Joe earned x dollars the first day he worked in December, where x is an integer. For each day after the first that he...

[BTGmoderatorLU]

Source: Manhattan Prep

Joe earned x dollars the first day he worked in December, where x is an integer. For each day after the first that he worked in December, Joe earned twice the amount he earned on the previous day. Did Joe earn less than $35 on the 4th day he worked in December?

1. Joe earned more than $120 in total for the first five days he worked in December.
2. Joe earned less than $148 on the 6th day he worked in December.

The OA is B

[Jay@ManhattanReview]

Source: Manhattan Prep

Joe earned x dollars the first day he worked in December, where x is an integer. For each day after the first that he worked in December, Joe earned twice the amount he earned on the previous day. Did Joe earn less than $35 on the 4th day he worked in December?

1. Joe earned more than $120 in total for the first five days he worked in December.
2. Joe earned less than $148 on the 6th day he worked in December.

The OA is B

Given the information, Joe earned $x on the 1st day, $2x on the 2nd day, $4x on the 3rd day and $8x on the 4th day.

So, we have to determine whether 8x < 35 or x < 4.37 or x ≤ 4 since x is an integer.

Let's take each statement one by one.

1. Joe earned more than $120 in total for the first five days he worked in December.

=> x + 2x + 4x + 8x + 16x > 120 => 31x > 120 => x > 3.... => x ≥ 4 since x is an integer. If x is $4, the answer is yes; however, if x is $5 or more, the answer is no. Insuffcient.

2. Joe earned less than $148 on the 6th day he worked in December.

=> 32x < 148 => x < 4.6... => x ≤ 4. Sufficient.

The correct answer: B

Hope this helps!

-Jay
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