If Δ and ∅ represent single digits in the correctly worked c : GMAT Problem Solving (PS)
Check GMAT Club App Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 09 Dec 2016, 22:30

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If Δ and ∅ represent single digits in the correctly worked c

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 10 Jul 2013
Posts: 335
Followers: 3

Kudos [?]: 306 [1] , given: 102

If Δ and ∅ represent single digits in the correctly worked c [#permalink]

### Show Tags

21 Aug 2013, 17:25
1
KUDOS
7
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

63% (04:14) correct 37% (02:27) wrong based on 189 sessions

### HideShow timer Statistics

Attachment:

rrrrrrrr.png [ 1.57 KiB | Viewed 3001 times ]
If Δ and ∅ represent single digits in the correctly worked computation above, what is the value of Δ times ∅?

A. 6
B. 10
C. 12
D. 15
E. 18
[Reveal] Spoiler: OA

_________________

Asif vai.....

Last edited by Bunuel on 22 Aug 2013, 03:04, edited 1 time in total.
Edited the question.
Manager
Joined: 31 Jul 2013
Posts: 52
Location: United States
Concentration: General Management, Entrepreneurship
GPA: 3.6
WE: Law (Entertainment and Sports)
Followers: 1

Kudos [?]: 26 [0], given: 4

Re: If Δ and ∅ represent single digits in the correctly worked c [#permalink]

### Show Tags

21 Aug 2013, 18:21
Ahh nevermind...miswrote the problem on my scratch paper, haha. Good question.
Manager
Joined: 31 Jul 2013
Posts: 52
Location: United States
Concentration: General Management, Entrepreneurship
GPA: 3.6
WE: Law (Entertainment and Sports)
Followers: 1

Kudos [?]: 26 [2] , given: 4

Re: If Δ and ∅ represent single digits in the correctly worked c [#permalink]

### Show Tags

21 Aug 2013, 18:40
2
KUDOS
Asifpirlo wrote:
If Δ and ∅ represent single digits in the correctly worked computation above,
what is the value of Δ times ∅?
A. 6
B. 10
C. 12
D. 15
E. 18

So we have 2X7 * Y14 = 80,698. Off the bat, I know that 200x400=80,000, so I immediately think it must be 414 and 207. I could calculate this out (to 85,698) but it would be a waste of time, since I know already that 4 and 0 can't be the combination given 0 isn't an answer choice. Therefore, Y must be 3. By this logic alone, I can eliminate B as it is not a multiple of 3.

For the other number, I do a quick estimate in my head, that 300 x 260 = 78,000. Given that 314 is a bit more than 300, our number must be less than 260. I try 314 x 257 and get 80,698. So 3 x 5 = 15, and D is the answer.
Manager
Joined: 19 Oct 2012
Posts: 214
Location: India
Concentration: General Management, Operations
GMAT 1: 660 Q47 V35
GPA: 3.81
WE: Information Technology (Computer Software)
Followers: 1

Kudos [?]: 1 [4] , given: 30

Re: If Δ and ∅ represent single digits in the correctly worked c [#permalink]

### Show Tags

23 Aug 2013, 11:53
4
KUDOS
1
This post was
BOOKMARKED
Good question.

I solved using the basic approach to multiply the two 3 digit numbers.

Let triangle be ^
and Theta be @

then our question becomes
2^7
x @14
--------
80,698

Doing basic multiplication.

2^7
x @14
--------
_ 8
7

---------
98 (here 9 can be only achieved when 7 gets added to 2 which can only happen when ^ is 5 and 4 x 5 =20 plus carry 2 from 4x7).

Replacing ^ by 5.

257
x @14
--------
1 0 2 8
2 5 7

---------
6 9 8 (again 6 here will only be possible when 5 gets added to 1, which is only possible when 7 gets multiplied to 3 resulting in 1 and carry 2).

Hence @ = 3

There for the answer is 3 x 5 =15.
_________________

Citius, Altius, Fortius

Manager
Status: Persevering
Joined: 15 May 2013
Posts: 225
Location: India
GMAT Date: 08-02-2013
GPA: 3.7
WE: Consulting (Consulting)
Followers: 1

Kudos [?]: 86 [0], given: 34

Re: If Δ and ∅ represent single digits in the correctly worked c [#permalink]

### Show Tags

24 Aug 2013, 05:42
replacing delta symbol with a and phi symbol with b

Here 2a7*b14; 4*7=28, so 2 carried over; The next digit after multiplication is (4*a+1*7+2(carried over))=10m+9
=> 4*a=0 or 4*a=10m; now only a=5 satisfies this. Look at the options only two are multiples of 5. So solve for third digit you get (4*2+a*1+7*b+2 (carried over))=10n+6; as a=5 =>9+7b=10n; only b=3 satisfies this

therefore D it is . I have used vedic multiplication here.
_________________

--It's one thing to get defeated, but another to accept it.

