Mary Poppins is choosing presents at a certain book shop. She wants

Question

Mary Poppins is choosing presents at a certain bookstore. She wants books on poetry to comprise more than 45% but less than 50% of all the books she picks in the shop. What is the least number of books on poetry she can possibly get in the shop? A. 1 B. 5 C. 6 D. 10 E. 11 https://gmatclub.com/forum/download/file.php?id=68786 MP.jpg

bellbell · Answer

x = poetry books/total of books So 0.45 total of books has to be at least 3 for 1 to satisfy x<0.5 But 1/3 = 0.33, smaller than 0.45 => eliminate B. 5 => total of books has to be at least 11 5/11 = 0.45 => eliminate C. 6 => total of books has to be at least 13 6/13 = 0.46 => satisfy 0.45

AarshiKhemka · Answer

Shouldn’t it be Option B since the percentage is 45.45% which is greater than 45% and less than 50%

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Bunuel · Answer

I'll only say that the OA is not C. Whether it's B or not we'll know on Tuesday 18th of October. Meanwhile you are welcome to post your solution!

ChanSu · Answer

B should be the answer

Out of a total of 11 or more books , he chose 5 poetry books such that

0.45< 5 poetry books will be <0.5

1 will not work because if it’s total 3 books, then 1 poetry of 2 total books= 0.50 . This is not possible because it has to be less than 0.50

1 will also not work because if it’s total 3 books, then 1 poetry of 3 total books= .333 is less than 0.45. The fraction should be greater than 0.45

If it’s total 4 books , then 1 poetry book out of 4 total books= 0.25 which is less than 0.45

As number of books increase , the 1 out those many total books goes further and further lower than 0.45

How I got it?

Say x/100 is the fraction of poetry books

45/100 < x/100 < 50/100

9/20 < x/100 < 10/20

9/20 < (x/20) * (1/5) < 10/20

1/5 is the odd fraction that needs to convert to an integer because number of books need to be an integer . So 5 is the answer I think. Choice B

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bellbell · Answer

LOL yeah that's true, I made a mistake in calculation.

Adarsh_24 · Answer

Trying out options.

1) 45T/100 < 1 < 50T/100
Separating out both sides
9T/20<1
T<20/9
T<2.22

1<T/2
T>2
T is a whole number. So not possible.

2) 45T/100 < 5 < 50T/100

Separating out.
9T/20 < 5
T<100/9
T<11.11

5<T/2
T>10

T=11. Possible.

Could it be solved directly without options?
I tried
45T/100 < P < 50/100
T<20P/9
Since, 20P/9 doesnt really need to be an integer due to inequality. P not necessarily a multiple of 9.
I hit a dead end after this step.
So moved to trying out options.

Kinshook · Answer

Given: Mary Poppins is choosing presents at a certain bookstore. She wants books on poetry to comprise more than 45% but less than 50% of all the books she picks in the shop.

Asked: What is the least number of books on poetry she can possibly get in the shop?

Let the number of books on poetry be x and total number of books be y.

x is between .45y & .5y and x & y are both positive integers

.45y < x < .5y

y < x/.45; y> x/.5
x/.5 < y < x/.45
2x < y < 20x/9 = 2 2/9 x

A. 1: x = 1; 2 < y < 2 2/9; Not feasible since number of books is a positive integer.
B. 5: x = 5; 10 < y < 100/9 = 11 1/9; y = 11; .45y = 4.95 < x=5 < 5.5= .5y; Feasible
C. 6
D. 10
E. 11

IMO B

Veerenk · Answer

Number of books must be always integer. As per the given problem, poetry books must be more than 45% of total and less than 50% of total books purchased If total books is T & Poetry books is P, The equation can be written as 0.45 < P/T < 0.5 1) Option -A: Poetry books - 1 0.45 < 1/T < 0.5 ==> 0.45 < 1/T & 1/T < 0.5 if o.45 < 1/T ==> T<2.22 or T<3 If 1/T < 0.5 ==> T>2 Since there wont be any whole number between 2 & 3, Option - A is not correct 2. Option-B: If Poetry books are 5 Then 0.45 < 5/T < 5 If 0.45 < 5/T ==> T < 11.11 i.e. T < 12 If 0.5 > 5/T ==> T > 10 i.e. T > 10 Since there is "11" between 10 & 12, Option -B is correct 3. Option - C: If Poetry Books are 6 Then 0.45 < 6/T < 5 If 0.45 < 6/T ==> T < 13.33 i.e. T < 14 If 0.5 > 6/T ==> T > 12 Though there is "13" between 12 & 14, Option - C is not correct. Because, the problem is asking for least number of Poetry books Hope that is clear

Mary Poppins is choosing presents at a certain book shop. She wants

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