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

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

by BTGmoderatorDC » Thu Nov 24, 2022 12:38 am

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## Global Stats 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

OA A

Source: GMAT Prep

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

by [email protected] » Sun Nov 27, 2022 7:06 am

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## Global Stats

BTGmoderatorDC wrote:
Thu Nov 24, 2022 12:38 am
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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

OA A

Source: GMAT Prep
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