- A, B, C, and D The fractions in the given inequality have the same numerator.
If two positive fractions have the same numerator, then the fraction with
the smaller denominator will be the greater value. Thus 5x must be less than
1,000. Now determine which values in the choices will satisfy the inequality:
5 x < 1,000. 5^4 = 625, so any integer value less than or equal to 4 will satisfy the
constraints. However, 5^5 = 3,125, so 5 and 6 are too large. The correct answers
are A, B, C, and D. - D Though you can certainly calculate the value of each fraction, such an
approach would be time-consuming. Since the question is asking you to
compare fractions, identify any choices that have the same numerator or
denominator. Notice that all of the fractions in Choices A, B, and D have the
same denominator. Among those three choices, the fraction that has the greatest
numerator will be the greatest: 21 > 3^2 > 2^2. Thus Choice D is the greatest among
those three fractions. Now compare C and E. Both fractions have the same
denominator, so the fraction with the greater numerator will be larger. 3^3 > 3^2
× 2, so the fraction in Choice C is greater than the fraction in Choice E. Now
compare C and D. To arrive at an equal denominator in both fractions, multiply
the numerator and denominator of the fraction in Choice D by 7:
21 × 7
75 × 5^3 × 7^ =
21 × 7
76 × 5^3Now that the fractions have the same denominator, compare their numerators:
Choice C: 3^3
Choice D: 21 × 721 × 7 > 3^3. Thus the fraction in Choice D is greater.- B Since $360,000 is split equally among three siblings, each sibling receives
$360,000
3 = $120,000. The sibling will then split this $120,000 into 4 parts (herself
and her three children), so each child receives $120,000 4 = $30,000. - D Choose a value for Janet’s monthly paycheck. Since the denominator of the
fraction is 3, a multiple of 3 would be a smart number. Let’s use 30. If Janet
earns $30/month, then she saves $10/month and spends $20/month. If she
spends $20 per month, then she spends $20 × 12 = $240/year. The fraction you
are solving for is 10/240 = 241. - D Since this question has only fractions and no given amounts, plug in
numbers. Bob’s and Peter’s savings are given in terms of Stan’s savings, so
choose a value for Stan’s savings. Since the fractions in the question have
denominators of 3 and 4, choose a multiple of 3 and 4 for Stan’s savings. Let’s
use $12. If Stan’s savings is $12, then Bob’s savings is^23 ($12) = $8 and Peter’s
savings is 2($12) = $24. Combined, Peter and Bob will invest $32. Originally,
Stan was going to invest all $12, but now he will invest only^34 of that amount.
3
4 (12) = 9, so Stan will invest $9. Stan’s investment as a fraction of Bob’s and
Peter’s investments is thus 329.
CHAPTER 10 ■ PART-TO-WHOLE RELATIONSHIPS 22503-GRE-Test-2018_173-312.indd 225 12/05/17 11:52 am