Ian has three pets: Barnum the cat, Bailey the cat, and

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Veritas Prep

Ian has three pets: Barnum the cat, Bailey the cat, and Daisy the dog, each of whom is older than 1. If the product of their ages is x, and the product of x and 36 1 is 361,361, how old is Ian's dog Daisy?

1. Daisy is not yet 10 years old.
2. The sum of the digits of Barnum's age is even.

OA A.

[Jay@ManhattanReview]

Veritas Prep

Ian has three pets: Barnum the cat, Bailey the cat, and Daisy the dog, each of whom is older than 1. If the product of their ages is x, and the product of x and 361 is 361,361, how old is Ian's dog Daisy?

1. Daisy is not yet 10 years old.
2. The sum of the digits of Barnum's age is even.

OA A.

To solve this question, it is important to assume that the ages are integers, else the answer is E. Since OA is A, the question-writer's intent is that the ages are integers.

Given: x*361 = 361,361

=> x = 1001 = 1*1*1001 = 7*11*13

Since each pet is older than 1 year, x ≠ 1*1*1001.

Thus, Daisy's age is one among 7, 11 and 13.

Let's take each statement one by one.

1. Daisy is not yet 10 years old.

Since among 7, 11 and 13, only 7 is less than 10, it is the answer. Sufficient.

2. The sum of the digits of Barnum's age is even.

The sums of digits of 11 and 13 are even, so Barnum's age is either 11 or 13. We can't get the age of Daisy. Insufficient.

The correct answer: A

Hope this helps!

-Jay
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[deloitte247]

How old is Daisy the dog
The 3 pets are older than 1
Product of their age is x
$$361\cdot x=\frac{361361}{361}$$
$$x=1001$$
which mean Barnum age * Bailey's age * Daisy's age =1001
The age of the three pets must be closer to 10 because
$$10^3=10\cdot10\cdot10=1000$$
using prime factorisation 1000=7*11*13
Hence the age of the three pets will be either one of 7, 11, and 13. I can say that Daisy is 7 years old; statement 1 is INSUFFICIENT.

Statement 2
The sum of the digit is Barnum's age is even, this means that Barnum's age is more than 1 digit hence it could be either 11 or 13 ,but it doesn't tell us Barnum's age because because the sum of the digit of both 11 and 13 are EVEN and no other information to find Daisy's age, hence statement 2 is INSUFFICIENT.

$$answer\ is\ option\ A$$