M09-14

Question

What is the value of  987 * 987 ?

A. 974,169
B. 974,219
C. 974,549
D. 975,019
E. 975,369

Bunuel · Accepted Answer

Official Solution:

What is the value of  987 * 987 ?

A. 974,169
B. 974,219
C. 974,549
D. 975,019
E. 975,369

APROACH 1:

987 * 987= 
 
= 987^2= 
 
= (1,000 - 13)^2= 
 
= 1,000^2 - 2*1000*13 + 13^2= 
 
= 1,000,000 - 26,000 + 169= 
 
= 9740,000 + 169= 
 
= 974,169 .

APROACH 2:

987 * 987= 
 
= 987^2= 
 
= 987^2-13^2+13^2= 
 
= (987 + 13)(987 - 13) + 13^2= 
 
 =1000*974 + 169= 
 
 =974,169=

Answer: A

JackSparr0w · Answer

Notice that the 10's digit of all the answer choices is different. Perform regular multiplication till you can calculate what the 10's digit will be.

987
  x987 
 6906 (multiplied 7 in denominator by the numerator)
 78960 (multiplied numerator by 8)

No need to multiply by the 9 in the denominator. We can see that the tens digit will be 6. We actually didn't need to multiply the 7 or the 8 all the way across either, but it's simple to do, and may help avoid errors.

Best

alandizzle · Answer

Thanks Brunnel! That was a great breakdown of using the difference of two squares to solve this problem!

Vikram_Katti · Answer

I think this is a  high-quality  question. Another approach - 987 x 987 = (1000-13) x (1000-13) = (1000-13)^2

nitsrj · Answer

The best way to solve this question (What is 987 * 987?) is by elimination method.

we know 987*987 has to be divisible by 9, since 987 is divisible by 3.
Using the divisor rule of 9 in the options: correct answer should be the one whose sum of digits is divisible by 9.

974,169= 36
974,219= 32
974,549= 38
975,019= 31
975,369= 39

only 36 is divisible by 9, so A is correct

CAMANISHPARMAR · Answer

Use  (a-b)^2  =  a^2+b^2-2ab  to solve the question.

987 * 987 = (1000-13)*(1000-13) = 1000^2+13^2-2*1000*13 = 1000000 + 169 - 26000 (STOP here) ...Don't solve it further. Just realise that the final solution will have 169 as the last 3 digits. Only option A has it. Correct Ans is A.

nghduc · Answer

I think the easier approach is that

987*987 = (1000-13)* (1000-13) = (1000-13)^2 = (1000)^2 + 13^2 -26000

Then because of 13^2 = 169, i should pick the choice with 169 at the tail. (1000^2 - 26000 will be a number with trailing zeros).

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

M09-14

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