2 gmatprep PS

Question

Can anyone please explain these?

Fig · Answer

Question 2) (D) for me

o = 3*9 = 27 o = 1/2*6 = 3 * = 27 * 3 = 81 Then, looking at every anwser response... We could eliminate and all evens because they are divided by 2 and below 81... So , and are out... Finally, to make a last check, we have : = 27 * 3 = 81

saikadelik · Answer

Q1. E (i do not know how the program picked up the other anwer)
Q2. D

rdg · Answer

1)

Given a@b = a+b-ab

  a@b = b@a
  a@0 = a
  (a@b)@c = a@(b@c)



  
Left hand side is:
a+b-ab
Right hand side is:
b+a-ba

Both sides are equal.


 
Left hand side is:
a+0-a*0 = a
Right hand side is:
a

Both sides are equal.


 
Left hand side is:
(a+b-ab)@c=a+b-ab+c-(a+b-ab)*c=a+b-ab+c-ac-bc+abc=a+b+c-ab-bc-ca+abc
Right hand side is:
a@(b+c-bc)=a+b+c-bc-a*(b+c-bc)=a+b+c-bc-ab-ac+abc=a+b+c-ab-bc-ca+abc

Both sides are equal.


So the answer is (E).

rdg · Answer

Answer 2)


Answer is (A).

  = 3*9 = 27
  = 1/2 * 6 = 3

 * =27*3=81

kyatin · Answer

I go with 

Q1. E
Q2. D

rdg, 
for question 2 answers also need to be applied with same rule for ODD as mentioned in Question stem. 
So if you pick answer A) which is 81 inside a square then value for it is actually 81*3 which is not what you calculated, right?
So answer is D which is equivalent of 27 * 3 = 81

rdg · Answer

Thanks kyatin.
I understand what you meant. It will be (D).

Summer3 · Answer

My answers:

(1) D - I and III are TRUE

(2) A - 81

-------------------------
Q1 Here I show how I solved it:

a@b = a + b - ab

a@b = a - ab + b = a  (-ab+)  b 

which means   @ = (-ab+)   .....then I checked it with all three I, II and III and found I and III are TRUE.

----------------------------
Q2: Answer is 81 which is (A) then why is everybody writing it (D)?

rdg · Answer

Lets do backward calc.

if,  =3m, when odd, result of  =243. 
Now if  x =  true,  x =243

but 

if   x   =  , the result  =27x3=81

If the answer choice (A) is 81 instead of  , then (A) must be true.

rdg · Answer

(II) a@0=a

if @=(-ab+), when a@b=a+b-ab, then

a@0 = a (-a*0+)0 =a(-0+0) = a

So (II) must be true as well.

Summer3 · Answer

Thanks rdg! 

The second question:

  *   = (3*9) * (6/2) = 81

But 81 and   are different so answer is NOT (A).

81 is an odd number so 3m =  will be applicable here.

81 = 3m = 3*27 =  

Answer is (D).

Summer3 · Answer

I checked the first question too. You are right, rdg! All I, II and III are TRUE.

Answer is (E).

Thanks!

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