The table above is a 3 by 3 grid of 9 numbers, 5 of which are given

Question

https://gmatclub.com/forum/download/file.php?id=31162 The table above is a 3 by 3 grid of 9 numbers, 5 of which are given. The 4 numbers that are not given are denoted by A, B, C, and D. The product of the numbers in each row and in each column is the same for all rows and columns. What is the value of the product ABCD ? A) 36 B) 72 C) 36\sqrt{2} D) 36\sqrt{3} E) 72\sqrt{6} Table.jpg

Kurtosis · Accepted Answer

A * B * sqrt(3) = 6*sqrt(6)
A * B = 6 * sqrt(2)

C * D * 2sqrt(3) = 6*sqrt(6)
C * D = 3 * sqrt(2)

A * B * C * D = 6 * 3 * 2 = 36

Answer: A

JeffTargetTestPrep · Answer

We can start with the middle column:

1 x √6 x 6 = 6√6.

Thus, we know that the entries in each row and in each column multiply to yield 6√6.

For Row 1:

A x 1 x 2√3 = 6√6

A = (6√6)/(2√3)

A = 3√2

For Column 1:

3√2 x B x √3 = 6√6

B x 3√6 = 6√6

B = (6√6)/(3√6)

B = 2

For Row 2:

2 x √6 x C = 6√6

C = (6√6)/(2√6)

C = 3

For Row 3:

√3 x 6 x D = 6√6

D = (6√6)/(6√3)

D = √2

Thus, ABCD =

3√2 x 2 x 3 x √2 = 18√2 x √2 = 36

Answer: A

HarveyKlaus · Answer

Hi all,

Does anyone know where 6*sqrt(6) is coming from?

Thank you.

Kurtosis · Answer

Refer to the center column that has numbers 1, 6 and sqrt(6). Multiply and you will get 6*sqrt(6).

daviddaviddavid · Answer

just square each number in the table and then the solution becomes obvious

A  1  12
B  6  6
3  6  D

so we need 6*6=36

cheers

Smokeybear00 · Answer

6^2 does not equal 6, (see column 2, row 3). Can you elaborate?

pushpitkc · Answer

If you look at the question, the middle column reads 1,6, \sqrt{6}  not 1,6,6
Hence squaring it will give you 1,36 and 6.

Btw, why are you squaring the numbers?

The solution to this problem is as follows : 
 
Since the product of each of the rows and columns must be equal, only the center row has all three values, 
the product of which is 6* \sqrt{6}

We need to find the product of A,B,C,D.

From the first row :  
A * B * sqrt(3) = 6*sqrt(6) ==> A * B = 6 * sqrt(2)
 From the third row : 
C * D * 2sqrt(3) = 6*sqrt(6) ==> C * D = 3 * sqrt(2)

Therefore product of A,B,C and D as asked in the question is (6*sqrt(2))*(3*sqrt(2)) =6*3*2 = 36 (Option A)

Hope it helps!

daviddaviddavid · Answer

well, Im sorry I made a careless mistake, but you should get the point

A 1 12 B 6 6 3 36 D

ydmuley · Answer

The table above is a 3 by 3 grid of 9 numbers, 5 of which are given. The 4 numbers that are not given are denoted by A, B, C, and D. The product of the numbers in each row and in each column is the same for all rows and columns. What is the value of the product ABCD ?

A) 36

B) 72

C) \(36\sqrt{2}\)

D) \(36\sqrt{3}\)

E) \(72\sqrt{6}\)

Show Spoiler

Attachment:

Table.jpg

From Second column we see that the multiplication for each row/columns should be  = 6 * \sqrt{6}

= 2 * 3 * \sqrt{3} * \sqrt{2}

AB * \sqrt{3}   = 2 * 3 * \sqrt{3} * \sqrt{2}

AB = 6 * \sqrt{2}

CD * 2\sqrt{3}   = 2 * 3 * \sqrt{3} * \sqrt{2}

CD = 3 * \sqrt{2}

AB * CD = 6 * \sqrt{2} * 3 * \sqrt{2}

AB * CD = 18 * 2

AB * CD = 36

Hence, Answer is A

lary301254M7 · Answer

A faster way to solve this

All product = 6√6

A x B x √3 = 6√6, AB = (6√6 / √3)
C x D x 2√3 = 6√6, CD = (6√6 / 2√3)
A x B x C x D = (6√6 / 2√3) x (6√6 / √3) = (6 x 6 x 6) / ( 2 x 3) = 36

Don't solve for individual value, waste too much time

GmatKnightTutor · Answer

Hello, people. Let's get into this!

The third column lets us know that the product of a single row or column is  6\sqrt{6}

The product of two columns is therefore  6\sqrt{6}  x  6\sqrt{6}

If we multiply the two columns that contain AB and CD, we can create the following expression:

ABCD x  \sqrt{3}  x  2\sqrt{3}  =  6\sqrt{6}  x  6\sqrt{6}

ABCD = ( 6\sqrt{6}  x  6\sqrt{6} ) / ( \sqrt{3}  x  2\sqrt{3} )

ABCD = (36 x 6) /

ABCD = 36

A is your answer.

The table above is a 3 by 3 grid of 9 numbers, 5 of which are given

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The table above is a 3 by 3 grid of 9 numbers, 5 of which are given

Prep Toolkit

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