Comparaison quantitative et raisonnement numérique
GRE General Test Sujet 3 2:15 Narration en anglais · Sous-titres anglais + 中文 incrustés
Chapitres
Transcript
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。