Seed \(X\) costs $5 per pound and Seed \(Y\) costs $7 per

[BTGmoderatorLU]

Source: Veritas Prep

Seed \(X\) costs $5 per pound and Seed \(Y\) costs $7 per pound. Seed \(Z\) is a blend of the two seeds, and 20 pounds of Seed \(Z\) contains \(a\) pounds of Seed \(X\) and \(b\) pounds of Seed \(Y\). Is \(a > 10\)?

1) 20 pounds of Seed \(Z\) costs less than $120.
2) \(b < 12\)

The OA is A

[deloitte247]

$$5a+7b=Total\ \cost$$
$$a+b=Total\ weight$$
Question=> is a > 10?
Statement 1: 20 pounds of seeds cost less than $120
$$a+b=20\ \ $$
Hence, [b = 20 - a] and [a = 20 -b].
$$5a+7b<120\ \ $$
$$5a+7(20-a)<120\ \ $$
$$5a+140\ -7a<120\ \ $$
$$-2a<-20\ \ $$
$$a<10$$

Statement 2: b < 12
Given that a + b = 20
Therefore, if b = 11, a < 10.
if b = 9, a > 10; Hence, statement 2 is INSUFFICIENT.

Therefore, Statement 1 alone is SUFFICIENT. The correct answer is option A