Manager
Joined: 11 Sep 2013
Posts: 115
Followers: 1

Kudos [?]: 67 [0], given: 26

Re: If Δ and ∅ represent single digits in the correctly worked c [#permalink]

### Show Tags

19 Sep 2013, 08:10
Asifpirlo wrote:
Attachment:
rrrrrrrr.png
If Δ and ∅ represent single digits in the correctly worked computation above, what is the value of Δ times ∅?

A. 6
B. 10
C. 12
D. 15
E. 18

2X7 * Y14 = (207+10X)(100Y+14) = 20,700Y+2,898+1000XY+140X=80698

=> 20,700Y+1000XY+140X=77,800
=> 2,070Y+100XY+14X=7,780
=> Y<=3

Y=3: 300X+14X=1570 => X=5
Y=2: X has 2 digits

So there is only one option: X=5, Y=3 => Result = 15 => Choose D
Manager
Joined: 23 May 2013
Posts: 127
Followers: 1

Kudos [?]: 54 [0], given: 110

Re: If Δ and ∅ represent single digits in the correctly worked c [#permalink]

### Show Tags

01 Oct 2013, 05:46
camlan1990 wrote:
Asifpirlo wrote:
Attachment:
rrrrrrrr.png
If Δ and ∅ represent single digits in the correctly worked computation above, what is the value of Δ times ∅?

A. 6
B. 10
C. 12
D. 15
E. 18

2X7 * Y14 = (207+10X)(100Y+14) = 20,700Y+2,898+1000XY+140X=80698

=> 20,700Y+1000XY+140X=77,800
=> 2,070Y+100XY+14X=7,780
=> Y<=3

Y=3: 300X+14X=1570 => X=5
Y=2: X has 2 digits

So there is only one option: X=5, Y=3 => Result = 15 => Choose D

how do you imply that Y<=3?

=> 2,070Y+100XY+14X=7,780
=> Y<=3
_________________

“Confidence comes not from always being right but from not fearing to be wrong.”

Current Student
Joined: 06 Sep 2013
Posts: 2035
Concentration: Finance
GMAT 1: 770 Q0 V
Followers: 60

Kudos [?]: 582 [1] , given: 355

Re: If Δ and ∅ represent single digits in the correctly worked c [#permalink]

### Show Tags

22 Jan 2014, 07:26
1
KUDOS
vabhs192003 wrote:
Good question.

I solved using the basic approach to multiply the two 3 digit numbers.

Let triangle be ^
and Theta be @

then our question becomes
2^7
x @14
--------
80,698

Doing basic multiplication.

2^7
x @14
--------
_ 8
7

---------
98 (here 9 can be only achieved when 7 gets added to 2 which can only happen when ^ is 5 and 4 x 5 =20 plus carry 2 from 4x7).

Replacing ^ by 5.

257
x @14
--------
1 0 2 8
2 5 7

---------
6 9 8 (again 6 here will only be possible when 5 gets added to 1, which is only possible when 7 gets multiplied to 3 resulting in 1 and carry 2).

Hence @ = 3

There for the answer is 3 x 5 =15.

Well done, and actually once you know that one of the digits is 5 you can proceed to pick the only answer choice that is a multiple of 5

Cheers +1 Kudos
J
Intern
Status: Student
Joined: 06 Oct 2013
Posts: 28
Location: Germany
Concentration: Operations, General Management
GMAT 1: 670 Q49 V35
GPA: 2.4
WE: Other (Consulting)
Followers: 1

Kudos [?]: 25 [0], given: 17

Re: If Δ and ∅ represent single digits in the correctly worked c [#permalink]

### Show Tags

22 Jan 2014, 10:19
ankur1901 wrote:
camlan1990 wrote:
Asifpirlo wrote:
Attachment:
rrrrrrrr.png
If Δ and ∅ represent single digits in the correctly worked computation above, what is the value of Δ times ∅?

