ARRT NUCLEAR MEDICINE BOARDS (MATH AND STATS) EXAM
QUESTIONS AND CORRECT ANSWERS |2026/2027 UPDATED
|GUARANTEED PASS.
A radioactive source of 137Cs (t1/2= 30 y) was calibrated on October 23, 2000, to contain 10 Ci.
This is used as a daily accuracy check source in the dose calibrator. Presuming the dose
calibrator is working properly, what activity should the dose calibrator show on April 23, 2006?
a. 9.6 µCi
b. 8.8 µCi
c. 5.4 µCi
d. 2.2 µCi - Answer -b. 8.8 µCi
The radioactive decay law can be algebraically rearranged (dividing both sides of the decay
equation by A0) as A/A0 = e-0.693(t/t1/2) .
A source of 18F (t1/2 = approximately 2 hr) is noted to contain 3 mCi at noon. What was the
radioactivity at 8:00 AM that same day?
a. 24 mCi
b. 18 mCi
c. 12 mCi
d. 6 mCi - Answer -c. 12 mCi
The radioactive decay law can be algebraically rearranged (dividing both sides of the decay
equation by A0) as: A/A0 = e-0.693 (t/t1/2)
The biological half-life of 131I in a particular patient is 30 days. The physical half-life is 193
hours. If the patient's thyroid is counted with the thyroid probe detector, what effective half-life
will be observed?
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,a. 26 days
b. 6.3 days
c. 5.1 days
d. 1.2 days - Answer -b. 6.3 days
Typically the patient's organ excretes the radiopharmaceutical with some biological half-life tB
while the radioactivity also decays physically with a physical half-life that is denoted as tP. The
counts observed by the gamma camera follow an exponential decay law based on the effective
half-life
A radioactive source decays from 20 mCi to 2.5 mCi in 18 hours. What is the physical half-life?
a. 8 hours
b. 7 hours
c. 6 hours
d. 5 hours - Answer -c. 6 hours
A sample shows a count rate of 36,000 cpm during a 3-minute counting period. Express this as
the count rate ± standard deviation.
a. 36,000 ± 220 cpm
b. 36,000 ± 110 cpm
c. 12,000 ± 55 cpm
d. 12,000 ± 28 cpm - Answer -b. 36,000 ± 110 cpm
Counting statistics, meaning the number of counts expected from a sample, follow the Poisson
distribution. In the Poisson distribution, the standard deviation (C) for any number of counts (C)
is fixed at the square root of C:
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, This fixed definition of standard deviation does not exist in Gaussian distributions; essentially
only counting statistics are Poisson. In this problem, cpm must be calculated first.
A long-lived radioactive source is counted for 1 minute and yields 10,000 counts. If this source is
counted immediately again, there is a 95% probability that the result will be in the range:
a. 9950 to 10,050
b. 9900 to 10,100
c. 9800 to 10,200
d. 9700 to 10,300 - Answer -c. 9800 to 10,200
Counting statistics, besides being Poisson, are also described by a Gaussian distribution as long
as the number of counts is greater than approximately 30. Hence given some number of counts
C, the standard deviation is automatically known. It is also known that 68% of repeat measures
of the sample fall within C ± and 95% of repeat measures of the sample fall within C ± , and so
on: 95% confidence = C ± 2c = C ± .
A 5-ml sample of a standard diluted 1:10,000 produces 27,200 counts in the well counter. A 5-ml
sample of patient plasma, counted for the same time as the diluted standard sample, produces
99,100 counts. What is the plasma volume?
a. 10.8 liter
b. 2.74 liter
c. 1.73 liter
d. 0.91 liter - Answer -b. 2.74 liter
The dilution principle can also be used to measure an unknown volume. Using the dilution
principle, it is possible to estimate a patient's plasma volume, C1V1 = C2V2. Because the
standard may be too concentrated, a portion of the standard is diluted and counted while the
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QUESTIONS AND CORRECT ANSWERS |2026/2027 UPDATED
|GUARANTEED PASS.
A radioactive source of 137Cs (t1/2= 30 y) was calibrated on October 23, 2000, to contain 10 Ci.
This is used as a daily accuracy check source in the dose calibrator. Presuming the dose
calibrator is working properly, what activity should the dose calibrator show on April 23, 2006?
a. 9.6 µCi
b. 8.8 µCi
c. 5.4 µCi
d. 2.2 µCi - Answer -b. 8.8 µCi
The radioactive decay law can be algebraically rearranged (dividing both sides of the decay
equation by A0) as A/A0 = e-0.693(t/t1/2) .
A source of 18F (t1/2 = approximately 2 hr) is noted to contain 3 mCi at noon. What was the
radioactivity at 8:00 AM that same day?
a. 24 mCi
b. 18 mCi
c. 12 mCi
d. 6 mCi - Answer -c. 12 mCi
The radioactive decay law can be algebraically rearranged (dividing both sides of the decay
equation by A0) as: A/A0 = e-0.693 (t/t1/2)
The biological half-life of 131I in a particular patient is 30 days. The physical half-life is 193
hours. If the patient's thyroid is counted with the thyroid probe detector, what effective half-life
will be observed?
1|Page
,a. 26 days
b. 6.3 days
c. 5.1 days
d. 1.2 days - Answer -b. 6.3 days
Typically the patient's organ excretes the radiopharmaceutical with some biological half-life tB
while the radioactivity also decays physically with a physical half-life that is denoted as tP. The
counts observed by the gamma camera follow an exponential decay law based on the effective
half-life
A radioactive source decays from 20 mCi to 2.5 mCi in 18 hours. What is the physical half-life?
a. 8 hours
b. 7 hours
c. 6 hours
d. 5 hours - Answer -c. 6 hours
A sample shows a count rate of 36,000 cpm during a 3-minute counting period. Express this as
the count rate ± standard deviation.
a. 36,000 ± 220 cpm
b. 36,000 ± 110 cpm
c. 12,000 ± 55 cpm
d. 12,000 ± 28 cpm - Answer -b. 36,000 ± 110 cpm
Counting statistics, meaning the number of counts expected from a sample, follow the Poisson
distribution. In the Poisson distribution, the standard deviation (C) for any number of counts (C)
is fixed at the square root of C:
2|Page
, This fixed definition of standard deviation does not exist in Gaussian distributions; essentially
only counting statistics are Poisson. In this problem, cpm must be calculated first.
A long-lived radioactive source is counted for 1 minute and yields 10,000 counts. If this source is
counted immediately again, there is a 95% probability that the result will be in the range:
a. 9950 to 10,050
b. 9900 to 10,100
c. 9800 to 10,200
d. 9700 to 10,300 - Answer -c. 9800 to 10,200
Counting statistics, besides being Poisson, are also described by a Gaussian distribution as long
as the number of counts is greater than approximately 30. Hence given some number of counts
C, the standard deviation is automatically known. It is also known that 68% of repeat measures
of the sample fall within C ± and 95% of repeat measures of the sample fall within C ± , and so
on: 95% confidence = C ± 2c = C ± .
A 5-ml sample of a standard diluted 1:10,000 produces 27,200 counts in the well counter. A 5-ml
sample of patient plasma, counted for the same time as the diluted standard sample, produces
99,100 counts. What is the plasma volume?
a. 10.8 liter
b. 2.74 liter
c. 1.73 liter
d. 0.91 liter - Answer -b. 2.74 liter
The dilution principle can also be used to measure an unknown volume. Using the dilution
principle, it is possible to estimate a patient's plasma volume, C1V1 = C2V2. Because the
standard may be too concentrated, a portion of the standard is diluted and counted while the
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