Answer
No.
Work Step by Step
To find if the salesman's claims are right or wrong, we need to find the maximum coefficient of performance of a refrigerator between two reservoirs of $T_H=(22+273)\;\rm K$ and $T_C=(2+273)\;\rm K$.
This coefficient of performance is called the Carnot coefficient which is given by
$$K_{\rm Carnot}=\dfrac{T_C}{T_H-T_C}$$
Plugging the known;
$$K_{\rm Carnot}=\dfrac{(2+273)}{(22+273)-(2+273)}=\bf 13.75$$
Now this is the maximum performance we can get from this refrigerator, so let's find the real coefficient of performance of it to compare the results.
$$K=\dfrac{Q_C}{W_{in}}\tag 1$$
We know that DreamFridge uses 100 W of power to remove 100 kJ of heat per minute.
This means that the work is given by
$$W_{in}=Pt$$
where $P$ is the power and $t$ is the time.
Plugging into (1);
$$K=\dfrac{Q_C}{Pt}$$
Plugging the known;
$$K=\dfrac{100\times 10^3}{100\times 60}=\bf16.67 $$
And since the real performance according to the claims of the salesman is greater than the Carnot performance, then he lies and you should not buy this one.
