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Teachers & SchoolsSAT Math 1.3 Numbers and Operations. x and y must be which of the following?

Basic Operations | Absolute Value |

Language | English Language |

Numbers and Operations | Properties of Integers |

Passport to Advanced Math | Interpreting nonlinear expressions |

Product Type | SAT Math |

SAT Math | Numbers and Operations |

Alright, we have one of those multiple part questions where we have to test choices I, II, and III.

Whenever we see those straight vertical lines,

also known as the absolute value sign. We know the answer that comes out of those

lines will always, always be positive. So, let's test each case by plugging in numbers for x and y.

Case I: Both x and y are positive.

If x = 5 and y = 5, the absolute value of 5 + 5 = 10, and the absolute value of 5 plus

the absolute value of 5 is also 10. Check, this one works.

Case II: Both x and y are negative.

If x = -5 and y = -5, then the absolute value of negative 5 plus negative 5 = 10, and the

absolute value of negative 5 plus the absolute value of negative 5 equals 10. Check.

Case III: x and y are opposite signs.

If x = 5 and y = -5. The absolute value of 5 plus negative 5 equals zero.

and the absolute value of 5 plus the absolute value of negative 5 equals 10.

Ehh, this one's a no-go.

Only cases I and II make the original premise true, so (D) is the correct answer.