Are there more engineers than salespeople working at Soho Corp?

The question asks to compare the number of engineers and the number of salespeople.

(1) is totally useless. We just know that there are less clerical staff in the company than engineers and salespeople combined. This statement does not help to compare the number of engineers and the number of salespeople.

(2) means that E + 3 = 2S.

Try some small numbers: If E = 1, then S = 2, so E < S.
Try some larger numbers: If E = 19, then S = 11, so E > S.

So, (2) is also not sufficient.

(1)+(2): (1) is totally useless and (2) is not sufficient itself. So, even together we cannot get the answer.

Answer: E.
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I would like to propose a mathematical way of solving this question. Though I seriously feel that mathematically, it would take more time to solve.
We can clearly notice that neither Statement 1 nor Statement 2 is individually correct.
Now we have to check if both the statement together can get us the answer.

From Statement 2, we have E+3 = 2S
From Statement 1, we have C=2/3(E+S)

Therefore, E+S+C=T (using T as the symbol for total)
After substituting the value of C from statement 1, and the value of E in the form of S from statement 2; we get,
E=(2T-5)/5
S=(T+5)/5
Now,
We have to compare which one is higher, E or S.
The values of E and S are clearly dependant on T. If we look at E and S a little closely, then we can surely say that for E to be greater than S, T must be greater than 5. We do not have any constraint on the value of T.

So let us say, if T=5, we get E=1, S=2, C=2. All conditions are satisfied. E<S
But if T=10, we get E=3, S=3, C=4. All conditions are satisfied. E=S
And if T=15, we get E=5, S=4, C=11. All conditions are satisfied. E>S.

Hence, both Statement 1 and Statement 2 together are not getting us the uniform answer.

Hi, Thanks for your reply.
However, I have confusion in 2nd statement.
when you say E=1, then in that acc to statement first you have add 3. So this becomes =4 and S remains 2.
Therefore, E > S.

pls, clarify this.

According to Statement 2, "If 3 more employees are employed", it does not mean that SOHO has employed more. Statement 2 is just provided to give you a condition to help you solve the question.

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