Joe earned x dollars the first day he worked in December, where x is a

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?

x,2x,4x,8x,16x,32x,.... he will earn on each day

(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>3.87
x>=4
4th day he would have earned >=32
Not sufficient.

(2) Joe earned less than $148 on the 6th day he worked in December.
32x<148
x<4.625
x<=4
4th day he would have earned <=32
Sufficient.

Option B.

We are getting
x<4.625 as the value in option 2
This means we get both yes and no as answer on multiplying with 8 for the 4th day
How can we get B as an answer

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.
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Correct me If I'm wrong
Thanks in advance.

Posted from my mobile device

Poorvi55, since x is an Integer, x < 4.62 means x <= 4 which is also <= than 4.3; x can't be 5.

Posted from my mobile device

When solving DS questions dealing with word problems, there are two things you always need to take care of before getting into the statements

1. Always translate the question stem, set up equations (limit the number of variables) and breakdown the question stem of possible
2. Never overlook the constraints the question provides.

Now the question stem tells us that on the

1st day Joe earned = x
2nd day = 2x
3rd day = 4x
4th day = 8x

Question stem: Did Joe earn less than $35 on the 4th day -----> 8x < 35 ----> x < 4.375

Since x is an integer, the question becomes 'Is x <= 4

Statement 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 > 3.9....

This gives us both a YES and a NO since x can be 4 or any integer greater than 4

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

32x < 148 ----> x < 4.625

Since x is an integer, x <=4. Sufficient.

Aditya
CrackVerbal Quant Expert
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Hello,

In St. 2, I would like to show you that
32x<148
x<148/32
Now, on 4th day his earnings were 8x
So 8x (his earnings) < 148x8/32
8x < 37
So his earnings are less than 37 which is not sufficient to answer.
Can you tell me whether this is wrong?

Thanks,
Rishov
_________________

Its given that x is an integer. So we have to solve for x first.

Day1 = x
Day2 = 2x
Day3 = 4x
Day4 =8x
Day5 =16x
Day6 =32x

(1)
x+2x+4x+8x+16x >120
31x>120
x>3.87
x>=4 (upward rounded since, x is an integer & sum is more than 120)
Day4 >=8*4
>=32
It can be more or less than 35
Thus, Not sufficient.

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

32x<148
x<4.625
x<=4 (downward rounded since, x is an integer & sum is less than 148)
Day4 <=8*4
<=32
Always less than 35
Thus, Sufficient.

IMO Answer is B.

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