GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 18 Jun 2019, 20:06

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# The integer x has a tens digit of 6 and a units digit of 7. The units

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 12 Aug 2015
Posts: 283
Concentration: General Management, Operations
GMAT 1: 640 Q40 V37
GMAT 2: 650 Q43 V36
GMAT 3: 600 Q47 V27
GPA: 3.3
WE: Management Consulting (Consulting)
The integer x has a tens digit of 6 and a units digit of 7. The units  [#permalink]

### Show Tags

17 Nov 2015, 03:14
1
5
00:00

Difficulty:

25% (medium)

Question Stats:

76% (01:55) correct 24% (01:47) wrong based on 174 sessions

### HideShow timer Statistics

The integer x has a tens digit of 6 and a units digit of 7. The units digit of integer y is 8. The product of x and y has a tens digit of 8. Which of the following is a possible tens digit of integer y?

A. 3
B. 4
C. 5
D. 6
E. 7

_________________
KUDO me plenty
CEO
Joined: 20 Mar 2014
Posts: 2622
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: The integer x has a tens digit of 6 and a units digit of 7. The units  [#permalink]

### Show Tags

17 Nov 2015, 03:21
3
1
The integer x has a tens digit of 6 and a units digit of 7. The units digit of integer y is 8. The product of x and y has a tens digit of 8. Which of the following is a possible tens digit of integer y?

A. 3
B. 4
C. 5
D. 6
E. 7

You can solve it by the following method:

X : 67
Y : a8

So

67*a8 should give you the tens digit as 3+7a = 8 ---> 7a = 5 and the only multiple of 7 that has a 5 in the units place is when you have 5*7 , giving you a=5.

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 7465
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: The integer x has a tens digit of 6 and a units digit of 7. The units  [#permalink]

### Show Tags

17 Nov 2015, 04:58
1
Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.

The integer x has a tens digit of 6 and a units digit of 7. The units digit of integer y is 8. The product of x and y has a tens digit of 8. Which of the following is a possible tens digit of integer y?

A. 3
B. 4
C. 5
D. 6
E. 7

Let x be 67 and y be a8. Then the product of x and y can be written as (60+7)*(10a+8)=600a + 480+70a+56=600a+536+70a. Since 600a dose not affect on the tens digit we can ignore 600a.
So tens digit should be the unit of 3+7a. That means 3+7a =8, 18, 28, 38, 48 or 58 (since 3+7a<=3+7*9=66) --->7a=5, 15, 25, 35, 45, 55. So the only possibility is a=5.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only \$149 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Manager
Joined: 13 Sep 2016
Posts: 118
GMAT 1: 800 Q51 V51
Re: The integer x has a tens digit of 6 and a units digit of 7. The units  [#permalink]

### Show Tags

03 Oct 2016, 23:04
MathRevolution wrote:
Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.

The integer x has a tens digit of 6 and a units digit of 7. The units digit of integer y is 8. The product of x and y has a tens digit of 8. Which of the following is a possible tens digit of integer y?

A. 3
B. 4
C. 5
D. 6
E. 7

Let x be 67 and y be a8. Then the product of x and y can be written as (60+7)*(10a+8)=600a + 480+70a+56=600a+536+70a. Since 600a dose not affect on the tens digit we can ignore 600a.
So tens digit should be the unit of 3+7a. That means 3+7a =8, 18, 28, 38, 48 or 58 (since 3+7a<=3+7*9=66) --->7a=5, 15, 25, 35, 45, 55. So the only possibility is a=5.

Hello,

Can you please elaborate how you arrived to below conclusion :-
"So tens digit should be the unit of 3+7a. That means 3+7a =8, 18, 28, 38, 48 or 58 (since 3+7a<=3+7*9=66) --->7a=5, 15, 25, 35, 45, 55. So the only possibility is a=5"
Thanks.
Current Student
Joined: 12 Aug 2015
Posts: 2610
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Re: The integer x has a tens digit of 6 and a units digit of 7. The units  [#permalink]

### Show Tags

23 Nov 2016, 09:33
1
I did it by Hit and trail.
Anyway here is my solution =>
x=67
y=p8
=> multiplying them => (10p+8)*67 => 670p+536 =>

Checking values
p=3 => Tens digit of the result =4
p=4 => Tens digit of the result =1
p=5 => Tens digit of the result =8
BINGO
Hence C
_________________
Intern
Joined: 16 Aug 2016
Posts: 7
Re: The integer x has a tens digit of 6 and a units digit of 7. The units  [#permalink]

### Show Tags

25 Nov 2016, 20:36
There hasn't been a lot of posting for quite some time.
However, could some please explain how we get to "3+7a" in the first place? How does this equation represent the tens digit?

Intern
Joined: 22 Jan 2017
Posts: 32
Re: The integer x has a tens digit of 6 and a units digit of 7. The units  [#permalink]

### Show Tags

17 Aug 2017, 19:32
I think I get where the confusion is. Admittedly I kind of stared at these solutions for a moment before understanding.

I did it a little differently (after getting it wrong the first time, naturally):

67 * (10a + 8)
670 * (a) + 536

Ok now we have some digit 'a' that has some bearing on what the 10's digit is going to be. What does 'a' interact with in that expression? The '0' on 670? yes, but it will be 0.

The '7' in 670? Yes --> ok then 7*a + 3 because the 3 comes from the 536 we need to add to our result in order to get a 10's digit of 8 for the product of x and y.

Therefore we have:

7a + 3 = 8
7a = 5
a = 5/7

In order for 'a' to be an integer, it needs to be a multiple of 7 and there's only one multiple of 7 in the answer choices.

Hope that helps!
Intern
Joined: 02 Jul 2017
Posts: 9
Re: The integer x has a tens digit of 6 and a units digit of 7. The units  [#permalink]

### Show Tags

17 Aug 2017, 20:04
67 * a8=
536
+ X 0=
Z86
7a=35 then x=5 will satisfy

Sent from my XT1706 using GMAT Club Forum mobile app
Non-Human User
Joined: 09 Sep 2013
Posts: 11396
Re: The integer x has a tens digit of 6 and a units digit of 7. The units  [#permalink]

### Show Tags

08 Jan 2019, 16:31
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: The integer x has a tens digit of 6 and a units digit of 7. The units   [#permalink] 08 Jan 2019, 16:31
Display posts from previous: Sort by