Danny bought some packets of pens, each packet at a cost of $4, and so

Good catch. I missed that. Kudos to you.

We are looking for packets of pens:pencils or pens/pencils

Statement 1:
4*pens + 3*pencils = 24
pens=3, pencils=4
3:4
Sufficient

Statement 2:
4*pens=3*pencil
pens/pencils = 3/4
Sufficient

We could also have listed out the multiples and taken the ratio from there. Numbers that work include 12, 24, 36, 48, etc

Answer: D

VERITAS PREP OFFICIAL SOLUTION:

Solution: (D)

To express this relationship mathematically, let’s say the number of packets of pens bought = X and that the number of packets of pencils bought = Y

The question asks for the ratio X:Y

Statement (1): According to this statement, 4X + 3Y = 24. X = 3 and Y = 4 satisfies this equation. The only other possible non negative values of X and Y that will satisfy this equation are X = 6, Y = 0 and X = 0, Y = 8, both of which are unacceptable since he buys some packets of each kind. Hence the ratio X:Y = 3:4.

Statement (1) alone is sufficient to answer the question.

Statement (2): The cost of one packet of pens: cost of one packet of pencils is 4:3. If he spent equal money on both types of packets, he must have bought them in the ratio 3:4. Hence X:Y = 3:4. Statement (2) alone is sufficient to answer the question.

Perfect. If I may ask, could we also use the unknown multiplier in this type of questions?

E.g if we have 4X+3Y=24, could we do 7x=24, and from there find the price for pens and pencils? Then, we can find how many of each he bought and the ratio.

Or it this not logical?

No.

x is the number of packets of pens bought and y is the number of packets of pencils bought. So, for (1) we have that 4x + 3y = 24. We cannot write it as 7x = 24 unless we know that the number of packets of pens bought is equal to the number of packets of pencils bought, so unless we know that x = y.

suppose Qp=# pens
Qr = # of pencils
we are asked Qp/Qr.

1. 4Qp+3Qr=24
only way it would work if Qp=3 and Qr=4. so we can find the ratio.

2. we know 4Qp=3Qr
we can set up the ratio, so sufficient.

D

Hi Bunuel

Isn't the 'some' instead of "non-zero" misleading in the question as the number of packet could be zero as well, and in that case ratio will be 'undefined'

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