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

1

This post received 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.

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

4

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

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

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

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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(offline until 20th of march because of university exams)