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What is the greatest number of identical bouquets that can be made out

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KrishnakumarKA1

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20 Mar 2017, 02:28

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GMAThirst

What is the greatest number of identical bouquets that can be made out of 21 white and 91 red tulips if no flowers are to be left out? (Two bouquets are identical whenever the number of red tulips in the two bouquets is equal and the number of white tulips in the two bouquets is equal.)

A. 3
B. 4
C. 5
D. 6
E. 7

Please show me how to solve.

maximum number of bouquets will be the number, which will divide 21 as well as 91
therefore the number of bouquets = HCF(21,91) = 7
Option E

mohshu

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28 Mar 2017, 23:58

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hi Bunuel ,,

(Two bouquets are identical whenever the number of red tulips in the two bouquets is equal and the number of white tulips in the two bouquets is equal.)

does it mean a bouquet should contain both white and red flowers??

Bunuel

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29 Mar 2017, 00:09

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mohshu

You cannot have identical bouquets made out of 21 white and 91 red tulips if each of the bouquets does not contain both white and red tulips.

The answer to the question is that we can make 7 identical bouquets made out of 21 white and 91 red tulips, each containing 3 white and 13 red tulips.

CyberStein

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23 Aug 2017, 15:12

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The conditional in this problem (i.e.) "if no flowers are to be left out" is the key to solving; you should interpret this conditional statement as "I need to find the Greatest common divisor among Red and White Tulips.

1. Red Tulips = 91 ; White Tulips = 21
2. To find the Greatest Common Divisor, the quickest method is prime factorization.
3. So, with prime factorization, red tulips = 91 = 7 x 13. White tulips = 21 = 3 x 7.
4. The divisor common in both (7 x 13) and (3 x 7) is 7.

Therefore, the answer to this problem is (E) 7

This problem is on both the 2013 and 2017 GMAT OG.

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05 Oct 2020, 00:10

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This is a clear GCF (Greatest Common Factor) question.

There are 21 white and 91 red flowers.

21 = 7 * 3
91 = 7 * 13

we see that 7 is the Greatest Common Factor present in 21 and 91. Hence we can form 7 Identical bouquets out of 21 white and 91 red flowers

Correct (E)

Question

- Bunuel What if we did the LCM (Least Common Multiple)?

I would like to know what happens when we do the LCM of 21 and 91?

LCM (21,91) = 3 * 7 * 21 = 273

What does this 273 represent?

chetan2u

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05 Oct 2020, 01:28

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Hoozan

Question

- Bunuel What if we did the LCM (Least Common Multiple)?

I would like to know what happens when we do the LCM of 21 and 91?

LCM (21,91) = 3 * 7 * 21 = 273

What does this 273 represent?

For LCM 21=3*7 91=7*13
Find product of all factors but the common should be taken only once
So 3*7*13=273, and 273 is the least common multiple.
That is the least number that will come in multiplication tables of both 21 and 91

Ganeshmantri

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30 Oct 2020, 09:41

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Bunuel

SOLUTION

What is the greatest number of identical bouquets that can be made out of 21 white and 91 red tulips if no flowers are to be left out? (Two bouquets are identical whenever the number of red tulips in the two bouquets is equal and the number of white tulips in the two bouquets is equal)

(A) 3
(B) 4
(C) 5
(D) 6
(E) 7

Since no flowers are to be left out, then the number of bouquets must be a factor of both 21 and 91. For example, we cannot have 2 bouquets since we cannot divide 91 red tulips into 2 bouquets without one tulip left over.

Only answer choice which is a factor of 91 is E (7).

Answer: E.

Hi Bunuel,

I get that no flowers must be left out. But it is also not mentioned that all the bouquets must be same.
What I mean by thet is that we can form, maybe 20 bouquets if 1 white and 1 red tulip, and another bouquet of 1 white and 71 red tulips. This is the reason why using HCF did not occur to me.

Kindly let me know your thoughts.
I reckon there something seriously wrong with my basocs since nowhere is anyone talking about what I think

Thanks as always!
Ganesh

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30 Oct 2020, 09:44

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Ganeshmantri

Bunuel

Thanks as always!
Ganesh

I think your doubt is addressed here: https://gmatclub.com/forum/what-is-the- ... l#p1828819 Hope it helps.

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31 Oct 2020, 13:38

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Ganeshmantri

Bunuel

Thanks as always!
Ganesh

Hi Ganesh,

The key word in this prompt is "IDENTICAL" (meaning that the bouquets must have the SAME flowers in it) - and the wording in the parentheses explains how a bouquet is identical with another bouquet as long as the number and type of flowers are the same.

For example:
A bouquet with 1 red flower and 1 white flower is the SAME as a bouquet with 1 white flower and 1 red flower
So RW and WR are the SAME bouquet

Another example:
RRW, RWR and WRR are all the SAME bouquet

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Rich