John starts reading a book from the first page onwards and reads eac

Question

John starts reading a book from the first page onwards and reads each page only once. Every day, he reads twice the number of pages read by him the previous day. If the book has 400 pages, will John still be reading the book on the 6th day after he starts reading it?

(1) On the fifth day of reading the book, John reads more than 180 pages

(2) John reads 52 more pages on the fourth day of reading the book than he reads on the third day

firas92 · Accepted Answer

Let John read x pages on the first day

So 2nd day: 2x
3rd day: 4x
4th day: 8x
5th day: 16x
6th day: 32x

We need to find if x+2x+4x+8x+16x+32x < 400 or is 21x < 400

Since x is an integer, the question becomes, is x≤19?

(1) On the fifth day of reading the book, John reads more than 180 pages

16x>180

x>11.yyy or x≥12

So x may or may not be less than or equal to 19

1 is not sufficient

(2) John reads 52 more pages on the fourth day of reading the book than he reads on the third day

8x-4x=52 or x=13

So we know that x≤19

2 is sufficient

Answer is (B)

Aswin12 · Answer

Hey Firas 92 i believe that there has been a slight calculation error in your solution, it should be "x+2x+4x+8x+16x<400" cause if the sum of the pages read in the first 5 days is less than 400 he would still be reading the book on the 6th day.
hence the calculation would be 31x<400 hence we should find if x<12.9
(i) From the first statement we get 16x>180 which leads us to x should be greater than 11.25 which would be insufficient to find the answer.
(ii) The second statement gives 8x-4x=52 and we can find that would give us a "x" value of 13 which is greater than 12.9 which is sufficient.

Hence the answer would be option B

Hope this helps

IanStewart · Answer

If he reads k pages on the first day, he reads 2k, 4k, 8k and 16k pages on the four subsequent days. So he reads a total of 31k pages on the first five days.

He reads 16k pages on the fifth day, and if this exceeds 180, then 16k > 180, and since k is an integer, k is at least 12. So the total he has read in the first five days is at least (31)(12) = 372 pages, and he may or may not have read all 400 pages, so Statement 1 is not sufficient.

If his reading doubles from the third day to the fourth, and also increases by 52 pages from the third day to the fourth, then he must have read precisely 52 pages on the third day and 104 pages on the fourth. From there we can work out how many pages he read each day and answer any question at all, so Statement 2 is automatically sufficient and the answer is B.

ohhno · Answer

Day 4 − Day 3 = 52:
8x−4x=528x-4x=52 4x=524x=52 x=13x=13
Therefore, total pages read in first 5 days:
31(13)=40331(13)=403
The book has only 400 pages, so John finishes before Day 6.
✅  Statement 2 alone is sufficient. 
Answer:  (B) 
 Statement 2 alone is sufficient, but statement 1 alone is not.

undeniablevirgin · Answer

I feel the first statement could have been worded properly. It was not clear if he read more than 180 pages on Day 5 alone, or is 180+ is the cumulative pages read by Day 5?

John starts reading a book from the first page onwards and reads eac

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