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GMAT/Data Sufficiency - Prima 57
Prima 57
If x, y, and z are positive integers such that x < y < z, is x a factor of the odd integer z?
(1) x and y are prime numbers, whose sum is a factor of 57
(2) z is a factor of 57
(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not.
(B) Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not.
(C) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient to answer the question.
(E) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question.
| ОТВЕТЫ И КОММЕНТАРИИ |
| Решение |
(1) SUFFICIENT: Since x and y are distinct prime numbers (we know that x < y), their sum must be greater than or equal to 5 (i.e. greater than or equal to the sum of the two smallest primes, 2 and 3). Further, the factors of 57 are 1, 3, 19, and 57. Note that the sum of x and y cannot be equal to 57, since if the sum of two distinct primes is odd, one of the two primes must be even (i.e. equal to 2). Since 55 (i.e.57 – 2) is not a prime number, 57 cannot be equal to the sum of two primes.
Since we already figured that the sum of two distinct primes must exceed 5, the only factor of 57 that can be equal to the sum of two primes is 19. Again, since the sum of the two primes is odd, one of the primes must be even. Thus, x = 2 and y = 19 – 2 = 17. Finally, since we know that x is even, it cannot be a factor of the odd integer z, since any even integer is never a factor of any odd integer. Therefore, we have sufficient information to conclude that x will not be a factor of z.
(2) INSUFFICIENT: First, note that z has to be greater than or equal to 3 (recall that x < y < z, where x, y, and z are positive integers). Thus, since the factors of 57 are 1, 3, 19, and 57, it follows that z can be equal to 3, 19, or 57. Since we have no further information about x, we cannot conclude whether x is a factor of z.
The correct answer is A. |
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At 9 A.M., a hiker was due south of point P. What direction was point P from
her position at noon?
(1) From 9 A.M. until 11 A.M., She walked due east at 2 miles per hour; and
from 11 A.M. until noon, she walked due north at 3 miles per hour.
(2) At noon, she is exactly 4.5 miles from point P.
A) if statement I alone is sufficient to answer the question, but statement 2
alone is not sufficient
B) if statement 2 alone is sufficient to answer the question, but statement I
alone is not sufficient
C) if both statements together are needed to answer the question, but neither
statement alone Is sufficient
D) if either statement by itself is sufficient to answer the question
E) if not enough facts are given to answer the question
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