A. 6
B. 10
C. 12
D. 15
E. 18

2X7 * Y14 = (207+10X)(100Y+14) = 20,700Y+2,898+1000XY+140X=80698

=> 20,700Y+1000XY+140X=77,800
=> 2,070Y+100XY+14X=7,780
=> Y<=3

Y=3: 300X+14X=1570 => X=5
Y=2: X has 2 digits

So there is only one option: X=5, Y=3 => Result = 15 => Choose D

how do you imply that Y<=3?

=> 2,070Y+100XY+14X=7,780
=> Y<=3

I guess you search for the maximal value of Y (with x=1) which gives us a total value below 7,780.
If y=4 the equation would be above the 7,780 no matter what value x is.
So if y=3 you have a result below 7,780 giving "some space" for x.
_________________

Thank You = 1 Kudos
B.Sc., International Production Engineering and Management
M.Sc. mult., European Master in Management Candidate

_______________________________________________________

#1 Official GMAT Prep 1: 530 (Q41 V21), 10/10/13
#2 Manhattan GMAT CAT 1: 600 (Q43 V30), 12/17/13
#3 Manhattan GMAT CAT 2: 640 (Q43 V34), 01/13/14
#4 Manhattan GMAT CAT 3: 660 (Q45 V35), 01/16/14
#5 Manhattan GMAT CAT 4: 650 (Q45 V34), 01/18/14
#6 Manhattan GMAT CAT 5: 660 (Q42 V38), 01/21/14
#7 Official GMAT Prep 2: 640 (Q48 V30), 01/26/14
GMAT 670 Q49 V34 AWA5 IR6 - TOEFL ibt 110

Intern
Status: Student
Joined: 06 Oct 2013
Posts: 28
Location: Germany
Concentration: Operations, General Management
GMAT 1: 670 Q49 V35
GPA: 2.4
WE: Other (Consulting)
Followers: 1

Kudos [?]: 25 [1] , given: 17

Re: If Δ and ∅ represent single digits in the correctly worked c [#permalink]

### Show Tags

22 Jan 2014, 10:25
1
KUDOS
I don't know if this solution is just luck or a good process:

$$\frac{80698}{217} = 371.88......$$

So we try y=3

$$\frac{80698}{314} = 257$$

works

if it doesn't work, one should try dividing by 297.
_________________

Thank You = 1 Kudos
B.Sc., International Production Engineering and Management
M.Sc. mult., European Master in Management Candidate

_______________________________________________________

#1 Official GMAT Prep 1: 530 (Q41 V21), 10/10/13
#2 Manhattan GMAT CAT 1: 600 (Q43 V30), 12/17/13
#3 Manhattan GMAT CAT 2: 640 (Q43 V34), 01/13/14
#4 Manhattan GMAT CAT 3: 660 (Q45 V35), 01/16/14
#5 Manhattan GMAT CAT 4: 650 (Q45 V34), 01/18/14
#6 Manhattan GMAT CAT 5: 660 (Q42 V38), 01/21/14
#7 Official GMAT Prep 2: 640 (Q48 V30), 01/26/14
GMAT 670 Q49 V34 AWA5 IR6 - TOEFL ibt 110

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 12904
Followers: 562

Kudos [?]: 158 [0], given: 0

Re: If Δ and ∅ represent single digits in the correctly worked c [#permalink]

### Show Tags

03 Feb 2015, 04:12
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.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 12904
Followers: 562

Kudos [?]: 158 [0], given: 0

Re: If Δ and ∅ represent single digits in the correctly worked c [#permalink]

### Show Tags

22 Aug 2016, 18:23
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: If Δ and ∅ represent single digits in the correctly worked c   [#permalink] 22 Aug 2016, 18:23
Similar topics Replies Last post
Similar
Topics:
In the above correctly worked addition sum, A,B,C and D represent diff 6 19 May 2016, 02:03
If a and b represent positive single digits in the correctly worked 6 23 Mar 2016, 11:19
5 If P represents a single digit in the four digit number x=17P6, how ma 5 11 Aug 2015, 13:20
2 If a and b represent positive single digits in the correctly worked co 4 27 Oct 2014, 07:41
3 In the correctly worked computation above A, B, C and D repr 3 14 May 2013, 07:31
Display posts from previous: Sort by

# If Δ and ∅ represent single digits in the correctly worked c

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.