of the subtotals for Product A is an integer multiple of the unit price for Product A, and thus the positive difference between any two different subtotals is a positive integer multiple of the unit price for Product A. It follows that the unit price for Product A cannot be greater than any of these positive differences. Therefore, if the positive difference between any two different subtotals is less than or equal to 3, then the unit price for Product A cannot be greater than 3. Sorting the table by column A, several different subtotals can be seen having a positive difference equal to 3, such as in receipt 2 and in receipt 3. Therefore, it can be determined that the unit price of Product A does NOT exceed €3.

The correct answer is Sufficient.

RO2
The same reasoning in the explanation for Product A applies to Product B. Sorting the table by column B, several different subtotals can be seen having a positive difference less than 3, such as in receipt 12 and in receipt 16. Therefore, it can be determined that the unit price of Product B does NOT exceed €3.

The correct answer is Sufficient.

RO3
The same reasoning in the explanation for Product A applies to Product C. Sorting the table by column C, several different subtotals can be seen having a positive difference equal to 3 (and one that is less than 3), such as in receipt 7 and in receipt 9. Therefore, it can be determined that the unit price of Product C does NOT exceed €3.

The correct answer is Sufficient.
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For each of 18 recent purchases that included each of Products AD 30 Jul 2024, 05:37
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­Watch this solution to see how mastering the "owning the dataset" approach can transform a seemingly complex question into a manageable challenge.
This video demonstrates the power of drawing inferences and developing a tailored problem-solving process when faced with a non-standard question.
You'll see how spending time to truly understand the data and craft a unique approach pays off.


This solution showcases how flexibility in your problem-solving strategy can be a game-changer in the exam environment.­
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For each of 18 recent purchases that included each of Products AD 08 Aug 2025, 11:27
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I have a doubt, the question is asking whether the information in the table is sufficient to determine if the unit value of each product A, B, and C is greater than 3 euros. So, do we need to solve it?
We can make the equation from receipts 1,2, and 2* of 10?
KarishmaB
ashutosh_73
For each of 18 recent purchases that included each of Products A–D, the table shows the product subtotals (the unit price for that product multiplied by the number of units bought as part of that purchase). For example, the table shows that, in the purchase corresponding to Receipt 1, €14.0 of the total purchase was due to the purchase of units of Product D. For each product, the number of units bought was always an integer and the unit price was the same for each of the 18 purchases.



For each of the following products, select Sufficient if the information provided is sufficient to determine whether the unit price of the product exceeds €3. Otherwise, select Insufficient.

­
­The units of any product bought are a positive integer value.

Product A - In a receipt, someone bought x units and gave €54. In another receipt, someone bought more than x units and gave €57.
This means that the one who gave €3 extra bought 1 or 2 or 3 or 4 or 5 etc. units of A extra.
So cost of each unit of A is at most €3 and can go down to €0.01 per unit theoretically. Hence cost of each unit of A is not more than €3.
Select Sufficient

Product B - In a receipt, someone bought x units and gave €27.5. In another receipt, someone bought more than x units and gave €30.
This means that the one who gave €2.5 extra bought 1 or 2 or 3 or 4 or 5 etc. units of B extra.
So cost of each unit of B is at most €2.5 and can go down to €0.01 per unit theoretically. Hence cost of each unit of B is not more than €3.
Select Sufficient

Product C - In a receipt, someone bought x units and gave €16.5. In another receipt, someone bought more than x units and gave €18.
This means that the one who gave €1.5 extra bought 1 or 2 or 3 or 4 or 5 etc. units of C extra.
So cost of each unit of C is at most €1.5 and can go down to €0.01 per unit theoretically. Hence cost of each unit of C is not more than €3.
Select Sufficient
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For each of 18 recent purchases that included each of Products AD 08 Aug 2025, 12:09
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You don't really need to calculate much, you just need to find the difference between the total costs in receipts as that will indicate the range that each product cost can have.
AnushkaTanwar
I have a doubt, the question is asking whether the information in the table is sufficient to determine if the unit value of each product A, B, and C is greater than 3 euros. So, do we need to solve it?
We can make the equation from receipts 1,2, and 2* of 10?
KarishmaB
ashutosh_73
For each of 18 recent purchases that included each of Products A–D, the table shows the product subtotals (the unit price for that product multiplied by the number of units bought as part of that purchase). For example, the table shows that, in the purchase corresponding to Receipt 1, €14.0 of the total purchase was due to the purchase of units of Product D. For each product, the number of units bought was always an integer and the unit price was the same for each of the 18 purchases.



For each of the following products, select Sufficient if the information provided is sufficient to determine whether the unit price of the product exceeds €3. Otherwise, select Insufficient.

­
­The units of any product bought are a positive integer value.

Product A - In a receipt, someone bought x units and gave €54. In another receipt, someone bought more than x units and gave €57.
This means that the one who gave €3 extra bought 1 or 2 or 3 or 4 or 5 etc. units of A extra.
So cost of each unit of A is at most €3 and can go down to €0.01 per unit theoretically. Hence cost of each unit of A is not more than €3.
Select Sufficient

Product B - In a receipt, someone bought x units and gave €27.5. In another receipt, someone bought more than x units and gave €30.
This means that the one who gave €2.5 extra bought 1 or 2 or 3 or 4 or 5 etc. units of B extra.
So cost of each unit of B is at most €2.5 and can go down to €0.01 per unit theoretically. Hence cost of each unit of B is not more than €3.
Select Sufficient

Product C - In a receipt, someone bought x units and gave €16.5. In another receipt, someone bought more than x units and gave €18.
This means that the one who gave €1.5 extra bought 1 or 2 or 3 or 4 or 5 etc. units of C extra.
So cost of each unit of C is at most €1.5 and can go down to €0.01 per unit theoretically. Hence cost of each unit of C is not more than €3.
Select Sufficient
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For each of 18 recent purchases that included each of Products AD 16 Oct 2025, 10:54
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I am still confused here, as to if I can state that for Product A, the Price can be 1.5$ or 3$ or 6$, in that case, how can the first answer be sufficient? If the answer oscillates between More than 3 and less than 3, how can it be sufficient?
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For each of 18 recent purchases that included each of Products AD Updated on: 15 Sep 2026, 12:41
Originally posted by Bunuel on 17 Oct 2025, 01:39.
Last edited by Bunuel on 15 Sep 2026, 12:41, edited 1 time in total.
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chattyyee
I am still confused here, as to if I can state that for Product A, the Price can be 1.5$ or 3$ or 6$, in that case, how can the first answer be sufficient? If the answer oscillates between More than 3 and less than 3, how can it be sufficient?
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How can it be €6 per unit? Between two receipts, the subtotal for Product A rises from €57 to €60, which is a €3 difference. If each unit cost €6, then even one more unit would make the subtotal jump by €6, not €3. So the unit price cannot be €6, it must be €3 or less. That’s why the information is sufficient to determine that the price does not exceed €3.
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