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GRE General Test 주제 11 2:49 영어 내레이션 · 영어 + 중국어 자막 burned-in
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This unit uses prime factorisation for divisibility, greatest common factors and least common multiples, interprets remainders with the original divisor, and combines ratios and percentage changes with the correct reference total.
本单元用质因数分解处理整除、最大公因数和最小公倍数，按原除数解释余数，并以正确的参照总量合并比例和百分比变化。
A number divisible by d is d k; a remainder r gives d k plus r, with r from 0 up to d.
能被 d 整除的数是 dk；余数为 r 时写成 dk + r，0 ≤ r < d。
The greatest common factor takes shared prime powers at their smaller exponents, and the least common multiple takes every prime at its larger exponent.
最大公因数取共有质因数的较小指数，最小公倍数取每个质因数的较大指数。
Keep parity and sign facts separate.
奇偶性和正负性要分开考虑。
A ratio a to b splits a whole into a plus b equal parts: 250 in the ratio 2 to 3 gives 100 and 150.
比 a : b 把整体分成 a + b 等份：250 按 2 : 3 分得 100 和 150。
A percentage change multiplies by 1 plus or minus r, and successive changes multiply.
百分比变化是乘以 1 ± r，连续变化要连乘。
A part of a part changes the reference group, so label each denominator.
部分中的部分会改变参照群体，所以要标明每个分母。
Shared smaller powers give GCF six, and needed larger powers give LCM seventy-two.
共有质因数取较小指数得最大公因数 6，所需质因数取较大指数得最小公倍数 72。
If n is 5k plus 2, then 2n is 5 times 2k plus 4: remainder four.
若 n = 5k + 2，则 2n = 5(2k) + 4：余数为 4。
For a model price of 100 CNY decreased then increased by 20 percent, the result is 96 CNY: the second change uses a different base.
100 元的价格先降 20% 再升 20%，结果是 96 元：第二次变化的基数不同。
Equal percentage increases and decreases use different bases.
相同百分比的增加和减少，基数不同。
A remainder must be reported relative to the named divisor.
余数必须相对于题目指定的除数来报告。
Factor 36 and 60: the GCF is 12 and the LCM 180, and their product equals 36 times 60.
分解 36 和 60：最大公因数 12，最小公倍数 180，两者之积等于 36 × 60。
The price multiplier is 1.25 times 0.80, which is exactly 1: zero change.
价格乘数是 1.25 × 0.80 = 1：没有变化。
Adding plus 25 and minus 20 would wrongly give a 5 percent rise.
把 +25 和 −20 相加会错误地得到上涨 5%。
Write n as 8k plus 5.
把 n 写成 8k + 5。
Then 3n plus 7 is 8 times 3k plus 2, plus 6: remainder six for every integer k, negative included.
则 3n + 7 = 8(3k + 2) + 6：对每个整数 k（包括负数）余数都是 6。
The value grows by 1.1 times 1.2, which is 1.32; dividing back needs a cut of 8 over 33, about 24.24 percent, not 30.
数值增长为 1.1 × 1.2 = 1.32 倍；还原需要减少 8/33，约 24.24%，不是 30%。
Check yourself.
自我检测。
18 and 24 have GCF 6 and LCM 72.
18 和 24 的最大公因数是 6，最小公倍数是 72。
2n leaves 4 on division by 5.
2n 除以 5 余 4。
100 CNY down then up 20 percent ends at 96.
100 元先降后升 20% 得 96 元。
Up 25 then down 20 is no change.
先升 25% 再降 20% 不变。
And undoing 1.32 needs about a 24.24 percent cut.
还原 1.32 倍约需减少 24.24%。