If 7! + 8! + 9! = a and 11! - 10! - 9! = a * b, what is the value of

Question

If 7! + 8! + 9! = a and 11! - 10! - 9! = a * b, what is the value of b?

A, 11
B. 72
C. 81
D. 88
E. 99

M47-48

Bunuel · Accepted Answer

GMAT Club Official Solution:

a = 
= 7! + 8! + 9! =
= 7!(1 + 8 + 8 * 9) = 
= 7! * 81

a * b = 
= 11! - 10! - 9! = 
= 9!(10 * 11 - 10 - 1) = 
= 9! * 99 = 
= (7! * 8 * 9)(99) =
= (7! * 8 * 9)(9 * 11) =
= (7! * 81)(8 * 11)

Since a = 7! * 81, it follows that:
a * b = (a)(8 * 11)
b = 88.

Answer: D.

shivani1351 · Answer

Given:
7! + 8! + 9! = a 
11! - 10! - 9! = a * b

This can be written as:
7!(1+8+8*9) = a
7!(81) = a

Also, 9!(10*11-10-1) = a*b
9!(110-11) = a*b

=> 9!(99) = 7!(81)b
=> b = 88

Hence, the correct answer is  Option D - 88  (Ans)

Dereno · Answer

If 7! + 8! + 9! = a and 11! - 10! - 9! = a * b, then b =?

Taking 7! Common from the below equation, we get

7! + 8! + 9! = a = 7! (1+ 8 + 9*8) =  7! * (81)

Given that,  11! - 10! - 9! = a * b, we can take 9! as common.

(11*10 - 10 - 1) * 9! = a*b

99*9! = a*b

Substitute a, we get b = (99*9!) / ( 81* 7!)

solving, we get b =  88

Option D

Edskore · Answer

The key skill here is factorial factoring — the GMAT never expects you to compute 11! = 39,916,800. It expects you to simplify by pulling out a common term.

Step 1 — Simplify the expression for a
7! + 8! + 9! = 7! + 7!·8 + 7!·8·9
= 7!(1 + 8 + 72)
= 7!(81)
So a = 81 · 7!

Step 2 — Simplify the expression for a·b
11! - 10! - 9!
Factor out 9!:
= 9!(11·10 - 10 - 1)
= 9!(110 - 10 - 1)
= 9!(99)
So a·b = 99 · 9!

Step 3 — Solve for b
b = (a·b) / a = (99 · 9!) / (81 · 7!)
= (99/81) · (9!/7!)
= (99/81) · 9 · 8
= (99/81) · 72

Simplify 99/81 = 11/9
b = (11/9) · 72 = 11 · 8 = 88

Answer: D

Common trap: Most students who go wrong here either try to compute 11! directly (time killer) or forget to factor out the same base from both expressions, leaving them with an unsolvable division. The moment you see consecutive factorials being added or subtracted, factor out the smallest one immediately — the sum inside the brackets will always be a manageable integer.

Takeaway: On any factorial arithmetic question, factor out the smallest factorial in the expression first — you will almost always end up with a clean integer inside the brackets.

— Kavya | 725 (GMAT Focus) | Founder @ edskore.com

poojaarora1818 · Answer

Solution:

a= 7! + 8! + 9!

a= 7!(1+ 8 + 72)

a= 7!(81)

a * b = 11! - 10! - 9!

7!(81) * b = 9!(110 - 10 -1)

7!(81) * b = 9!(99)

b =  \frac{9!(99)}{7!(81)}

b= 88

Hence, Option D

vasu1104 · Answer

a= 7! + 8! + 9!
11! - 10! - 9! = a*b

we can put value of a in second equation and find B.

11! - 10! - 9! = (7!+ 8! + 9!) * b
from LHS we can take 9! common and from RHS 7!.

b= 9! (11*10 - 10 - 1) / 7! ( 1 +8 + 8*9)
72(99) / 81

upon solving this we get B= 88
ans D

If 7! + 8! + 9! = a and 11! - 10! - 9! = a * b, what is the value of

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If 7! + 8! + 9! = a and 11! - 10! - 9! = a * b, what is the value of

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