Mind the wording when decoding comparison expressions
by Gustavo Luyo
Many comparison expressions in the GMAT are hard to decode for us native speakers of Spanish, because most of the times they sound reversed in our mind. Let us review two of such mind-boggling expressions.
“X is n more than Y”
There is a tendency among native Spanish speakers to decode this as:
X = n + Y
This is not actually wrong as the true meaning of the expression indeed implies the addition of both n and Y, notwithstanding the order in which the two terms are considered, which is a consequence of the commutative law of addition. But the original verbal expression correctly highlights not the mere fact that the two quantities are being added but, rather, the fact that X exceeds or surpasses Y by a certain amount n. Thus, the correct rendering would be:
X = Y + n,
as the focus of the comparison with X is not n but Y. In fact, the relevance of the order of the terms in the rendered math expression can be fully appreciated in the next item discussed.
“X is n less than Y”
Reading this expression in quant problems in a hurry will often lead Spanish speakers to a common mistranslation, in math terms:
X = n – Y
The mistake arises from the fact that Spanish has the same word for translating ‘less’ and ‘-’ (hyphen), when the latter symbol refers to the subtraction operation (they are both read as ‘menos’). However, English refers distinctively to the subtraction operator between two amounts as ‘minus’ rather than ‘less’. Thus, hastily focusing on the word ‘less’ and disregarding the word ‘than’ would often lead to a misguided rendering of the expression. For the above rendered expression to be correct, the problem statement involving the expression should go along something like “… X equals n minus Y…”. On the contrary, what our subject expression intends to get across is the fact that, in comparison with Y, the quantity X is diminished in or lacking an amount that equals n. So, the correct math rendering would be:
X = Y – n
Incidentally, when the above expression is read out, it should be “X equals Y minus n”, not “X equals Y less n “.
It goes without saying the crucial importance of correctly understanding this expression in the GMAT. In Problem Solving, a wrong answer often goes unnoticed until the very moment that your answer is found not to match any of the five possible answer choices. The test takers might lose invaluable time checking the accuracy of whatever calculations were done to yield their answer; and in most cases this would lead to abandoning the question without understanding what went wrong, oblivious to the fact the mistake was literally ‘under their nose’.
Sometimes, the wrong answer choice might appear before the test-taker’s eyes, so their doom would be invariable.
Let us consider the following PS example:
Let x, y, w, and z be numbers on the number line, though not necessarily in that order. It is known that x is 2 more than y, and x is √2 less than z. If w is 2√2 less than y, then what is the value of z in terms of w?
- w + 2 – √2
- w – 2 – √2
- w + 2 – 3√2
- w + 2 +3√2
- w + 1-3√2
Let us consider what the solving could be like if the wrong assumption (X = n – Y) is considered:
Be x=2+y,also x= √2-z and w=2√2- y. Then, isolating z in terms of x yields:
z= √2-x. After substituting the value of x in terms of y we have: z= √2-2-y.
Finally, we substitute the value of y in terms of w: z=√2-2-(2√2-w), which finally yields:
z=w-2-√2 (option B).
On the contrary, correctly formulating the first approach to the relationship among the variables leads to the following:
Be x=y+2, also let x=z-√2 and w=y-2√2.
Then, equating the first two equations yields:
Substituting the value of y from the third premise equation yields:
z=(w+2√(2))+2+√2, which finally becomes z=w+2+3√2 (option D).
As for Data Sufficiency, the situation becomes even worse, since there is no answer choice against which to verify the validity of their assumptions or calculations. Therefore, the mistake here would unobtrusively lead to a wrong answer choice.