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Math Expert V
Joined: 02 Sep 2009
Posts: 56368
If 893 × 78 = p, which of the following is equal to 893 × 79?  [#permalink]

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14 00:00

Difficulty:   5% (low)

Question Stats: 90% (00:41) correct 10% (00:57) wrong based on 1326 sessions

### HideShow timer Statistics If 893 × 78 = p, which of the following is equal to 893 × 79?

(A) p + 1
(B) p + 78
(C) p + 79
(D) p + 893
(E) p + 894

Kudos for a correct solution.

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Joined: 12 Sep 2015
Posts: 3857
Re: If 893 × 78 = p, which of the following is equal to 893 × 79?  [#permalink]

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7
4
Bunuel wrote:
If 893 × 78 = p, which of the following is equal to 893 × 79?

(A) p + 1
(B) p + 78
(C) p + 79
(D) p + 893
(E) p + 894

Kudos for a correct solution.

Given: 893 x 78 = P

893 x 79 = 893 x (78 + 1)
= (893)(78) + (893)(1)
= P + 893
= D

Cheers,
Brent
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Re: If 893 × 78 = p, which of the following is equal to 893 × 79?  [#permalink]

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893x79= 893x(78+1)
= 893x 78 + 893x1
= p+ 893
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Intern  Joined: 01 Dec 2014
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GMAT 1: 640 Q49 V27 Re: If 893 × 78 = p, which of the following is equal to 893 × 79?  [#permalink]

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1
Given: 893 * 78 = p;

To Find: 893 * 79?

893 * 78 = p ---- Eq. 1
893 * 79 = 893 * (78+1) = 893*78 + 893*1 ---Eq. 2 Substituting Eq 1 in Eq 2 (893*78=p)
Hence,
p+893

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Joined: 16 Aug 2015
Posts: 7631
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: If 893 × 78 = p, which of the following is equal to 893 × 79?  [#permalink]

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2
Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.

If 893 × 78 = p, which of the following is equal to 893 × 79?

(A) p + 1
(B) p + 78
(C) p + 79
(D) p + 893
(E) p + 894

Since 893 × 78 = p and 79=78+1, we have 893 × 79 = 893 ×(78+1)=893×78 + 893 ×1 = p + 893.

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Re: If 893 × 78 = p, which of the following is equal to 893 × 79?  [#permalink]

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1
893*78=p (given)
893*79 = 893*(78+1)
78=p/893
893*(p/893+1)
=p+893
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GMAT 1: 620 Q48 V27 Re: If 893 × 78 = p, which of the following is equal to 893 × 79?  [#permalink]

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4
No need to do all these steps if you are clear about the concept of multiplication you can straight away mark the answer within 10 seconds. We know that any constant number multiplied by increment of 1 actually adds the same constant to the previous result. For instance 4*2 = 8
4*3 = 12 which is 8 from previous result + constant 4 which is being multiplied everytime. Multiplication is repeated addition. Hence answer is p+893
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Manager  S
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Location: United States
Concentration: Finance, Technology
Schools: LBS '18, IE April '17
GMAT 1: 620 Q48 V27 Re: If 893 × 78 = p, which of the following is equal to 893 × 79?  [#permalink]

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1
No need to do all these steps if you are clear about the concept of multiplication you can straight away mark the answer within 10 seconds. We know that any constant number multiplied by increment of 1 actually adds the same constant to the previous result. For instance 4*2 = 8
4*3 = 12 which is 8 from previous result + constant 4 which is being multiplied everytime. Multiplication is repeated addition. Hence answer is p+893
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Re: If 893 × 78 = p, which of the following is equal to 893 × 79?  [#permalink]

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Re: If 893 × 78 = p, which of the following is equal to 893 × 79?  [#permalink]

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I have a doubt in Option E
So P+894= 893*78+894 = (893*78)+ (893+1)=893(78+1)=893*79
Im sure that there is some mistake with the method that i followed above but Im not understanding where am i going wrong because if you back solve from the above method 893(78+1)=893*78+893. Can someone help ?
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Joined: 12 Sep 2015
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Re: If 893 × 78 = p, which of the following is equal to 893 × 79?  [#permalink]

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Top Contributor
longhaul123 wrote:
I have a doubt in Option E
So P+894= 893*78+894 = (893*78)+ (893+1)=893(78+1)=893*79
Im sure that there is some mistake with the method that i followed above but Im not understanding where am i going wrong because if you back solve from the above method 893(78+1)=893*78+893. Can someone help ?

There's a problem where you get 893(78+1)=893*79

You are correct to say that P+894= 893*78+894 = (893*78)+ (893+1)
However, the next step cannot be the one you took
You are treating (893+1) as though it were (893*1)

Notice that if we have (893*78)+ (893*1), then we can factor out the 893 to get: (893*78)+ (893*1) = 893(78 + 1)
However, If we have (893*78) + (893+1), we cannot factor out the 893 (as I did above)

Does that help?

Cheers,
Brent
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Re: If 893 × 78 = p, which of the following is equal to 893 × 79?  [#permalink]

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1
Bunuel wrote:
If 893 × 78 = p, which of the following is equal to 893 × 79?

(A) p + 1
(B) p + 78
(C) p + 79
(D) p + 893
(E) p + 894

We are given that 893 x 78 = p and need to determine, in terms of p, the value of 893 x 79.

893 x 79 can be expressed as: 893 x (1 + 78) = 893 + 893 x 78.

Since p = 893 x 78, we can substitute p for 893 x 78 in the expression 893 + 893 x 78.

Thus, 893 x 79 = 893 + p

Alternate Solution:

The multiplication 893 x 78 means that we add 893 a total of 78 times, and this sum is equal to p. Now if we perform the multiplication problem 893 x 79, it means that we will add one more 893 to the previous sum, so we have p + 893 as our answer.

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Re: If 893 × 78 = p, which of the following is equal to 893 × 79?  [#permalink]

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1
Bunuel wrote:
If 893 × 78 = p, which of the following is equal to 893 × 79?

(A) p + 1
(B) p + 78
(C) p + 79
(D) p + 893
(E) p + 894

Kudos for a correct solution.

what's the difference between 893 x 78 and 893 x 79.

In 893 x 79, 893 was counted once more.

It means , 893 x 78 + 893 = p + 893. Re: If 893 × 78 = p, which of the following is equal to 893 × 79?   [#permalink] 28 Sep 2018, 06:54
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