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Each of the letters in the table above represents one of the

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Each of the letters in the table above represents one of the

by AAPL » Thu Apr 25, 2019 5:25 am

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Each of the letters in the table above represents one of the numbers 1 to 9 inclusive and each of the numbers occurs exactly once. What is the value of i?

1) i is the product of the prime numbers d and e.
2) i is the sum of two even numbers d and f

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Source: — Data Sufficiency |
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by deloitte247 » Tue Apr 30, 2019 1:04 pm

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Question ==> What is the value of i?
Each letter is > 0 and < 10 and occur once.
$$Hence,\ 1\le i\le9$$
Statement 1 ==> i is the product of the prime numbers 'd' and 'e'. d and e are prime numbers
$$i=d\cdot e$$
Prime numbers between 1 and 9 include 2,3,5 and 7.
$$2\cdot3=6,\ 2\cdot5=10,\ 2\cdot7=14,\ 3\cdot5=15,\ 3\cdot7=21$$
$$The\ only\ product\ that\ is\ \le9\ is\ 2\ and\ 3$$
Hence, 'd' and 'e' = 2 and 3.
STATEMENT 1 IS SUFFICIENT

Statement 2 ===> i is the sum of two even numbers 'd' and 'f'.
Even numbers between 1 and 9 includes 2, 4, 6 and 8.
$$2+4=6,\ 2+6=8,\ 2+8=10,\ 4+6=10,\ 4+8=12$$
This means that i can either be =8 or =6.
The information given is not enough to arrive at a specific answer for the value of i. Hence, STATEMENT 2 IS NOT SUFFICIENT.

Therefore, state 1 alone is SUFFICIENT. Answer is option A
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