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22 Mar 2018, 23:56
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
(low)
Question Stats:
93% (01:04) correct
7%
(01:04)
wrong
based on 44
sessions
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Solution X contains 4*10^(–2) grams of sugar. Solution Y contains 8*10^2 grams of sugar. The number of grams of sugar in solution Y is how many times the number of grams of sugar in solution X?
(A) 0.0002
(B) 0.002
(C) 200
(D) 2,000
(E) 20,000
(A) 0.0002
(B) 0.002
(C) 200
(D) 2,000
(E) 20,000
23 Mar 2018, 00:19
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Bunuel
8x10^2/4x10^ -2
= 2 x 10^2 / 10^-2 = 2 x 10^4
(E) imo
23 Mar 2018, 08:53
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Bunuel
Y, number of grams of sugar = \(8*10^2\)
X, number of grams of sugar = \(4*10^{-2}\)
Number of grams of sugar in Y is how many times the number of grams of sugar in X?
\(\frac{Y}{X}=\frac{8*10^2}{4*10^{-2}}=\)?
1) Move \(10^{-2}\) to the numerator.
Any number with a negative power in the denominator can be moved to the numerator.
Change the exponent's sign
\(\frac{Y}{X}=\frac{8*10^2}{4*10^{-2}}=\frac{8*10^2*10^2}{4}=\)
\(\frac{8*10^{(2+2)}}{4}=\frac{8*10^4}{4}=2*10^{4}=20,000\)
OR
2) Division of exponents (same base) =
Keep the base, subtract the exponents
\(\frac{Y}{X}=\frac{8*10^2}{4*10^{-2}}=\frac{8*10^{2-(-2)}}{4}=\)
\(\frac{8*10^{2+2}}{4}=\frac{8*10^4}{4}=2*10^4=20,000\)
OR
3) divide integers, then powers of 10.
Integers and powers of 10 are factors of the numbers. Results of separate operations are also factors -- i.e., multiply the results
Number in Y is how many times number in X?
Number in Y = \(8*10^2\)
Number in X = \(4*10^{-2}\)
\(\frac{8}{4} = 2\)
\(\frac{10^2}{10^{-2}}=10^{2-(-2)}=10^{2+2}=10^4\)
Multiply results: \(2*10^4=20,000\)
Answer E
