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

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Senior Manager
Joined: 10 Jul 2013
Posts: 273
If Δ and ∅ represent single digits in the correctly worked c  [#permalink]

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Updated on: 22 Aug 2013, 03:04
2
10
00:00

Difficulty:

85% (hard)

Question Stats:

62% (03:00) correct 38% (03:06) wrong based on 205 sessions

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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

Originally posted by Asifpirlo on 21 Aug 2013, 17:25.
Last edited by Bunuel on 22 Aug 2013, 03:04, edited 1 time in total.
Edited the question.
Senior Manager
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Re: If Δ and ∅ represent single digits in the correctly worked c  [#permalink]

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23 Aug 2013, 11:53
4
1
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.
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Re: If Δ and ∅ represent single digits in the correctly worked c  [#permalink]

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21 Aug 2013, 18:21
Ahh nevermind...miswrote the problem on my scratch paper, haha. Good question.
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Re: If Δ and ∅ represent single digits in the correctly worked c  [#permalink]

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21 Aug 2013, 18:40
3
1
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.
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Re: If Δ and ∅ represent single digits in the correctly worked c  [#permalink]

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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.
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Joined: 11 Sep 2013
Posts: 103
Re: If Δ and ∅ represent single digits in the correctly worked c  [#permalink]

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19 Sep 2013, 08:10
1
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
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Re: If Δ and ∅ represent single digits in the correctly worked c  [#permalink]

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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
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Joined: 06 Sep 2013
Posts: 1494
Concentration: Finance
Re: If Δ and ∅ represent single digits in the correctly worked c  [#permalink]

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22 Jan 2014, 07:26
1
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
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Re: If Δ and ∅ represent single digits in the correctly worked c  [#permalink]

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

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22 Jan 2014, 10:25
1
1
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.
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Re: If Δ and ∅ represent single digits in the correctly worked c  [#permalink]

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16 Aug 2019, 05:39
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Re: If Δ and ∅ represent single digits in the correctly worked c   [#permalink] 16 Aug 2019, 05:39