268 MCGRAW-HILL’S SAT
sum of all the scores: (30)(80) + (20)(70) and
(50)(x). Since these must be equal,2,400 + 1,400 = 50x
Simplify: 3,800 = 50x
Divide by 50: 76 = x- 42 Do the prime factorization of 168: 2^3 × 3 ×7.
Since, in a perfect square, all prime factors “pair
up,” we need to multiply at least one more factor
of 2, one more factor of 3, and one more factor of
7 to make a perfect square: 2^4 × 32 × 72 = 7,056 = 84^2.
(Notice that now every factor appears an even
number of times.) Therefore, k= 2 × 3 ×7 = 42.