A teacher has 120 pens, consisting of 72 black pens and 48 red pens.

Question

A teacher has 120 pens, consisting of 72 black pens and 48 red pens. The teacher wants to put together packets for her students in which she uniformly distributes the black and red pens among the packets so that none of the pens are left over and all the packets have the same ratio of black pens to red pens. What is the greatest number of packets the teacher can make?

(A) 8
(B) 12
(C) 16
(D) 24
(E) 30

(A) 8
(B) 12
(C) 16
(D) 24
(E) 30

D3N0 · Answer

Ans: D (24)
Ratio: 72:48 = 3:2 so total 24 packets of such ratios can be made..

ans is D

RohitGoyal1123 · Answer

This can be done by finding the HCF of number of black and red pens, so that the none is left over, and all packets are of same size

HCF (72,48) = 24

Hence 24 is the max number of packets the teacher can make.

Correct option  D

balaji4799 · Answer

If one doesn't remember HCF or ratios properly, we can solve this question using logical reasoning as follows. 
We start with options. Since we need max packets we start with bigger number 30. Now Total pens=120. As the distribution is uniform across packets , the number of pens in one packet = 120/30 = 4. Now with this lets look if we can fill Blue and Red pens. For ex, consider 3 Blue and 1 Red (Since blue pens are more in number than red). The number of packets we produce will be 72/3= 24, and we can fit only 24 Red pens and 24 pens are remaining hence 30 (E) is wrong. Now consider option (D) 24, here number of pens in one packet =120/24 = 5. 3 blue 2 red pens per packet, we get 72/3 = 24 packets and 48/2 = 24 packets. Hence D is right answer. 
My answer could be overtly wordy. At this point am thinking I should probably revise HCF concept.

el2010 · Answer

We're looking for the greatest number of packets so we need to find the greatest common factor between 72 and 48. 72 broken down by prime factorization is 3x3x2x2x2, while 48 is 2x2x2x2x3. The greatest common factor is 2x2x2x3 = 24. Answer choice D.

seed · Answer

72= 2^3 * 3^2  and 48= 2^4 * 3

GCD of (72,48) =  2^3 * 3 =24.

Answer: (D).

ScottTargetTestPrep · Answer

We see that the greatest common factor of 72 and 48 is 24.

Thus, we see each packet can have 3 black pens and 2 red pens. Since there are 5 pens in each packet, there are a total of 120/5 = 24 packets.

Alternate Solution:

We see that the ratio of black to red pens is 72 : 48, which is equivalent (in lowest reduced form) to 3 : 2, or 3x : 2x. Since we have 120 pens, we create the equation:

3x + 2x = 120

5x = 120

x = 24

Thus, with the ratio reduced to its lowest equivalent form, we can create a maximum of 24 packets, each containing 3 black pens and 2 red pens.

Answer: D

push12345 · Answer

Indirectly question is asking for HCF between 72 and 48

=72=2^3*3^2
=48=2^4*3

So HCF is (2^3)*3= 24

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A teacher has 120 pens, consisting of 72 black pens and 48 red pens.

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A teacher has 120 pens, consisting of 72 black pens and 48 red pens.

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