The Patel, Lopez, and Russo families all had parties recently. There were 152 adults at the Lopez party. The ratio of...

[BTGmoderatorLU]

Source: Manhattan Prep

The Patel, Lopez, and Russo families all had parties recently. There were 152 adults at the Lopez party. The ratio of adults to children at the Russo party was 5 to 4. What was the ratio of adults to children at the Patel party?

1) The Russo party had 31 more adults than children, and 47 more adults than did the Patel party.

2) The Patel party had 40 more children, though 4 fewer people in total, than did the Lopez party, where the ratio of adults to children was 8 to 5.

The OA is B

[Jay@ManhattanReview]

Source: Manhattan Prep

The Patel, Lopez, and Russo families all had parties recently. There were 152 adults at the Lopez party. The ratio of adults to children at the Russo party was 5 to 4. What was the ratio of adults to children at the Patel party?

1) The Russo party had 31 more adults than children, and 47 more adults than did the Patel party.

2) The Patel party had 40 more children, though 4 fewer people in total, than did the Lopez party, where the ratio of adults to children was 8 to 5.

The OA is B

Given:

Lopez party: Adults = 152 and children = ?;

Russo party: Adults = 5x and children = 4x => Total = 9x

Patel party: Adults = Say A and children = Say C

We have to get the value of A : C.

Let's take each statement one by one.

1) The Russo party had 31 more adults than children and 47 more adults than did the Patel party.

=> 5x – 4x = x = 31 => # of adults in Russo party = 5x = 5*31 = 155

=> # of adults in Patel party = A = 155 – 47 = 108.

But we do not know the value of C, so we cannot get the value of A : C. Insufficient.

2) The Patel party had 40 more children, though 4 fewer people in total, than did the Lopez party, where the ratio of adults to children was 8 to 5.

Say in Lopez party, the no. of adults and that of children were 8x and 5x.

=> 8x = 152 => x = 19
=> No. of children in Lopez party = 5x = 5*19 = 95

Total no. of people in Lopez party = 152 + 95 = 247

=> Total no. of people in Patel party = 247 – 4 = 243
=> Total no. of children in Patel party = 95 + 40 = 135
=> Total no. of adults in Patel party = 243 – 135 = 108

=> required ratio = 108 : 135. Sufficient.

Correct answer: B

Hope this helps!

-Jay
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