In the multiplication problem below, each capital letter represents a

Question

In the multiplication problem below, each capital letter represents a positive digit, and the tens digit of the product is zero. What is the value of digit B?

Attachment:

Arithmetic_2.jpg [ 11.68 KiB | Viewed 7459 times ]

A. 2
B. 4
C. 7
D. 8
E. 9

Kudos for a correct solution.

Show Answer

Official Answer

D

DesiGmat · Answer

Here we go:

9*9 = 63

This will generate 6 to be carried forward

and B + 6 = 10 (out of which 1 will be carried forward leaving 0)

B has to 4

Option B is correct

DesiGmat · Answer

Here we go:

9*9 = 81

This will generate 8 to be carried forward

and B*9 + 8 = X0

B has to 8

Option D is correct

chetan2u · Answer

hi..
 ans D 8...
initially it becomes a bit confusing as we have almost 16 letters for 10 digits...
but then since the question stems asks us to concentrate only at B, the method is as follows...
 HB9
  x 9 
 S0W
 it means w=1 as 9*9=81 and 9*B+8=a0..
B=8 as only this value gives us a 0 as units digit for eq

chetan2u · Answer

hi desigmat u have wrongly written 9*9 as 63 it is 81 :wink:

ModularArithmetic · Answer

My solution revolves around the trick of testing the anwser choices, however I would love to see an algebraic approach for this problem.

The information provided is that 9*9 = 81, the result of this is that the 8 is carried one place to the left. The problem asks you to seek for a solution that adds 2 to the tens digit place.

By testing the answer choices, what in my opinion is a tedious process, we can figure out the answer.

A) 29*9 = (9*9) + (9*20) = 81 + 180 = 261 - incorrect
B) 49*9 = (9*9) + (9*40) = 81 + 360 = 441 - incorrect
C) 79*9 = (9*9) + (9*70) = 81 + 630 = 711 - incorrect
D) 89*9 = (9*9) + (9*80) = 81 + 720 = 801 - correct
E) 99*9 = (9*9) + (9*90) = 81 + 810 = 891 - incorrect (for completeness)

Answer: D

Again, I would love to see an algebraic approach less tedious than this one. :-D

chetan2u · Answer

hi i dont think you have to get into such calculations..
you have rightly said 9*9=81..
and next step= 9*b+8= a 0... this means  a 0 -8 =9*B...only b as 8 gives 2 inunits digit

PareshGmat · Answer

Answer = D = 8

9*9 = 81, which gives w = 1 & creates a carry of 8

Setting up the equation (For tens digit)

9*B + 8 = 0

To give a "0" at the end, we require 9*B to give "2" in the units place

Only 9*8 = 72 satisfies the condition

KarishmaB · Answer

This question works toward helping you develop the "Math instinct" we talk about. 
You get B*9 + 8 = ..0
So you know that B*9 should end with 2. Immediately 8*9 = 72 will come to your mind. Along with it, what should also come to your mind is that in the multiplication table of 9, every product ends with a different digit.

9*1 =  9 
9*2 = 1 8 
9*3 = 2 7 
9*4 = 3 6 
9*5 = 4 5 
9*6 = 5 4 
9*7 = 6 3 
9*8 = 7 2 
9*9 = 8 1 
9*10 = 9 0

This happens for tables of 1, 3, 7 and 9 - i.e. all odd numbers except 5. So if this were a DS question, you would know that this is sufficient information without running through the table of 9.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

In the multiplication problem below, each capital letter represents a

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

In the multiplication problem below, each capital letter represents a

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards