Events & Promotions
|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Apr 2308:00 PM PDT
-09:00 PM PDT
Video explanations + diagnosis of 10 weakest areas + 150+ short videos + study plan!
Apr 2301:30 AM EDT
-02:30 AM EDT
Struggling with GMAT Verbal as a non-native speaker? Harsh improved his score from 595 to 695 in just 45 days—and scored a 99 %ile in Verbal (V88)! Learn how smart strategy, clarity, and guided prep helped him gain 100 points.
Apr 2512:30 AM EDT
-01:30 AM EDT
At one point, she believed GMAT wasn’t for her. After scoring 595, self-doubt crept in and she questioned her potential. But instead of quitting, she made the right strategic changes. The result? A remarkable comeback to 695. Check out how Saakshi did it.
Apr 2610:00 AM EDT
-11:00 AM EDT
The Target Test Prep course represents a quantum leap forward in GMAT preparation, a radical reinterpretation of the way that students should study. Try before you buy with a 5-day, full-access trial of the course for FREE!
Apr 2711:00 AM EDT
-12:00 PM EDT
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors
Apr 2808:00 AM PDT
-11:00 AM PDT
Whether you are just beginning your MBA journey or fine-tuning your path to a 700+ score, GMAT Day is designed to give you a competitive edge.
08 Apr 2026, 19:00
Kudos
Bookmarks
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
63% (01:42) correct
37%
(02:26)
wrong
based on 60
sessions
History
Date
Time
Result
Not Attempted Yet
Among the following functions, for which one is f(a – b) = f(a) * f(–b) for all integer values of a and b?
A. f(t) = t/10
B. f(t) = t + 10
C. f(t) = 10t
D. f(t) = 10^t
E. f(t) = t^10
A. f(t) = t/10
B. f(t) = t + 10
C. f(t) = 10t
D. f(t) = 10^t
E. f(t) = t^10
09 Apr 2026, 06:02
Kudos
Bookmarks
Among the following functions, for which one is f(a – b) = f(a) * f(–b) for all integer values of a and b?
Algebraic Approach
A. f(t) = t/10
(a - b)/10 ≠ -ab/100
B. f(t) = t + 10
(a - b) + 10 ≠ (a + 10)(-b + 10)
C. f(t) = 10t
10(a - b) ≠ (10a)(-10b)
D. f(t) = 10^t
10^(a - b) = (10^a)(10^-b)
E. f(t) = t^10
(a - b)^10 ≠ (a^10)(-b^10)
Smart Numbers Approach (very fast)
Let a and b be 1.
A. f(t) = t/10
0/10 ≠ -1/100
B. f(t) = t + 10
0 + 10 ≠ (1 + 10)(-1 + 10)
C. f(t) = 10t
10 * 0 ≠ 10 * -10
D. f(t) = 10^t
10^0 = (10^1)(10^-1)
E. f(t) = t^10
0^10 ≠ (1^10)(-1^10)
Also, we can save time by noticing that, since the left side of the equation involves subtraction whereas the right side involves multiplication, the correct answer must be in a form such that subtraction and multiplication are related. Having seen that, we can try (D) first because subtraction of exponents is related to multiplying positive and negative exponents.
Correct answer: D
Algebraic Approach
A. f(t) = t/10
(a - b)/10 ≠ -ab/100
B. f(t) = t + 10
(a - b) + 10 ≠ (a + 10)(-b + 10)
C. f(t) = 10t
10(a - b) ≠ (10a)(-10b)
D. f(t) = 10^t
10^(a - b) = (10^a)(10^-b)
E. f(t) = t^10
(a - b)^10 ≠ (a^10)(-b^10)
Smart Numbers Approach (very fast)
Let a and b be 1.
A. f(t) = t/10
0/10 ≠ -1/100
B. f(t) = t + 10
0 + 10 ≠ (1 + 10)(-1 + 10)
C. f(t) = 10t
10 * 0 ≠ 10 * -10
D. f(t) = 10^t
10^0 = (10^1)(10^-1)
E. f(t) = t^10
0^10 ≠ (1^10)(-1^10)
Also, we can save time by noticing that, since the left side of the equation involves subtraction whereas the right side involves multiplication, the correct answer must be in a form such that subtraction and multiplication are related. Having seen that, we can try (D) first because subtraction of exponents is related to multiplying positive and negative exponents.
Correct answer: D
09 Apr 2026, 06:33
Kudos
Bookmarks
The key is spotting what mathematical structure lets subtraction in the input "match" multiplication in the output. Most people test all five options, but there's a faster path.
Notice the left side has a minus sign in the argument (a - b), while the right side has separate function values multiplied together. For that to work, the function needs to convert subtraction into division — and the only function type that does this is an exponential, via the exponent rule x^(a-b) = x^a * x^(-b).
1. Set up the condition: f(a - b) = f(a) * f(-b) for all integers a and b.
2. Test choice D: f(t) = 10^t.
Left side: f(a - b) = 10^(a - b).
Right side: f(a) * f(-b) = 10^a * 10^(-b) = 10^(a - b).
Both sides are equal. This works for all integers.
3. Why the others fail:
A. f(t) = t/10. Left: (a-b)/10. Right: (a/10) * (-b/10) = -ab/100. Not the same.
B. f(t) = t + 10. Left: a - b + 10. Right: (a + 10)(-b + 10). Not the same.
C. f(t) = 10t. Left: 10(a - b). Right: (10a)(-10b) = -100ab. Not the same.
E. f(t) = t^10. Left: (a - b)^10. Right: a^10 * (-b)^10 = a^10 * b^10. These are only equal for specific values, not all integers.
The small trap in D is thinking that f(-b) = 10^(-b) is somehow problematic. It's not. Negative exponents are fine — 10^(-b) is just 1/10^b, and the exponent rule still applies cleanly.
Shortcut if you're pressed for time: as soon as you recognize that the left side has (a - b) inside a function and the right side is a product, think "exponents turn subtraction into division" and go straight to D. That's the only function family where this holds.
Answer: D
Notice the left side has a minus sign in the argument (a - b), while the right side has separate function values multiplied together. For that to work, the function needs to convert subtraction into division — and the only function type that does this is an exponential, via the exponent rule x^(a-b) = x^a * x^(-b).
1. Set up the condition: f(a - b) = f(a) * f(-b) for all integers a and b.
2. Test choice D: f(t) = 10^t.
Left side: f(a - b) = 10^(a - b).
Right side: f(a) * f(-b) = 10^a * 10^(-b) = 10^(a - b).
Both sides are equal. This works for all integers.
3. Why the others fail:
A. f(t) = t/10. Left: (a-b)/10. Right: (a/10) * (-b/10) = -ab/100. Not the same.
B. f(t) = t + 10. Left: a - b + 10. Right: (a + 10)(-b + 10). Not the same.
C. f(t) = 10t. Left: 10(a - b). Right: (10a)(-10b) = -100ab. Not the same.
E. f(t) = t^10. Left: (a - b)^10. Right: a^10 * (-b)^10 = a^10 * b^10. These are only equal for specific values, not all integers.
The small trap in D is thinking that f(-b) = 10^(-b) is somehow problematic. It's not. Negative exponents are fine — 10^(-b) is just 1/10^b, and the exponent rule still applies cleanly.
Shortcut if you're pressed for time: as soon as you recognize that the left side has (a - b) inside a function and the right side is a product, think "exponents turn subtraction into division" and go straight to D. That's the only function family where this holds.
Answer: D
