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The exact cost price to make each unit of a widget is \(\$7.6xy7,\) where \(x\) and \(y\) represent single digits. What

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The exact cost price to make each unit of a widget is \(\$7.6xy7,\) where \(x\) and \(y\) represent single digits. What

by Vincen » Fri Jul 10, 2020 3:02 am

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The exact cost price to make each unit of a widget is \(\$7.6xy7,\) where \(x\) and \(y\) represent single digits. What is the value of \(y?\)

(1) When the cost is rounded to the nearest cent, it becomes \(\$7.65.\)
(2) When the cost is rounded to the nearest tenth of a cent, it becomes \(\$7.65.\)

[spoiler]OA=B[/spoiler]

Source: Veritas Prep
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Source: — Data Sufficiency |
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Re: The exact cost price to make each unit of a widget is \(\$7.6xy7,\) where \(x\) and \(y\) represent single digits. W

by deloitte247 » Sun Jul 12, 2020 8:16 am

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Given that the cost price of each unit => $7.6xy7; where x and y represents single digits


Target question => What is the value of y?


Statement 1 => When the cost is rounded to the nearest cent, it becomes $7.65


i.e when $7 and 6xy7 cent is rounded to the nearest cent it becomes $7 and 65 cents
This means 6xy7 lies in the range of numbers between 6457 and 6547. All the numbers within that range will give 65 when rounded to two digits, so the exact value of y cannot be evaluated.
Hence, statement 1 is NOT SUFFICIENT


Statement 2 => When the cost is rounded to the nearest tenth of a cent, it becomes $7.65


7.6xy7 is rounded to the nearest tenth (3 places after the decimal point) to give 7.65. That means 7.6xy7 was rounded to 7.650
For 7.6xy7 to be 7.650, 7.6xy7 must be 7.6497; the last 7 becomes 1 because it is greater than or equal to 5, therefore the 1 is added to 9 to give 10 but since 10 is not a single digit, we will write down 0 and add 1 to 4 to give 7.650


Therefore, the value of x = 4 and y = 9. Statement 2 alone is SUFFICIENT


Answer = B
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