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If Δ and ∅ represent single digits in the correctly worked c
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Updated on: 22 Aug 2013, 04:04
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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
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Originally posted by Asifpirlo on 21 Aug 2013, 18:25.
Last edited by Bunuel on 22 Aug 2013, 04:04, edited 1 time in total.
Edited the question.




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Re: If Δ and ∅ represent single digits in the correctly worked c
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23 Aug 2013, 12:53
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
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21 Aug 2013, 19:21
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
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21 Aug 2013, 19:40
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
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24 Aug 2013, 06:42
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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Re: If Δ and ∅ represent single digits in the correctly worked c
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19 Sep 2013, 09:10
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



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Re: If Δ and ∅ represent single digits in the correctly worked c
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01 Oct 2013, 06:46
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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Re: If Δ and ∅ represent single digits in the correctly worked c
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22 Jan 2014, 08:26
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
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22 Jan 2014, 11:19
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<=3I 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
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22 Jan 2014, 11:25
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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