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GRE General Test 주제 3 2:15 영어 내레이션 · 영어 + 중국어 자막 burned-in
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This unit compares quantities across all allowed values, uses arithmetic, ratios, divisibility and powers, and recognises when the relationship cannot be determined.
本单元在所有允许的取值下比较两个量，使用算术、比例、整除和乘方，并识别关系无法确定的情形。
Quantitative comparison has four fixed answers: A greater, B greater, equal, or cannot be determined.
数量比较题有四个固定答案：A 大、B 大、相等、无法确定。
A fixed relationship needs a proof for every allowed value; cannot be determined needs two allowed cases that disagree.
固定关系需要对每个允许的值都成立的证明；无法确定则需要两个结论不同的允许情形。
Check all constraints: a variable can be negative, zero or fractional unless the stem restricts it.
检查所有约束：除非题干限制，变量可以是负数、零或分数。
Strategic substitutions can disprove a fixed relation, but a few examples never prove one.
有针对性的代入可以否定固定关系，但几个例子永远证明不了它。
Simplify without dividing by a value that could be zero or negative.
化简时不要除以可能为零或为负的量。
Given x squared equals 9, x can be 3 or minus 3.
已知 x² = 9，x 可以是 3 或 −3。
Quantity A is x and B is 0.
量 A 是 x，量 B 是 0。
A is greater for 3 and smaller for minus 3, so the relationship cannot be determined.
x = 3 时 A 大，x = −3 时 A 小，所以关系无法确定。
If x is positive, only 3 is allowed and A is greater.
若 x 为正，只允许 3，A 大。
Figures are not necessarily drawn to scale.
图形不一定按比例绘制。
Given labels and constraints carry the evidence.
给出的标注和约束条件才是依据。
Without the added condition, x equals 4 makes A greater and x equals minus 4 makes B greater: D.
没有附加条件时，x = 4 使 A 大，x = −4 使 B 大：选 D。
With x positive, only 4 is permitted: A.
加上 x > 0 后，只允许 4：选 A。
The principal square root of 16 is four, but the equation has both roots.
16 的算术平方根是 4，但这个方程有两个根。
With a equals 2 and b minus 1, B is greater.
a = 2、b = −1 时 B 大。
With a equals 1 and b minus 2, A is greater.
a = 1、b = −2 时 A 大。
With a equals 1 and b minus 1, they are equal.
a = 1、b = −1 时两者相等。
Equality needs a squared equal to b squared, so a equals minus b.
相等需要 a² = b²，即 a = −b。
Multiplying by the negative product a b reverses an inequality.
乘以负的乘积 ab 会使不等号反向。
Check yourself.
自我检测。
x squared equals 9 against zero is D, and with x positive it is A.
x² = 9 时 x 与 0 比较选 D，加上 x > 0 选 A。
Examples cannot prove a fixed relation.
例子证明不了固定关系。
A figure's look is not evidence.
图形的样子不是证据。
And a over b against b over a, with opposite signs, is D.
符号相反时 a/b 与 b/a 比较选 D。