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# If a, b, c, and d denote positive integers in the figure above, what

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Re: If a, b, c, and d denote positive integers in the figure above, what [#permalink]
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Bunuel wrote:

If a, b, c, and d denote positive integers in the figure above, what is the value of the product abcd ?

(1) In each of columns S and T, the product of the three numbers equals the product of the four numbers in row R.
(2) a + b + c + d = 26
DS20356
Attachment:
1.png

Given: a, b, c, and d denote positive integers in the figure above

Target question: What is the value of the product abcd ?

Statement 1: In each of columns S and T, the product of the three numbers equals the product of the four numbers in row R.
The product of the four numbers in row R = (2)(3)(4)(5) = 120
So, from column S, we can write: (a)(3)(c) = 120
Divide both sides of the equation by 3 to get: ac = 40

So, From column T, we can write: (b)(4)(d) = 120
Divide both sides of the equation by 4 to get: bd = 30

So, abcd = (ac)(bd) = (40)(30) = 1200
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: a + b + c + d = 26
There are several values of a, b, c, and d that satisfy statement 2. Here are two:
Case a: a = 1, b = 1, c = 1 and d = 23. In this case, abcd = (1)(1)(1)(26) = 26
Case b: a = 3, b = 3, c = 10 and d = 10. In this case, abcd = (3)(3)(10)(10) = 900
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Cheers,
Brent
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If a, b, c, and d denote positive integers in the figure above, what [#permalink]
Bunuel wrote:

If a, b, c, and d denote positive integers in the figure above, what is the value of the product abcd ?

(1) In each of columns S and T, the product of the three numbers equals the product of the four numbers in row R.
(2) a + b + c + d = 26

DS20356

Attachment:
1.png

#1
In each of columns S and T, the product of the three numbers equals the product of the four numbers in row R.
product is 120
so column s & t can have
3*ac = 120
ac= 40
4*bd = 120
bd= 30
ac*bd ; sufficient

#2
a + b + c + d = 26
clearly insufficient

option a
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Re: If a, b, c, and d denote positive integers in the figure above, what [#permalink]
Bunuel wrote:

If a, b, c, and d denote positive integers in the figure above, what is the value of the product abcd ?

(1) In each of columns S and T, the product of the three numbers equals the product of the four numbers in row R.
(2) a + b + c + d = 26

DS20356

What is the product of abcd?

(1) $$3ac = 2 * 3 * 4 * 5$$
$$4bd = 2 * 3 * 4 * 5$$

$$bd = 2*3*5$$
$$ac = 2*4*5$$

SUFFICIENT.

(2) $$a + b + c + d = 26$$

We can't determine anything conclusive with this information; INSUFFICIENT.

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Re: If a, b, c, and d denote positive integers in the figure above, what [#permalink]
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Re: If a, b, c, and d denote positive integers in the figure above, what [#permalink]
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