In the expression (__)*(__) + (__)*(__) each blank is to be filled in

Question

In the expression (__)*(__) + (__)*(__) each blank is to be filled in with one of the digits 1, 2, 3, or 4, with each digit being used once. How many different values can be obtained?

A. 2
B. 3
C. 4
D. 6
E. 24

Archit3110 · Answer

pair can be made in
1*2+3*4=14
,1*3+2*4=11
,1*4+2*3=10
, 2*3+1*4=10
2*4+3*1=11
3*4 +2*1=14
6 possiblities ; 3 different values
IMO B

eswarchethu135 · Answer

Total number of possible cases are:

1*2 + 3*4 = 14
1*3 + 2*4 = 11
1*4 + 2*3 = 10
2*3 + 1*4 = 10
2*4 + 1*3 = 11
3*4 + 1*2 = 14

Of the 6 cases possible, there are only 3 unique values can be obtained.

OPTION:  B

rocky620 · Answer

3 Different values  can be obtained by using any pair

Option B is correct

ChiragSabharwal · Answer

Is There any way to solve this question using permutation and combination?

Regor60 · Answer

This is the well known problem of how to distribute 4 different things into two groups of two where neither the order of the items within a group nor the ordering of the groups makes a difference.

This can be done by selecting two items from four:

4!/2!2! = 6. Remember that by using combinations the order of the selected items is treated as not mattering. The other two are selected at the same time only 1 way:

2!/2!0! = 1

Because this approach treats 12 34 and 34 12 as distinct groups, the total above, 6, needs to be divided by 2 equalling

3.

The reason this can be done this way is that the order of two numbers within a multiplication doesn't matter and whether a given multiplication is first or second in the addition also doesn't matter.

Finally, any pair of numbers creates a unique multiplication and the additions also unique numbers, otherwise the result of 3 would possibly be reduced.

The way to do it using permutations:

4 3 2 1
_ _ _ _

= 12*2 = 24.

But as discussed each has to be divided by 2 because the order within a group doesn't matter:

24/2*2 = 6.

And the above needs to be divided by 2 because the order of the groups themselves also doesn't matter:

6/2 = 3

Posted from my mobile device

DyutiB · Answer

We know product and addition is symmetrical. For example, 4*3 = 3*4, 4+3 = 3+4. This does not hold true for subtraction and division. 
 Keeping this concept in mind, we can check the below. 
 Now let's consider the total possible order = 4P4 = 24 
 Now let's see for one sum, 
 4*3 + 2*1 = 4*3 + 1*2 = 3*4 + 2*1 = 3*4 + 1*2 = 2*1 + 4*3 = 2*1 + 3*4 = 1*2 + 4*3 = 1*2 + 3*4 = 14 
 So in 24 possible orders, 8 different orders will give same value. 
 So the total different values that we can get = 24/8 = 3

Ans : B

In the expression ()() + ()() each blank is to be filled in

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions