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Director  V
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The table above is a 3 by 3 grid of 9 numbers, 5 of which are given  [#permalink]

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2
17 00:00

Difficulty:   25% (medium)

Question Stats: 79% (02:27) correct 21% (02:54) wrong based on 307 sessions

### HideShow timer Statistics 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) $$72\sqrt{6}$$

Attachment: Table.jpg [ 6.52 KiB | Viewed 13663 times ]

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Originally posted by NandishSS on 30 Jul 2016, 06:05.
Last edited by Bunuel on 30 Jul 2016, 07:16, edited 1 time in total.
Edited the question.
Marshall & McDonough Moderator D
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Re: The table above is a 3 by 3 grid of 9 numbers, 5 of which are given  [#permalink]

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9
2
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

##### General Discussion
Manager  Joined: 18 Feb 2015
Posts: 81
Re: The table above is a 3 by 3 grid of 9 numbers, 5 of which are given  [#permalink]

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Hi all,

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

Thank you.
Marshall & McDonough Moderator D
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Location: India
Re: The table above is a 3 by 3 grid of 9 numbers, 5 of which are given  [#permalink]

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HarveyKlaus wrote:
Hi all,

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

Thank you.

Refer to the center column that has numbers 1, 6 and sqrt(6). Multiply and you will get 6*sqrt(6).
Manager  B
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Re: The table above is a 3 by 3 grid of 9 numbers, 5 of which are given  [#permalink]

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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
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Re: The table above is a 3 by 3 grid of 9 numbers, 5 of which are given  [#permalink]

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daviddaviddavid wrote:
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

6^2 does not equal 6, (see column 2, row 3). Can you elaborate?
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The table above is a 3 by 3 grid of 9 numbers, 5 of which are given  [#permalink]

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Smokeybear00 wrote:
daviddaviddavid wrote:
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

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

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!
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Re: The table above is a 3 by 3 grid of 9 numbers, 5 of which are given  [#permalink]

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Smokeybear00 wrote:
daviddaviddavid wrote:
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

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

well, Im sorry I made a careless mistake, but you should get the point A 1 12
B 6 6
3 36 D
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Re: The table above is a 3 by 3 grid of 9 numbers, 5 of which are given  [#permalink]

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pushpitkc wrote:
Smokeybear00 wrote:
daviddaviddavid wrote:
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

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

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!

yes thanks, I made a careless mistake

I squared the numbers, because for me the problem becomes much easier
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Re: The table above is a 3 by 3 grid of 9 numbers, 5 of which are given  [#permalink]

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1
1
NandishSS wrote: 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) $$72\sqrt{6}$$

Attachment:
Table.jpg

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

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Re: The table above is a 3 by 3 grid of 9 numbers, 5 of which are given  [#permalink]

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1
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 ?

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

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

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

$$AB = 6 * \sqrt{2}$$

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

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

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

$$AB * CD = 18 * 2$$

$$AB * CD = 36$$

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Re: The table above is a 3 by 3 grid of 9 numbers, 5 of which are given  [#permalink]

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1
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
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Re: The table above is a 3 by 3 grid of 9 numbers, 5 of which are given  [#permalink]

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_________________ Re: The table above is a 3 by 3 grid of 9 numbers, 5 of which are given   [#permalink] 02 Dec 2019, 00:32
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