Manhattan Prep
Gurdeep is organizing his sunflower seeds, petunia seeds, and daffodil seeds by volume. If the combined volume of all three seeds is 66 cm\(^3\), what is the volume of his daffodil seeds?
1) The volume of the petunia seeds is 10 percent of the combined volume of sunflower and daffodil seeds.
2) The volume of the daffodil seeds is 20 percent of the combined volume of sunflower and petunia seeds.
OA B
Gurdeep is organizing his sunflower seeds, petunia seeds,
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Let the volume of petunia seed = p
Let the volume of sunflower seed = s
Let the volume of daffodil seed = d
$$p+s+d=66cm^3$$
What is the volume of Gurdeep daffodil seeds (d)?
Statement 1: The volume of petunia seeds is 10 percent of the combined volume of sunflower and daffodil seeds.
$$p=0.1s+0.1d$$
$$p+s+d=66cm^3$$
$$0.1s+0.1d+s+d=66cm^3$$
$$1.1s+1.1d=66cm^3$$
$$d=\frac{66-1.1s}{1.1}$$
The value of s is unknown; hence, statement 1 is NOT SUFFICIENT.
Statement 2: The volume of the daffodil seed is 20 percent of the combined volume of sunflower and petunia seeds.
$$d=0.2\cdot\left(s+p\right)$$
$$d=0.2s+0.2p$$
$$From\ p+s+d=66cm^3$$
$$p=66-s-d$$
$$d=0.2s+0.2\left(66-s-d\right)$$
$$d=0.2s+13.2-0.2s-0.2d$$
$$d+0.2d=13.2$$
$$1.2d=13.2$$
$$d=\frac{13.2}{1.2}=11cm^3$$
Therefore, statement 2 alone is SUFFICIENT.
Answer = option B
Let the volume of sunflower seed = s
Let the volume of daffodil seed = d
$$p+s+d=66cm^3$$
What is the volume of Gurdeep daffodil seeds (d)?
Statement 1: The volume of petunia seeds is 10 percent of the combined volume of sunflower and daffodil seeds.
$$p=0.1s+0.1d$$
$$p+s+d=66cm^3$$
$$0.1s+0.1d+s+d=66cm^3$$
$$1.1s+1.1d=66cm^3$$
$$d=\frac{66-1.1s}{1.1}$$
The value of s is unknown; hence, statement 1 is NOT SUFFICIENT.
Statement 2: The volume of the daffodil seed is 20 percent of the combined volume of sunflower and petunia seeds.
$$d=0.2\cdot\left(s+p\right)$$
$$d=0.2s+0.2p$$
$$From\ p+s+d=66cm^3$$
$$p=66-s-d$$
$$d=0.2s+0.2\left(66-s-d\right)$$
$$d=0.2s+13.2-0.2s-0.2d$$
$$d+0.2d=13.2$$
$$1.2d=13.2$$
$$d=\frac{13.2}{1.2}=11cm^3$$
Therefore, statement 2 alone is SUFFICIENT.
Answer = option B
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Statement 1:AAPL wrote: ↑Thu Nov 07, 2019 11:58 amManhattan Prep
Gurdeep is organizing his sunflower seeds, petunia seeds, and daffodil seeds by volume. If the combined volume of all three seeds is 66 cm\(^3\), what is the volume of his daffodil seeds?
1) The volume of the petunia seeds is 10 percent of the combined volume of sunflower and daffodil seeds.
2) The volume of the daffodil seeds is 20 percent of the combined volume of sunflower and petunia seeds.
p : (s+d) = 10:100 = 1:10
Of every 11 cm^3, p = 1 cm^3 and s+d = 10 cm^3, implying that s+d constitutes 10/11 of the total volume.
No way to determine the value of d.
INSUFFICIENT.
Statement 2:
d : (s+p) = 20:100 = 1:5
Of every 6 cm^3, d = 1 cm^3 and s+p = 5 cm^3, implying that d constitutes 1/6 of the total volume:
d = 1/6 * 66 = 11 cm^3
SUFFICIENT.
The correct answer is B.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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