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Bunuel
If x=1034*1033, which of the following is equal to 1033*1032 ?

A. x − 1033
B. x − 1034
C. x − 2066
D. x − 2067
E. 2x − 2065

Hi,

Let us assume 1032 as a, hence 1033=a+1 and 1034=a+2.
This means that x=(a+2) * (a+1) and we have to find an option that equals (a+1) * a.
Substituting the value of x in the options, we get C as the answer as -
    x - 2066
    = ((a+2) * (a+1)) - (2 * (a+1))
    =(a + 1) (a+2 - 2)
    =(a+1) * a
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1032*1033 can also be written as (1034-2)*1033 = (1034*1033) - (2*1033) = x - 2066.

Hence, C.
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Solution



Given

    • X = 1034 × 1033

To Find

    • 1033 × 1032 in terms of x.

Approach and Working Out

    • We can interpret x as, 1034 number of 1033s.
      o 1033 × 1032 is 1032 number of 1033s, this is two 1033s fewer.
      o Hence, the difference in my answer should be 1033 × 2 fewer than X.

Correct Answer: Option C
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Bunuel
If x=1034*1033, which of the following is equal to 1033*1032 ?

A. x − 1033
B. x − 1034
C. x − 2066
D. x − 2067
E. 2x − 2065

Asked: If x=1034*1033, which of the following is equal to 1033*1032 ?

1033*1032 = 1033*(1034-2) = x - 2*1033 = x - 2066

IMO C
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Once you know x=1034*1033, you know the units digit of X is 2.
If 1033*1032 has 6 as the units digit, the difference between them should be another number that ends with 6

Only possible option = 2066
C

Isn't it correct?
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I should work on being more formulaic, but you can also logic your way through this one.
x = 1034 * 1033
y = 1033 * 1032

Really, I know that whatever the difference is on x, it's going to be about the distance between that 1034 and 1032, since the 1033 appears on both. The difference is 2, but two of what? Thinking it through, it's two of 1033, which is the matching comparison unit. You could also change it so it's
1033(1032-1034) if you like to see it in a formula I guess.

Hopefully that helps people who are trying to push through.
Bunuel
If x=1034*1033, which of the following is equal to 1033*1032 ?

A. x − 1033
B. x − 1034
C. x − 2066
D. x − 2067
E. 2x − 2065
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