Each panel below shows a GMAT math sample problem with a breakdown of the slow/hard way and the fast/easy way to solve it:
Albert will receive $14,600 over the period of one year in equal monthly payments.
How much will he have received after three months?
Then multiply by three to find the three-month total: $1220 x 3 = $3660
The arithmetic involved in this fast/easy solution is one short division (dividing by 3).
Which of the following values of p results in an integer value for the expression (77 +p) / p:
A) (77+4)/4 = 81/4…..Not an integer
B) (77+5)/5 = 82/5…..Not an integer
C) (77+6)/6 = 83/6…..Not an integer
D) (77+7)/7 = 84/7…..Bingo
E) (77+8)/8 = 85/8…..Not an integer
The +1 doesn’t affect the integer status of the result. So the question becomes: which of the following values of p makes 77 / p an integer?
Expressed differently, which value of p goes into 77? The answer is immediately seen to be 7 because 77 is 7 times 11.
Given the equation 30 + x = y – 42, which statement below would be sufficient to determine the value of y?
A) x = 3
B) y/x = 25
C) A and B are each sufficient on their own
D) A and B are sufficient only when combined
D) None of the above
A) Plugging in x=3 transforms the equation into 30+3 = y – 42 or y=42+30+3 =75. Conclusion: the information is sufficient.
B) Given y/x=25, we have y=25x. Substituting this, the original equation becomes 30+x = 25x – 42 or24x=72. This gives x=3, and so the equation can be solved for y in Statement B.
A) The equation given in the root is a linear equation in x and y. When a value of x is given, the equation becomes a linear equation one unknown, which has a solution; so the information is sufficient.
B) The equation given in the root is a linear equation in x and y, and the equation y/x=25, or y=25x, is another linear equation in two unknowns. Two independent linear equations in two unknowns determine a unique solution. So the information is sufficient.